Satoshi Dice -- Statistical Analysis

[byronbb]

I always thought the point of an IPO would be to increase the size of their bankroll. Essentially borrowing btc and paying interest at a rate just below that of expected earnings. Whales love to gamble big in low edge games. The asian market for high limits low edge is very real. Baccarat (1 % house edge "coin flip" game) is commonly dealt in Macau for 100k a hand.

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[smickles]

I always thought the point of an IPO would be to increase the size of their bankroll. Essentially borrowing btc and paying interest at a rate just below that of expected earnings. Whales love to gamble big in low edge games. The asian market for high limits low edge is very real. Baccarat (1 % house edge "coin flip" game) is commonly dealt in Macau for 100k a hand.

Heh, well, as I understood it, most of the btc from the public offering was earmarked for Mr. Voorhees wallet. The rest was for advertising and such.

[smickles]

Oh, and dooglus, thanks for keeping up the analysis. It's especially useful to have those current month charts

[dooglus]

Oh, and dooglus, thanks for keeping up the analysis. It's especially useful to have those current month charts

You're welcome.  Today's report is a little later than usual, but here it is:

Total of 4 bets unaccounted for.

Results: 2013-Jan-04 04:21pm (up to block 215196)

   Address  Target   Should Win |    #Bets |       Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
---------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    61688 |      0 (0.00000) |   60582 |    1106 |     521.76 |       0.01 |    85.47 |    521.74 |   0.004
 1dice1Qf4       2      0.00003 |     3129 |      0 (0.00000) |    2637 |     492 |      45.91 |       0.00 |    16.23 |     45.90 |   0.010
 1dice2pxm       4      0.00006 |     5113 |      1 (0.00021) |    4694 |     418 |      67.88 |     159.96 |     8.45 |    -92.07 | 235.642
 1dice2vQo       8      0.00012 |     7706 |      2 (0.00027) |    7284 |     420 |     111.39 |      16.09 |    10.02 |     95.30 |  14.445
 1dice2WmR      16      0.00024 |     9321 |      1 (0.00011) |    8913 |     407 |     231.62 |       4.39 |    18.65 |    227.23 |   1.898
 1dice2xkj      32      0.00049 |     9393 |      3 (0.00033) |    9001 |     389 |     534.00 |     303.50 |     1.36 |    230.49 |  56.836
 1dice2zdo      64      0.00098 |    12249 |     12 (0.00101) |   11839 |     398 |     805.35 |     155.67 |    55.70 |    649.67 |  19.330
 1dice37Ee     128      0.00195 |    15249 |     28 (0.00189) |   14794 |     427 |    1862.30 |    1318.93 |    48.31 |    543.36 |  70.823
 1dice3jkp     256      0.00391 |    16951 |     71 (0.00428) |   16505 |     375 |    2017.32 |    2909.06 |    13.16 |   -891.74 | 144.205
 1dice4J1m     512      0.00781 |    25079 |    183 (0.00750) |   24228 |     668 |    4283.68 |    3929.39 |     9.94 |    354.29 |  91.729
 1dice5wwE    1000      0.01526 |    73573 |   1132 (0.01548) |   72004 |     437 |   19187.01 |   16975.60 |     1.91 |   2211.41 |  88.474
 1dice61SN    1500      0.02289 |    19700 |    461 (0.02382) |   18891 |     348 |    6386.73 |    6445.79 |    15.06 |    -59.06 | 100.925
 1dice6DPt    2000      0.03052 |    43386 |   1341 (0.03118) |   41669 |     376 |   20449.30 |   17618.11 |     9.31 |   2831.19 |  86.155
 1dice6gJg    3000      0.04578 |    22660 |   1030 (0.04629) |   21223 |     407 |    8364.31 |    9417.42 |    25.08 |  -1053.11 | 112.591
 1dice6GV5    4000      0.06104 |    28397 |   1725 (0.06153) |   26311 |     361 |    6155.78 |    5670.90 |    31.25 |    484.88 |  92.123
 1dice6wBx    6000      0.09155 |    32391 |   3008 (0.09398) |   28999 |     384 |   13062.40 |   14621.86 |     7.11 |  -1559.46 | 111.939
 1dice6YgE    8000      0.12207 |   133225 |  16351 (0.12313) |  116443 |     431 |   52047.40 |   50562.91 |   100.18 |   1484.48 |  97.148
 1dice7EYz   12000      0.18311 |    49859 |   9169 (0.18547) |   40267 |     423 |   83630.16 |   82390.71 |  3314.63 |   1239.44 |  98.518
 1dice7fUk   16000      0.24414 |   156905 |  38117 (0.24364) |  118332 |     456 |  176065.51 |  176285.68 |  1617.02 |   -220.17 | 100.125
 1dice7W2A   24000      0.36621 |   129086 |  47361 (0.36826) |   81246 |     479 |  172067.32 |  168793.04 |  1012.85 |   3274.27 |  98.097
 1dice8EMZ   32000      0.48828 |   824185 | 401957 (0.48850) |  420890 |    1338 |  549893.39 |  541052.14 |  2923.90 |   8841.25 |  98.392
 1dice97EC   32768      0.50000 |   356741 | 177702 (0.49922) |  178257 |     782 |  389166.79 |  380144.06 |  5720.12 |   9022.73 |  97.682
 1dice9wcM   48000      0.73242 |   239032 | 175545 (0.73595) |   62984 |     503 |  243277.31 |  237788.01 |  5454.76 |   5489.30 |  97.744
 1dicec9k7   52000      0.79346 |    42929 |  33809 (0.79483) |    8727 |     393 |   48583.24 |   47635.97 |  1187.12 |    947.27 |  98.050
 1dicegEAr   56000      0.85449 |    32303 |  27307 (0.85677) |    4565 |     431 |   44547.03 |   43898.65 |   400.12 |    648.38 |  98.544
 1diceDCd2   60000      0.91553 |    38841 |  35197 (0.91568) |    3241 |     403 |   48643.47 |   48444.10 |     0.09 |    199.36 |  99.590
 1dice9wVt   64000      0.97656 |    11560 |  10728 (0.98098) |     208 |     624 |   21300.30 |   20951.43 |   239.42 |    348.86 |  98.362
---------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  2322145 | 944100           | 1364657 |   13388 |  537213.00 |  525605.43 |   203.68 |  11607.56 |  97.839
            big (bets >= 4 BTC) |    78506 |  38141           |   40077 |     288 | 1376095.78 | 1351888.06 | 22123.70 |  24207.71 |  98.241
---------------------------------------------------------------------------------------------------------------------------------------------
                                |  2400651 | 982241           | 1404734 |   13676 | 1913308.78 | 1877493.50 | 22327.38 |  35815.27 |  98.128
---------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      35815.27597646 BTC (1.872%)
Cumulative Fees Paid:        1596.06607500 BTC
SD Profit after fees:       34219.20990146 BTC (1.788%)
Pending Liabilities:           -1.96051998 BTC
Final SD Profit:            34221.17042144 BTC (1.789%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  7852791  :  SatoshiDice Tx:  4407687  (56.1%)
Blockchain MB:   3343.6  :  SatoshiDice MB:   1811.4  (54.2%)

[etotheipi]

Just an update that's hasn't been mentioned here:  evoorhees says that they just switched to the per-TxOut method of computing lucky numbers, instead of per-transaction.   That means that bets on SD are no longer correlated:  you get a different lucky number for each output in a single transaction.  If betting continues exactly the same way, SD will have the exact same expected profit, but with much lower overall variance.  It will cut down quite a bit on those enormous swings.

[Bugpowder]

Just an update that's hasn't been mentioned here:  evoorhees says that they just switched to the per-TxOut method of computing lucky numbers, instead of per-transaction.   That means that bets on SD are no longer correlated:  you get a different lucky number for each output in a single transaction.  If betting continues exactly the same way, SD will have the exact same expected profit, but with much lower overall variance.  It will cut down quite a bit on those enormous swings.

I hope the whales are satisfied with this new setup.  Maybe we can get some higher max bets then, up to 1000BTC for less than 64000, and 500 for less than 32000?  We know there should be sufficient house capital to handle it now.

[dooglus]

I hope the whales are satisfied with this new setup.  Maybe we can get some higher max bets then, up to 1000BTC for less than 64000, and 500 for less than 32000?  We know there should be sufficient house capital to handle it now.

At 2013-01-03 00:00 GMT (In about an hour) the logic for calculating the bet hash which was hmac512(secret, bet_transaction_id) will be changed to hmac512(secret, bet_transaction_id + ":" + bet_output_index)

The change happened on the 3rd.  The betting has really dropped off since then.  I guess time will tell whether the change has scared the whale off or not.  It's not like he was constantly betting before the change.

Here's a chart showing the bet volume over the last couple of months.  The whale activity is around the same time each week, and never around the weekends.  The labels on the X axis are Saturdays:

[dooglus]

Results: 2013-Jan-05 10:43am (up to block 215298)

   Address  Target   Should Win |    #Bets |       Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
---------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    62099 |      0 (0.00000) |   60993 |    1106 |     530.40 |       0.01 |    85.47 |    530.38 |   0.004
 1dice1Qf4       2      0.00003 |     3142 |      0 (0.00000) |    2650 |     492 |      46.04 |       0.00 |    16.23 |     46.03 |   0.010
 1dice2pxm       4      0.00006 |     5116 |      1 (0.00021) |    4697 |     418 |      67.91 |     159.96 |     8.45 |    -92.04 | 235.538
 1dice2vQo       8      0.00012 |     7708 |      2 (0.00027) |    7286 |     420 |     111.41 |      16.09 |    10.02 |     95.32 |  14.442
 1dice2WmR      16      0.00024 |     9324 |      1 (0.00011) |    8916 |     407 |     231.78 |       4.39 |    18.65 |    227.39 |   1.897
 1dice2xkj      32      0.00049 |     9412 |      3 (0.00033) |    9020 |     389 |     534.40 |     303.50 |     1.36 |    230.89 |  56.793
 1dice2zdo      64      0.00098 |    12257 |     12 (0.00101) |   11847 |     398 |     806.52 |     155.68 |    55.70 |    650.83 |  19.303
 1dice37Ee     128      0.00195 |    15259 |     28 (0.00189) |   14804 |     427 |    1862.88 |    1318.93 |    48.31 |    543.95 |  70.801
 1dice3jkp     256      0.00391 |    16962 |     71 (0.00428) |   16516 |     375 |    2017.59 |    2909.06 |    13.16 |   -891.47 | 144.185
 1dice4J1m     512      0.00781 |    25092 |    184 (0.00753) |   24240 |     668 |    4284.37 |    3941.88 |     9.94 |    342.48 |  92.006
 1dice5wwE    1000      0.01526 |    73807 |   1134 (0.01546) |   72236 |     437 |   19195.57 |   16982.65 |     1.91 |   2212.91 |  88.472
 1dice61SN    1500      0.02289 |    19718 |    461 (0.02380) |   18909 |     348 |    6388.43 |    6445.80 |    15.06 |    -57.37 | 100.898
 1dice6DPt    2000      0.03052 |    43580 |   1344 (0.03111) |   41860 |     376 |   20452.79 |   17621.95 |     9.31 |   2830.84 |  86.159
 1dice6gJg    3000      0.04578 |    22672 |   1030 (0.04626) |   21235 |     407 |    8364.65 |    9417.42 |    25.08 |  -1052.77 | 112.586
 1dice6GV5    4000      0.06104 |    28416 |   1727 (0.06156) |   26328 |     361 |    6157.32 |    5675.69 |    31.25 |    481.62 |  92.178
 1dice6wBx    6000      0.09155 |    32451 |   3011 (0.09390) |   29056 |     384 |   13070.09 |   14626.68 |     7.11 |  -1556.59 | 111.910
 1dice6YgE    8000      0.12207 |   133429 |  16378 (0.12315) |  116619 |     432 |   52060.12 |   50569.22 |   100.18 |   1490.90 |  97.136
 1dice7EYz   12000      0.18311 |    50094 |   9208 (0.18538) |   40463 |     423 |   83649.94 |   82407.32 |  3314.63 |   1242.61 |  98.515
 1dice7fUk   16000      0.24414 |   157392 |  38223 (0.24356) |  118713 |     456 |  176118.27 |  176325.79 |  1617.02 |   -207.51 | 100.118
 1dice7W2A   24000      0.36621 |   129814 |  47635 (0.36831) |   81699 |     480 |  172184.82 |  168905.35 |  1012.86 |   3279.46 |  98.095
 1dice8EMZ   32000      0.48828 |   827324 | 403444 (0.48844) |  422542 |    1338 |  552537.34 |  543825.80 |  2923.90 |   8711.53 |  98.423
 1dice97EC   32768      0.50000 |   357837 | 178231 (0.49917) |  178824 |     782 |  390104.68 |  380959.60 |  5720.12 |   9145.07 |  97.656
 1dice9wcM   48000      0.73242 |   239439 | 175848 (0.73596) |   63088 |     503 |  243748.60 |  238226.33 |  5454.76 |   5522.26 |  97.734
 1dicec9k7   52000      0.79346 |    43085 |  33932 (0.79481) |    8760 |     393 |   48616.03 |   47669.06 |  1187.12 |    946.97 |  98.052
 1dicegEAr   56000      0.85449 |    32379 |  27372 (0.85677) |    4576 |     431 |   44640.83 |   44003.11 |   400.12 |    637.71 |  98.571
 1diceDCd2   60000      0.91553 |    39072 |  35407 (0.91567) |    3261 |     404 |   48768.82 |   48572.87 |     0.10 |    195.94 |  99.598
 1dice9wVt   64000      0.97656 |    11576 |  10744 (0.98101) |     208 |     624 |   21305.44 |   20956.59 |   239.42 |    348.84 |  98.363
---------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  2329723 | 947169           | 1369163 |   13391 |  538204.11 |  526533.86 |   203.69 |  11670.25 |  97.832
            big (bets >= 4 BTC) |    78733 |  38262           |   40183 |     288 | 1379653.04 | 1355467.00 | 22123.70 |  24186.04 |  98.247
---------------------------------------------------------------------------------------------------------------------------------------------
                                |  2408456 | 985431           | 1409346 |   13679 | 1917857.16 | 1882000.87 | 22327.39 |  35856.29 |  98.130
---------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      35856.29460173 BTC (1.870%)
Cumulative Fees Paid:        1603.88207500 BTC
SD Profit after fees:       34252.41252673 BTC (1.786%)
Pending Liabilities:           -3.88524394 BTC
Final SD Profit:            34256.29777067 BTC (1.786%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  7881500  :  SatoshiDice Tx:  4422350  (56.1%)
Blockchain MB:   3355.2  :  SatoshiDice MB:   1817.4  (54.2%)

[dooglus]

Results: 2013-Jan-06 02:46pm (up to block 215473)

   Address  Target   Should Win |    #Bets |       Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
---------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    62395 |      0 (0.00000) |   61284 |    1111 |     533.84 |       0.01 |    85.94 |    533.82 |   0.004
 1dice1Qf4       2      0.00003 |     3164 |      0 (0.00000) |    2672 |     492 |      46.38 |       0.00 |    16.23 |     46.38 |   0.010
 1dice2pxm       4      0.00006 |     5133 |      1 (0.00021) |    4714 |     418 |      68.27 |     159.96 |     8.45 |    -91.68 | 234.279
 1dice2vQo       8      0.00012 |     7717 |      2 (0.00027) |    7295 |     420 |     111.59 |      16.09 |    10.02 |     95.50 |  14.419
 1dice2WmR      16      0.00024 |     9426 |      1 (0.00011) |    9018 |     407 |     249.67 |       4.43 |    18.65 |    245.23 |   1.778
 1dice2xkj      32      0.00049 |     9498 |      3 (0.00033) |    9106 |     389 |     539.06 |     303.50 |     1.36 |    235.55 |  56.302
 1dice2zdo      64      0.00098 |    12344 |     12 (0.00100) |   11934 |     398 |     810.09 |     155.68 |    55.70 |    654.40 |  19.218
 1dice37Ee     128      0.00195 |    15277 |     28 (0.00189) |   14822 |     427 |    1864.10 |    1318.93 |    48.31 |    545.16 |  70.755
 1dice3jkp     256      0.00391 |    17229 |     73 (0.00433) |   16781 |     375 |    2173.31 |    3209.54 |    13.16 |  -1036.23 | 147.680
 1dice4J1m     512      0.00781 |    25209 |    186 (0.00758) |   24355 |     668 |    4295.54 |    3955.64 |     9.94 |    339.89 |  92.087
 1dice5wwE    1000      0.01526 |    74566 |   1147 (0.01547) |   72982 |     437 |   19250.01 |   17119.07 |     1.91 |   2130.94 |  88.930
 1dice61SN    1500      0.02289 |    19741 |    461 (0.02377) |   18932 |     348 |    6389.90 |    6445.80 |    15.06 |    -55.90 | 100.875
 1dice6DPt    2000      0.03052 |    44015 |   1365 (0.03128) |   42274 |     376 |   20495.34 |   17696.45 |     9.31 |   2798.88 |  86.344
 1dice6gJg    3000      0.04578 |    22695 |   1031 (0.04626) |   21257 |     407 |    8375.60 |    9432.40 |    25.08 |  -1056.79 | 112.618
 1dice6GV5    4000      0.06104 |    28432 |   1728 (0.06156) |   26343 |     361 |    6160.80 |    5678.90 |    31.25 |    481.89 |  92.178
 1dice6wBx    6000      0.09155 |    32531 |   3016 (0.09382) |   29131 |     384 |   13119.58 |   14677.64 |     7.11 |  -1558.05 | 111.876
 1dice6YgE    8000      0.12207 |   134019 |  16442 (0.12308) |  117145 |     432 |   52171.42 |   50664.06 |   100.18 |   1507.36 |  97.111
 1dice7EYz   12000      0.18311 |    50645 |   9318 (0.18554) |   40904 |     423 |   83689.14 |   82450.96 |  3314.63 |   1238.17 |  98.521
 1dice7fUk   16000      0.24414 |   157849 |  38334 (0.24356) |  119059 |     456 |  176226.72 |  176449.36 |  1617.02 |   -222.63 | 100.126
 1dice7W2A   24000      0.36621 |   131447 |  48233 (0.36828) |   82734 |     480 |  172535.80 |  169292.01 |  1012.86 |   3243.78 |  98.120
 1dice8EMZ   32000      0.48828 |   830117 | 404824 (0.48846) |  423955 |    1338 |  554276.92 |  545583.85 |  2923.90 |   8693.07 |  98.432
 1dice97EC   32768      0.50000 |   359541 | 179084 (0.49918) |  179675 |     782 |  391799.92 |  382927.35 |  5720.12 |   8872.56 |  97.735
 1dice9wcM   48000      0.73242 |   240445 | 176584 (0.73594) |   63358 |     503 |  244200.16 |  238667.14 |  5454.76 |   5533.01 |  97.734
 1dicec9k7   52000      0.79346 |    43198 |  34023 (0.79484) |    8782 |     393 |   48633.26 |   47687.04 |  1187.12 |    946.22 |  98.054
 1dicegEAr   56000      0.85449 |    32565 |  27527 (0.85663) |    4607 |     431 |   44690.71 |   44055.50 |   400.12 |    635.20 |  98.579
 1diceDCd2   60000      0.91553 |    39569 |  35851 (0.91538) |    3314 |     404 |   49736.99 |   49411.33 |     0.10 |    325.65 |  99.345
 1dice9wVt   64000      0.97656 |    11601 |  10769 (0.98105) |     208 |     624 |   21356.39 |   21007.76 |   239.42 |    348.63 |  98.368
---------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  2341410 | 951657           | 1376357 |   13396 |  540958.80 |  529573.42 |   204.16 |  11385.38 |  97.895
            big (bets >= 4 BTC) |    78958 |  38386           |   40284 |     288 | 1382841.85 | 1358797.13 | 22123.70 |  24044.71 |  98.261
---------------------------------------------------------------------------------------------------------------------------------------------
                                |  2420368 | 990043           | 1416641 |   13684 | 1923800.66 | 1888370.55 | 22327.86 |  35430.10 |  98.158
---------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      35430.10370197 BTC (1.842%)
Cumulative Fees Paid:        1615.81567500 BTC
SD Profit after fees:       33814.28802697 BTC (1.758%)
Pending Liabilities:            0.63098455 BTC
Final SD Profit:            33813.65704242 BTC (1.758%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  7922239  :  SatoshiDice Tx:  4444261  (56.1%)
Blockchain MB:   3372.1  :  SatoshiDice MB:   1826.4  (54.2%)

[kidgorgeous]

Woah, Max bets have been raised. You can now bet BTC500 on alot of bets.... anyone want to loan me BTC10000? I swear I'll gamble it away and make things interesting in here for atleast a little bit.

[dooglus]

I made a post in the newbie forum's satoshidice thread, but didn't get any replies.  Maybe this is a better place to post it?

The thing is that the Martingale strategy with the 50% bets is basically identical to repeatedly playing the 85-97% winning odds bets with the amount of Bitcoin that you would risk at maximum with your Martingale strategy.

That's interesting.

I looked into this, and found a surprising result:

If I bet on "lessthan 8000", and keep increasing my bet each time I lose such that my overall profit when I win is constant, and commit to making 19 bets if necessary, I am effectively placing a large bet on "lessthan 60012.5":

Code:

>>> (1-(1-8000/65536.0)**19)*65536
60012.49314412828

That's a little easier to win than "lessthan 60000", which pays out 1.071x.  Since I'm placing multiple bets, and getting a slightly easier-to-win bet than "lessthan 60000", you would expect my payout in the event of a win to be a little less than 1.071x, but it's actually a little higher:

Code:

win on turn  1 : bet =  18.34444122, spent =   18.34494122, win =  146.76222078, lose =   0.09122220, back =   0.00000000, profit = 128.41727956 (87.793% to lose all)
win on turn  2 : bet =  20.95186542, spent =   39.29730664, win =  167.62263649, lose =   0.10425932, back =   0.09122220, profit = 128.41655205 (77.076% to lose all)
win on turn  3 : bet =  23.92990113, spent =   63.22770777, win =  191.44808952, lose =   0.11914950, back =   0.19548152, profit = 128.41586327 (67.667% to lose all)
win on turn  4 : bet =  27.33122595, spent =   90.55943371, win =  218.66002143, lose =   0.13615612, back =   0.31463102, profit = 128.41521874 (59.407% to lose all)
win on turn  5 : bet =  31.21600495, spent =  121.77593866, win =  249.73977624, lose =   0.15558002, back =   0.45078714, profit = 128.41462472 (52.155% to lose all)
win on turn  6 : bet =  35.65295485, spent =  157.42939351, win =  285.23711477, lose =   0.17776477, back =   0.60636716, profit = 128.41408842 (45.789% to lose all)
win on turn  7 : bet =  40.72055959, spent =  198.15045311, win =  325.77993920, lose =   0.20310279, back =   0.78413193, profit = 128.41361802 (40.199% to lose all)
win on turn  8 : bet =  46.50845857, spent =  244.65941167, win =  372.08539985, lose =   0.23204229, back =   0.98723472, profit = 128.41322290 (35.292% to lose all)
win on turn  9 : bet =  53.11903225, spent =  297.77894393, win =  424.97258068, lose =   0.26509516, back =   1.21927701, profit = 128.41291376 (30.984% to lose all)
win on turn 10 : bet =  60.66921318, spent =  358.44865710, win =  485.37698775, lose =   0.30284606, back =   1.48437217, profit = 128.41270282 (27.202% to lose all)
win on turn 11 : bet =  69.29255432, spent =  427.74171142, win =  554.36709722, lose =   0.34596277, back =   1.78721823, profit = 128.41260403 (23.881% to lose all)
win on turn 12 : bet =  79.14159147, spent =  506.88380289, win =  633.16325523, lose =   0.39520795, back =   2.13318100, profit = 128.41263334 (20.966% to lose all)
win on turn 13 : bet =  90.39054140, spent =  597.27484429, win =  723.15926428, lose =   0.45145270, back =   2.52838895, profit = 128.41280894 (18.407% to lose all)
win on turn 14 : bet = 103.23838355, spent =  700.51372784, win =  825.94703784, lose =   0.51569191, back =   2.97984165, profit = 128.41315165 (16.160% to lose all)
win on turn 15 : bet = 117.91237969, spent =  818.42660753, win =  943.34475917, lose =   0.58906189, back =   3.49553356, profit = 128.41368520 (14.187% to lose all)
win on turn 16 : bet = 134.67209391, spent =  953.09920144, win = 1077.42904272, lose =   0.67286046, back =   4.08459545, profit = 128.41443673 (12.455% to lose all)
win on turn 17 : bet = 153.81398395, spent = 1106.91368539, win = 1230.57166670, lose =   0.76856991, back =   4.75745591, profit = 128.41543722 (10.935% to lose all)
win on turn 18 : bet = 175.67664520, spent = 1282.59083059, win = 1405.48152682, lose =   0.87788322, back =   5.52602582, profit = 128.41672205 ( 9.600% to lose all)
win on turn 19 : bet = 200.64679995, spent = 1483.23813054, win = 1605.25255315, lose =   1.00273399, back =   6.40390904, profit = 128.41833165 ( 8.428% to lose all)

I'm risking 1483.23813054 BTC in total, to win 128.41 BTC.  That's a payout of 1.0866x:

Code:

>>> 128.41833165 / 1483.23813054 + 1
1.0865797129981056

How can it be that committing to 19 "lessthan 8000" bets gets me a bigger chance of winning than placing a single "lessthan 60000" bet, but at the same time gets me a higher payout multiplier, as well as a bigger effective "max bet" (it's not possible to bet 1483 BTC on "lessthan 60000" directly, but using Martingale betting I can effectively do just that).

tldr: Using Martingale betting it seems to be possible to effectively bet far more than the maximum bet, increase your chances of winning, and increase the payout multipler too - Win/Win/Win.  Is there a flaw in my reasoning here?

[dooglus]

            txid:n   block               date   game (lucky - result   )                            address   stake  payout  profit cumulative profit
------------------  ------ ------------------ ------  -----   ---------  ----------------------------------   -----  ------  ------ -----------------
1c00068ac1bd8c9b:0  215621 13:07:57 Jan-07-13 <32768 (11058 - WIN      ) 168Nt1JoLtPo97fgmBtXvfjKLPrHDxtkuV    0.84    1.64    0.80    0.80
41391737873fe6ee:1  215621 13:07:57 Jan-07-13 <32768 (33266 - LOSE     ) 12nTHxQMem9ciUyWhsG8raAdDPn3azv4hJ    1.65    0.01   -1.64   -0.84
63b8b8f26d07e54a:0  215621 13:07:57 Jan-07-13 <48000 (54152 - LOSE     ) 1KyQrWyqFwbaPkdWR1sVTCm82JFyhVyiNy    0.17    0.00   -0.17   -1.01
e19b23ea4533bb97:1  215621 13:07:57 Jan-07-13 <32768 ( 8309 - WIN      ) 1Cao4JaCAuRKTP8kHh5fM8fUAQhWAknZnz    0.01    0.02    0.01   -1.00
                                                                                                              -----   -----   -----
                                                                                                               2.67    1.67   -1.00

Total of 4 bets unaccounted for.

Results: 2013-Jan-07 01:10pm (up to block 215621)

   Address  Target   Should Win |    #Bets |       Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
---------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    63376 |      0 (0.00000) |   62254 |    1122 |     544.75 |       0.01 |    86.85 |    544.73 |   0.004
 1dice1Qf4       2      0.00003 |     3170 |      0 (0.00000) |    2678 |     492 |      46.58 |       0.00 |    16.23 |     46.58 |   0.010
 1dice2pxm       4      0.00006 |     5140 |      1 (0.00021) |    4721 |     418 |      68.88 |     159.96 |     8.45 |    -91.07 | 232.204
 1dice2vQo       8      0.00012 |     7731 |      2 (0.00027) |    7309 |     420 |     111.74 |      16.09 |    10.02 |     95.65 |  14.399
 1dice2WmR      16      0.00024 |     9474 |      1 (0.00011) |    9066 |     407 |     260.19 |       4.47 |    18.65 |    255.71 |   1.719
 1dice2xkj      32      0.00049 |     9501 |      3 (0.00033) |    9109 |     389 |     539.13 |     303.50 |     1.36 |    235.62 |  56.295
 1dice2zdo      64      0.00098 |    12360 |     12 (0.00100) |   11950 |     398 |     810.43 |     155.68 |    55.70 |    654.74 |  19.210
 1dice37Ee     128      0.00195 |    15333 |     28 (0.00188) |   14878 |     427 |    1866.33 |    1318.94 |    48.31 |    547.38 |  70.670
 1dice3jkp     256      0.00391 |    17241 |     73 (0.00433) |   16793 |     375 |    2175.16 |    3209.55 |    13.16 |  -1034.38 | 147.555
 1dice4J1m     512      0.00781 |    25231 |    186 (0.00757) |   24377 |     668 |    4295.89 |    3955.64 |     9.94 |    340.24 |  92.080
 1dice5wwE    1000      0.01526 |    75074 |   1155 (0.01547) |   73482 |     437 |   19274.98 |   17129.98 |     1.91 |   2145.00 |  88.872
 1dice61SN    1500      0.02289 |    19746 |    461 (0.02377) |   18937 |     348 |    6390.09 |    6445.80 |    15.06 |    -55.71 | 100.872
 1dice6DPt    2000      0.03052 |    44358 |   1375 (0.03126) |   42607 |     376 |   20535.58 |   17740.06 |     9.31 |   2795.51 |  86.387
 1dice6gJg    3000      0.04578 |    22705 |   1031 (0.04624) |   21267 |     407 |    8376.04 |    9432.40 |    25.08 |  -1056.36 | 112.612
 1dice6GV5    4000      0.06104 |    28456 |   1728 (0.06151) |   26367 |     361 |    6168.80 |    5678.93 |    31.25 |    489.87 |  92.059
 1dice6wBx    6000      0.09155 |    32580 |   3018 (0.09374) |   29178 |     384 |   13122.57 |   14678.81 |     7.11 |  -1556.24 | 111.859
 1dice6YgE    8000      0.12207 |   134305 |  16482 (0.12312) |  117391 |     432 |   52245.49 |   50721.53 |   100.18 |   1523.95 |  97.083
 1dice7EYz   12000      0.18311 |    51020 |   9396 (0.18570) |   41201 |     423 |   83822.02 |   82643.17 |  3314.63 |   1178.85 |  98.594
 1dice7fUk   16000      0.24414 |   158709 |  38562 (0.24367) |  119691 |     456 |  176505.11 |  176728.29 |  1617.02 |   -223.18 | 100.126
 1dice7W2A   24000      0.36621 |   132216 |  48518 (0.36830) |   83218 |     480 |  172904.21 |  169639.95 |  1012.86 |   3264.26 |  98.112
 1dice8EMZ   32000      0.48828 |   832674 | 406055 (0.48844) |  425281 |    1338 |  555397.89 |  546582.98 |  2923.90 |   8814.90 |  98.413
 1dice97EC   32768      0.50000 |   361580 | 180122 (0.49923) |  180676 |     782 |  392612.70 |  383789.60 |  5720.12 |   8823.09 |  97.753
 1dice9wcM   48000      0.73242 |   241194 | 177126 (0.73591) |   63565 |     503 |  244566.71 |  239023.65 |  5454.76 |   5543.06 |  97.734
 1dicec9k7   52000      0.79346 |    43314 |  34109 (0.79469) |    8812 |     393 |   48671.59 |   47728.63 |  1187.12 |    942.96 |  98.063
 1dicegEAr   56000      0.85449 |    32718 |  27649 (0.85635) |    4638 |     431 |   45288.57 |   44661.42 |   400.12 |    627.15 |  98.615
 1diceDCd2   60000      0.91553 |    39899 |  36162 (0.91561) |    3333 |     404 |   49793.38 |   49463.51 |     0.10 |    329.86 |  99.338
 1dice9wVt   64000      0.97656 |    11630 |  10797 (0.98101) |     209 |     624 |   21377.65 |   21029.06 |   239.42 |    348.58 |  98.369
---------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  2351645 | 955588           | 1382650 |   13407 |  543211.69 |  531759.31 |   205.07 |  11452.37 |  97.892
            big (bets >= 4 BTC) |    79090 |  38464           |   40338 |     288 | 1384560.90 | 1360482.41 | 22123.70 |  24078.48 |  98.261
---------------------------------------------------------------------------------------------------------------------------------------------
                                |  2430735 | 994052           | 1422988 |   13695 | 1927772.59 | 1892241.73 | 22328.77 |  35530.85 |  98.157
---------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      35530.85250800 BTC (1.843%)
Cumulative Fees Paid:        1626.18877500 BTC
SD Profit after fees:       33904.66373300 BTC (1.759%)
Pending Liabilities:           -1.00139025 BTC
Final SD Profit:            33905.66512325 BTC (1.759%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  7959268  :  SatoshiDice Tx:  4463481  (56.1%)
Blockchain MB:   3387.8  :  SatoshiDice MB:   1834.3  (54.1%)

[kidgorgeous]

Hmmm, what I think you're seeing is actually satoshidice fudging the payout multiplier and to make nice even numbers as well as you end up compounding some differences because the payout multiplier is rounded to three decimal places. I think maybe the less than 8000 bet should be 7.980x or something, but 8x looks a whole lot better.

I thought that computing the expected values of each bet would illuminate this but it's just confusing me more. Since the house edge is supposed to be 1.9% all of the EV's should all be around 0.981 but they're not, so unless I'm missing something satoshidice is fudging some numbers, making their house edge a little fatter than they're letting on 0.976 since .005 is returned with losing bets. Then the question is why are there bets that seem to pay out more?

Feel free to double check my math, also the odds of winning are only truncated for display but that math is based off of calculating the actual odds:

Code:

Bet	Odds	        Payout	       Expected Value
1	0.000015259	64000.000	0.9765625000
2	0.000030518	31981.573	0.9760001526
4	0.000061035	15990.789	0.9760003052
8	0.000122070	7995.397	0.9760006104
16	0.000244141	3997.701	0.9760012207
32	0.000488281	1998.853	0.9760024414
64	0.000976563	999.429	        0.9760048828
128	0.001953125	499.717	        0.9760097656
256	0.003906250	249.861	        0.9760195313
512	0.007812500	124.933	        0.9760390625
1000	0.015258789	63.968	        0.9760742188
1500	0.022888184	42.647	        0.9761123657
2000	0.030517578	31.987	        0.9761657715
3000	0.045776367	21.326	        0.9762268066
4000	0.061035156	15.996	        0.9763183594
6000	0.091552734	10.666	        0.9765014648
8000	0.122070313	8.000	        0.9765625000
12000	0.183105469	5.335 	        0.9768676758
16000	0.244140625	4.003 	        0.9772949219
24000	0.366210938	2.670 	        0.9777832031
32000	0.488281250	2.004 	        0.9785156250
32768	0.500000000	1.957         	0.9785000000
48000	0.732421875	1.338           0.9799804688
52000	0.793457031	1.235           0.9799194336
56000	0.854492188	1.147 	        0.9801025391
60000	0.915527344	1.071 	        0.9805297852
64000	0.976562500	1.004 	        0.9804687500

There is an interesting correlation though , the less than 60000 bet is the highest EV and less than 8000 is a bit lower with the less than 2 bet being the lowest. What happens with your strategy if you try a martingale on the less than 2 (ignoring mins and max bets for hypothetical purposes)?

[etotheipi]

I thought that computing the expected values of each bet would illuminate this but it's just confusing me more. Since the house edge is supposed to be 1.9% all of the EV's should all be around 0.981 but they're not, so unless I'm missing something satoshidice is fudging some numbers, making their house edge a little fatter than they're letting on.

I haven't had time to dig into the math, yet, but I wanted to point out that what you observed isn't fudging.  You just haven't taken into account that you get 0.5% of your bet back even when you lose.  Then your 0.976 payouts add up to 0.981.

[dooglus]

Hmmm, what I think you're seeing is actually satoshidice fudging the payout multiplier and to make nice even numbers

I wasn't using the published multipliers, because as you say they're rounded.  I was calculating the actual multipliers using a formula which I derived like this:

Code:

(lessthan * payout + (65536 - lessthan) * 0.005) / 65536 = 0.981    (multiply both sides by 65536)
(lessthan * payout + (65536 - lessthan) * 0.005) = 0.981 * 65536    (subtract (65536 - lessthan) * 0.005 from both sides)
(lessthan * payout) = 0.981 * 65536 - (65536 - lessthan) * 0.005    (divide both sides by lessthan)
so, payout = (0.981 * 65536 - (65536 - lessthan) * 0.005) / lessthan

If you compare the values that gives you for the payout multiplier with the published values, you find it's very close in every case except for the "lessthan 1", where the site is actually a little over generous (but that's deliberate - they state the hose edge is slightly smaller for that bet):

Code:

>>> for (lessthan, actual) in [(64000, 1.004), (60000, 1.071), (56000, 1.147), (52000, 1.235), (48000, 1.338), (32768, 1.957), (32000, 2.004), (24000, 2.670), (16000, 4.003), (12000, 5.335), (8000, 8.000), (6000, 10.666), (4000, 15.996), (3000, 21.326), (2000, 31.987), (1500, 42.647), (1000, 63.968), (512, 124.933), (256, 249.861), (128, 499.717), (64, 999.429), (32, 1998.853), (16, 3997.701), (8, 7995.397), (4, 15990.789), (2, 31981.573), (1, 64000.000)]:
...   print "lessthan %5d payout %9.3f (error %9.6f)" % (lessthan, actual, actual - (0.981 * 65536 - (65536 - lessthan) * 0.005) / lessthan)
... 
lessthan 64000 payout     1.004 (error -0.000424)
lessthan 60000 payout     1.071 (error -0.000052)
lessthan 56000 payout     1.147 (error -0.000199)
lessthan 52000 payout     1.235 (error -0.000060)
lessthan 48000 payout     1.338 (error  0.000435)
lessthan 32768 payout     1.957 (error  0.000000)
lessthan 32000 payout     2.004 (error  0.000152)
lessthan 24000 payout     2.670 (error -0.000131)
lessthan 16000 payout     4.003 (error  0.000304)
lessthan 12000 payout     5.335 (error -0.000261)
lessthan  8000 payout     8.000 (error -0.000392)
lessthan  6000 payout    10.666 (error  0.000477)
lessthan  4000 payout    15.996 (error  0.000216)
lessthan  3000 payout    21.326 (error -0.000045)
lessthan  2000 payout    31.987 (error  0.000432)
lessthan  1500 payout    42.647 (error -0.000091)
lessthan  1000 payout    63.968 (error -0.000136)
lessthan   512 payout   124.933 (error  0.000000)
lessthan   256 payout   249.861 (error  0.000000)
lessthan   128 payout   499.717 (error  0.000000)
lessthan    64 payout   999.429 (error  0.000000)
lessthan    32 payout  1998.853 (error  0.000000)
lessthan    16 payout  3997.701 (error  0.000000)
lessthan     8 payout  7995.397 (error  0.000000)
lessthan     4 payout 15990.789 (error  0.000000)
lessthan     2 payout 31981.573 (error  0.000000)
lessthan     1 payout 64000.000 (error 36.859000)

What happens with your strategy if you try a martingale on the less than 2 (ignoring mins and max bets for hypothetical purposes)?

Let's not ignore the mins and maxes.  They're currently 0.01 and 0.1844 (though they seem to change every few seconds now).

Here's a strategy to win 319 BTC betting on lessthan 2 in 91761 bets, starting at min bet and working up to max bet:

Code:

win on turn  1 : bet =   0.01000000, spent =   0.01050000, win = 319.81523000, lose =   0.00000001, back =   0.00000000, profit = 319.80473000 (99.997% to lose all)
win on turn  2 : bet =   0.01000033, spent =   0.02100033, win = 319.82573031, lose =   0.00000001, back =   0.00000001, profit = 319.80472999 (99.994% to lose all)
win on turn  3 : bet =   0.01000066, spent =   0.03150098, win = 319.83623095, lose =   0.00000001, back =   0.00000002, profit = 319.80472999 (99.991% to lose all)
win on turn  4 : bet =   0.01000099, spent =   0.04200197, win = 319.84673192, lose =   0.00000001, back =   0.00000003, profit = 319.80472998 (99.988% to lose all)
win on turn  5 : bet =   0.01000131, spent =   0.05250328, win = 319.85723322, lose =   0.00000001, back =   0.00000004, profit = 319.80472998 (99.985% to lose all)

win on turn 91757 : bet =   0.18437485, spent = 5580.49620770, win = 5896.59719089, lose =   0.00042187, back =   3.70328891, profit = 319.80427210 ( 6.080% to lose all)
win on turn 91758 : bet =   0.18438062, spent = 5580.68108832, win = 5896.78164963, lose =   0.00042190, back =   3.70371078, profit = 319.80427209 ( 6.079% to lose all)
win on turn 91759 : bet =   0.18438638, spent = 5580.86597470, win = 5896.96611411, lose =   0.00042193, back =   3.70413268, profit = 319.80427209 ( 6.079% to lose all)
win on turn 91760 : bet =   0.18439215, spent = 5581.05086685, win = 5897.15058433, lose =   0.00042196, back =   3.70455461, profit = 319.80427209 ( 6.079% to lose all)
win on turn 91761 : bet =   0.18439792, spent = 5581.23576477, win = 5897.33506029, lose =   0.00042198, back =   3.70497657, profit = 319.80427209 ( 6.079% to lose all)

It risks 5581.23576477 to win 319.80427209 and has a 6.079% chance of losing everything.

That's a payout of 1.057x and has the same risk as "lessthan 61552" (if it existed):

Code:

>>> 319.80427209 / 5581.23576477 + 1
1.0572999037433028
>>> 65536 * (1 - 6.079/100)
61552.06656

If satoshidice offered "lessthan 61552", they'd payout 1.044x on it:

Code:

>>> lessthan = 65536 * (1 - 6.079/100); (0.981 * 65536 - (65536 - lessthan) * 0.005) / lessthan
1.04417121836437

So again it's better to martingale a series of high-multiplier bets than to play a single large low-multiplier bet.

Why??

[dooglus]

Total of 28 bets unaccounted for.

Results: 2013-Jan-08 11:42am (up to block 215756)

   Address  Target   Should Win |    #Bets |       Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
---------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    63618 |      0 (0.00000) |   62496 |    1122 |     549.83 |       0.01 |    86.85 |    549.81 |   0.004
 1dice1Qf4       2      0.00003 |     3230 |      0 (0.00000) |    2738 |     492 |      47.26 |       0.00 |    16.23 |     47.26 |   0.010
 1dice2pxm       4      0.00006 |     5242 |      1 (0.00021) |    4823 |     418 |      70.03 |     159.96 |     8.45 |    -89.92 | 228.401
 1dice2vQo       8      0.00012 |     7788 |      2 (0.00027) |    7366 |     420 |     112.31 |      16.09 |    10.02 |     96.22 |  14.326
 1dice2WmR      16      0.00024 |     9552 |      1 (0.00011) |    9144 |     407 |     267.35 |       4.49 |    18.65 |    262.85 |   1.681
 1dice2xkj      32      0.00049 |     9509 |      3 (0.00033) |    9117 |     389 |     539.44 |     303.50 |     1.36 |    235.93 |  56.263
 1dice2zdo      64      0.00098 |    12389 |     12 (0.00100) |   11979 |     398 |     810.72 |     155.68 |    55.70 |    655.03 |  19.203
 1dice37Ee     128      0.00195 |    15347 |     28 (0.00188) |   14892 |     427 |    1867.79 |    1318.94 |    48.31 |    548.84 |  70.615
 1dice3jkp     256      0.00391 |    17248 |     73 (0.00433) |   16800 |     375 |    2176.63 |    3209.55 |    13.16 |  -1032.92 | 147.455
 1dice4J1m     512      0.00781 |    25255 |    186 (0.00756) |   24401 |     668 |    4296.39 |    3955.64 |     9.94 |    340.74 |  92.069
 1dice5wwE    1000      0.01526 |    75148 |   1155 (0.01546) |   73556 |     437 |   19296.96 |   17130.07 |     1.91 |   2166.89 |  88.771
 1dice61SN    1500      0.02289 |    19754 |    461 (0.02376) |   18945 |     348 |    6392.27 |    6445.81 |    15.06 |    -53.53 | 100.838
 1dice6DPt    2000      0.03052 |    44400 |   1376 (0.03126) |   42648 |     376 |   20579.07 |   17740.59 |     9.31 |   2838.47 |  86.207
 1dice6gJg    3000      0.04578 |    22712 |   1031 (0.04622) |   21274 |     407 |    8376.23 |    9432.40 |    25.08 |  -1056.16 | 112.609
 1dice6GV5    4000      0.06104 |    28467 |   1728 (0.06148) |   26378 |     361 |    6173.72 |    5678.95 |    31.25 |    494.76 |  91.986
 1dice6wBx    6000      0.09155 |    32637 |   3022 (0.09370) |   29231 |     384 |   13130.03 |   14681.40 |     7.11 |  -1551.37 | 111.815
 1dice6YgE    8000      0.12207 |   134407 |  16496 (0.12313) |  117479 |     432 |   52362.72 |   50904.08 |   100.18 |   1458.63 |  97.214
 1dice7EYz   12000      0.18311 |    51163 |   9412 (0.18549) |   41328 |     423 |   84392.38 |   82709.33 |  3314.63 |   1683.04 |  98.006
 1dice7fUk   16000      0.24414 |   159171 |  38673 (0.24366) |  120042 |     456 |  177874.34 |  177835.60 |  1617.02 |     38.73 |  99.978
 1dice7W2A   24000      0.36621 |   132800 |  48722 (0.36821) |   83598 |     480 |  174919.57 |  172451.25 |  1012.86 |   2468.31 |  98.589
 1dice8EMZ   32000      0.48828 |   835135 | 407257 (0.48844) |  426540 |    1338 |  557610.42 |  548062.95 |  2923.90 |   9547.46 |  98.288
 1dice97EC   32768      0.50000 |   364002 | 181330 (0.49923) |  181890 |     782 |  394004.16 |  385119.70 |  5720.12 |   8884.45 |  97.745
 1dice9wcM   48000      0.73242 |   242574 | 178144 (0.73592) |   63927 |     503 |  244853.15 |  239313.11 |  5454.76 |   5540.04 |  97.737
 1dicec9k7   52000      0.79346 |    43449 |  34213 (0.79462) |    8843 |     393 |   48699.62 |   47756.76 |  1187.12 |    942.85 |  98.064
 1dicegEAr   56000      0.85449 |    32910 |  27814 (0.85637) |    4665 |     431 |   45389.11 |   44762.89 |   400.12 |    626.22 |  98.620
 1diceDCd2   60000      0.91553 |    40464 |  36686 (0.91578) |    3374 |     404 |   49891.53 |   49564.97 |     0.10 |    326.55 |  99.345
 1dice9wVt   64000      0.97656 |    11680 |  10847 (0.98110) |     209 |     624 |   21386.33 |   21037.76 |   239.42 |    348.57 |  98.370
---------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  2360751 | 960122           | 1387222 |   13407 |  545125.12 |  533553.42 |   205.07 |  11571.69 |  97.877
            big (bets >= 4 BTC) |    79300 |  38551           |   40461 |     288 | 1390944.36 | 1366198.21 | 22123.70 |  24746.15 |  98.221
---------------------------------------------------------------------------------------------------------------------------------------------
                                |  2440051 | 998673           | 1427683 |   13695 | 1936069.48 | 1899751.64 | 22328.77 |  36317.84 |  98.124
---------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      36317.84369285 BTC (1.876%)
Cumulative Fees Paid:        1635.60487500 BTC
SD Profit after fees:       34682.23881785 BTC (1.791%)
Pending Liabilities:           40.68659544 BTC
Final SD Profit:            34641.55222241 BTC (1.789%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  7994821  :  SatoshiDice Tx:  4480860  (56.0%)
Blockchain MB:   3404.2  :  SatoshiDice MB:   1841.5  (54.1%)

[Bowjob]

I still find it hard to believe that some of the addresses, particularly Satoshi less than 3000 consistently lose all the time. The amount of money wagered shouldn't make a difference.. it still bothers me. I mean, if I scale it up with 750 BTC, you mean I could make some decent profits out it? Unfortunately, I can't afford to lose 10 grand so.. I can't test it for sure.

[dooglus]

I still find it hard to believe that some of the addresses, particularly Satoshi less than 3000 consistently lose all the time. The amount of money wagered shouldn't make a difference.. it still bothers me. I mean, if I scale it up with 750 BTC, you mean I could make some decent profits out it? Unfortunately, I can't afford to lose 10 grand so.. I can't test it for sure.

I just went through the last 6 pages of this thread and pulled out all the 'lessthan 3000' lines from the reports:

   Address  Target   Should Win |    #Bets |       Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
---------------------------------------------------------------------------------------------------------------------------------------------
1dice6gJg    3000      0.04578 |    20511 |    934 (0.04645) |   19173 |     404 |    8154.32 |    9295.88 |    25.08 |  -1141.55 | 113.999
1dice6gJg    3000      0.04578 |    20515 |    934 (0.04644) |   19177 |     404 |    8154.89 |    9295.88 |    25.08 |  -1140.98 | 113.991
1dice6gJg    3000      0.04578 |    20560 |    937 (0.04649) |   19219 |     404 |    8156.33 |    9297.20 |    25.08 |  -1140.86 | 113.988
1dice6gJg    3000      0.04578 |    20791 |    949 (0.04655) |   19438 |     404 |    8164.30 |    9306.36 |    25.08 |  -1142.06 | 113.989
1dice6gJg    3000      0.04578 |    20898 |    950 (0.04636) |   19544 |     404 |    8167.00 |    9306.90 |    25.08 |  -1139.89 | 113.957
1dice6gJg    3000      0.04578 |    20917 |    951 (0.04636) |   19562 |     404 |    8167.47 |    9307.11 |    25.08 |  -1139.64 | 113.953
1dice6gJg    3000      0.04578 |    20959 |    954 (0.04641) |   19601 |     404 |    8168.57 |    9307.96 |    25.08 |  -1139.38 | 113.948
1dice6gJg    3000      0.04578 |    20988 |    956 (0.04644) |   19628 |     404 |    8168.97 |    9308.39 |    25.08 |  -1139.41 | 113.948
1dice6gJg    3000      0.04578 |    20998 |    956 (0.04642) |   19638 |     404 |    8179.64 |    9308.44 |    25.08 |  -1128.79 | 113.800
1dice6gJg    3000      0.04578 |    21013 |    957 (0.04644) |   19651 |     405 |    8179.81 |    9308.65 |    25.08 |  -1128.84 | 113.800
1dice6gJg    3000      0.04578 |    21021 |    957 (0.04642) |   19659 |     405 |    8179.90 |    9308.65 |    25.08 |  -1128.75 | 113.799
1dice6gJg    3000      0.04578 |    21051 |    957 (0.04635) |   19689 |     405 |    8187.80 |    9308.68 |    25.08 |  -1120.88 | 113.690
1dice6gJg    3000      0.04578 |    21090 |    958 (0.04632) |   19726 |     406 |    8189.94 |    9311.03 |    25.08 |  -1121.08 | 113.689
1dice6gJg    3000      0.04578 |    21165 |    964 (0.04644) |   19795 |     406 |    8192.48 |    9314.22 |    25.08 |  -1121.74 | 113.692
1dice6gJg    3000      0.04578 |    21192 |    964 (0.04638) |   19822 |     406 |    8194.11 |    9314.23 |    25.08 |  -1120.11 | 113.670
1dice6gJg    3000      0.04578 |    21206 |    964 (0.04635) |   19835 |     407 |    8195.82 |    9314.23 |    25.08 |  -1118.40 | 113.646
1dice6gJg    3000      0.04578 |    21220 |    965 (0.04637) |   19848 |     407 |    8196.73 |    9316.36 |    25.08 |  -1119.63 | 113.660
1dice6gJg    3000      0.04578 |    21406 |    972 (0.04629) |   20027 |     407 |    8206.00 |    9317.88 |    25.08 |  -1111.88 | 113.550
1dice6gJg    3000      0.04578 |    22382 |   1021 (0.04646) |   20954 |     407 |    8219.26 |    9328.96 |    25.08 |  -1109.69 | 113.501
1dice6gJg    3000      0.04578 |    22387 |   1022 (0.04650) |   20958 |     407 |    8219.41 |    9329.17 |    25.08 |  -1109.75 | 113.502
1dice6gJg    3000      0.04578 |    22402 |   1023 (0.04651) |   20972 |     407 |    8219.68 |    9329.38 |    25.08 |  -1109.70 | 113.501
1dice6gJg    3000      0.04578 |    22558 |   1028 (0.04641) |   21123 |     407 |    8353.23 |    9416.33 |    25.08 |  -1063.09 | 112.727
1dice6gJg    3000      0.04578 |    22568 |   1028 (0.04639) |   21133 |     407 |    8353.56 |    9416.33 |    25.08 |  -1062.76 | 112.722
1dice6gJg    3000      0.04578 |    22660 |   1030 (0.04629) |   21223 |     407 |    8364.31 |    9417.42 |    25.08 |  -1053.11 | 112.591
1dice6gJg    3000      0.04578 |    22672 |   1030 (0.04626) |   21235 |     407 |    8364.65 |    9417.42 |    25.08 |  -1052.77 | 112.586
1dice6gJg    3000      0.04578 |    22695 |   1031 (0.04626) |   21257 |     407 |    8375.60 |    9432.40 |    25.08 |  -1056.79 | 112.618
1dice6gJg    3000      0.04578 |    22705 |   1031 (0.04624) |   21267 |     407 |    8376.04 |    9432.40 |    25.08 |  -1056.36 | 112.612
1dice6gJg    3000      0.04578 |    22712 |   1031 (0.04622) |   21274 |     407 |    8376.23 |    9432.40 |    25.08 |  -1056.16 | 112.609

That covers the last 4 weeks.  4 weeks ago the house was 1141.55 BTC down on "lessthan 3000" overall.  Now they're only 1056.16 BTC down on the same bet.  That means the house has won around 100 BTC on "lessthan 3000" in the last 4 weeks.  If you look at the profit column, you'll see the negative number is pretty consistently getting less negative day by day.  That means the house is consistently winning on lessthan 3000.  They just had a bad run of large bets some months ago and didn't recover from it yet.

[dooglus]

So again it's better to martingale a series of high-multiplier bets than to play a single large low-multiplier bet.

Why??

I think I found the reason:

I have to choose between two seeming equivalent betting strategies:

a) I commit to betting 1, 2, 4 on a bet that pays out 2x with a 1/2 probability of winning each time, and that the house takes 2% of everything I stake as a service charge.  I'm committed to risking up to 7 to win 1.

b) I bet the 7 all at once on a bet that pays out (8/7)x and which has a 7/8 probability of winning.  Again, the house takes its 2% service charge of all stakes.

In both cases I risk 7 to win 1.  In both cases I have a 1/8 probability of losing 7 chips.

The difference is in the service charge.  In a) there's a good (75%) chance that I won't need to bet the 4, because either the 1 or the 2 will win.  So I'll be paying less service charge.  In b) I pay 2% of the full 7 chips.

There's no service charge at satoshidice, but there's a house edge, which is effectively the same thing.  Breaking a single low-multiplier high-stake bet up into a martingale series of high-multiplier low-stake bets means on average I'll be staking less to achieve the same result.  So while it's true that martingale betting can't reduce the house edge, it's also true that martingale betting can be used to give a higher expected return than placing a single large equivalent bet by reducing the average amount that needs to be staked to achieve the desired return.

[Bugpowder]

Looking good for S.DICE...

Details   2013-01-09 01:51:31   lessthan 16000   de2012c9   3148068f   1HbHbFK   CONFIRMED   435.00000000   LOSE   2.17450000   41970
Details   2013-01-09 01:50:43   lessthan 16000   d463f567   faa9a2d8   19LQ1zn   CONFIRMED   435.00000000   LOSE   2.17450000   53146
Details   2013-01-09 01:49:33   lessthan 16000   f3d916d3   c4273fff   1Bw9MTr   CONFIRMED   435.00000000   LOSE   2.17450000   52002
Details   2013-01-09 01:48:04   lessthan 16000   881eda89   5a2d111b   1Fh2Rjd   CONFIRMED   327.68000000   LOSE   1.63790000   39752
Details   2013-01-09 01:47:12   lessthan 16000   8a50052a   dcd5405b   19nKhcW   CONFIRMED   163.84000000   LOSE   0.81870000   16205
Details   2013-01-09 01:46:03   lessthan 16000   b7ed8b5e   1306b724   19nKhcW   CONFIRMED   81.92000000   LOSE   0.40910000   24206


OUCH...  This is the tail end of a Martingale that started on 0.01BTC, doubling each loss, and ending very very badly.