Satoshi Dice -- Statistical Analysis

[dooglus]

If it weren't for the big bets, SatoshiDice would be almost 4000 BTC up by now, but instead they're 500 BTC down.

Sounds like SatoshiDice is lazy and use big amounts for their statistics-skewing transactions masqueraded as real bets.</AlexJones>

It occurred to me that it was their way of taking a profit.  But if that's the case, why have they lowered the max bet and kept it low?  It doesn't make any sense to be decreasing the bet sizes as the profits grow.

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[dooglus]

Results: 2012-Jul-02 01:23pm (up to block 187242)

   Address   Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |    BTC In    |   BTC Out    |    Profit    |   RTP 
-----------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p        1      0.00002 |     6250 |      0 (0.00000) |   5992 |     257 |        21.71 |         0.01 |        21.69 |   0.088
 1dice1Qf4        2      0.00003 |      888 |      0 (0.00000) |    821 |      67 |         7.15 |         0.00 |         7.14 |   0.025
 1dice2pxm        4      0.00006 |     1397 |      0 (0.00000) |   1367 |      30 |        12.15 |         0.00 |        12.15 |   0.046
 1dice2vQo        8      0.00012 |     1102 |      0 (0.00000) |   1064 |      38 |        15.19 |         0.00 |        15.18 |   0.031
 1dice2WmR       16      0.00024 |     1358 |      0 (0.00000) |   1330 |      28 |        21.01 |         0.01 |        20.99 |   0.076
 1dice2xkj       32      0.00049 |     3092 |      1 (0.00032) |   3080 |      11 |        89.89 |       100.38 |       -10.48 | 111.666
 1dice2zdo       64      0.00098 |     4460 |      5 (0.00113) |   4438 |      17 |       176.73 |       110.74 |        65.99 |  62.661
 1dice37Ee      128      0.00195 |     5901 |     12 (0.00205) |   5840 |      47 |      1197.34 |      1142.16 |        55.17 |  95.392
 1dice3jkp      256      0.00391 |     4399 |     20 (0.00456) |   4366 |      12 |       458.86 |       330.67 |       128.18 |  72.064
 1dice4J1m      512      0.00781 |     5462 |     32 (0.00587) |   5424 |       5 |       748.28 |       330.60 |       417.67 |  44.182
 1dice5wwE     1000      0.01526 |     6656 |     93 (0.01398) |   6558 |       2 |      1377.12 |       711.48 |       665.64 |  51.664
 1dice61SN     1500      0.02289 |     5172 |    108 (0.02091) |   5057 |       6 |      1913.72 |      2135.76 |      -222.03 | 111.602
 1dice6DPt     2000      0.03052 |     5628 |    174 (0.03096) |   5447 |       3 |      1786.52 |      1635.04 |       151.47 |  91.521
 1dice6gJg     3000      0.04578 |     5518 |    277 (0.05028) |   5232 |       7 |      3791.62 |      4916.50 |     -1124.87 | 129.667
 1dice6GV5     4000      0.06104 |     5586 |    344 (0.06163) |   5238 |       3 |      1619.49 |      1429.16 |       190.33 |  88.247
 1dice6wBx     6000      0.09155 |     9550 |    893 (0.09358) |   8650 |       4 |      6146.27 |      6745.93 |      -599.66 | 109.756
 1dice6YgE     8000      0.12207 |    10612 |   1297 (0.12232) |   9306 |       0 |      2952.77 |      2544.50 |       408.26 |  86.173
 1dice7EYz    12000      0.18311 |    14629 |   2789 (0.19087) |  11823 |       5 |      5962.82 |      6312.56 |      -349.74 | 105.865
 1dice7fUk    16000      0.24414 |    35975 |   8723 (0.24258) |  27236 |       6 |      9011.21 |      8694.07 |       317.13 |  96.481
 1dice7W2A    24000      0.36621 |    24066 |   8887 (0.36977) |  15147 |      30 |     10854.86 |     11103.44 |      -248.57 | 102.290
 1dice8EMZ    32000      0.48828 |   272702 | 132734 (0.48701) | 139817 |     121 |     80984.06 |     82596.47 |     -1612.40 | 101.991
 1dice97EC    32768      0.50000 |   106458 |  53176 (0.49984) |  53210 |      64 |     36476.09 |     35805.28 |       670.81 |  98.161
 1dice9wcM    48000      0.73242 |    66349 |  48731 (0.73487) |  17581 |      32 |     38074.31 |     36695.62 |      1378.68 |  96.379
 1dice9wVt    64000      0.97656 |     5694 |   4598 (0.97457) |    120 |     975 |      4901.49 |      4709.70 |       191.79 |  96.087
-----------------------------------------------------------------------------------------------------------------------------------------
                                 |   608904 |
-----------------------------------------------------------------------------------------------------------------------------------------

Cumulative Wagers:             212865.75014757 BTC
Cumulative Rewards:            212275.45778249 BTC
Cumulative Fees Paid:             306.38627500 BTC
Cumulative Unreturned:             39.71568201 BTC
----
SD Profit on Completed Bets :       244.19040807 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  1761683  :  SatoshiDice Tx: 1136393  (64.5%)
Blockchain MB:  746.3  :  SatoshiDice Tx: 462.7  (62.0%)

[gmaxwell]

It occurred to me that it was their way of taking a profit.  But if that's the case, why have they lowered the max bet and kept it low?  It doesn't make any sense to be decreasing the bet sizes as the profits grow.

It makes sense after you've seen people argue that their 'losses' and betcaps are "proof" that a favored gambling strategy is a "sure win".

Same reason casinos promote grand stories of card counting blackjack sharks bilking casinos and pretend to be concerned about card counters,  while simultaneously employing multi deck continuous shuffling machines that moot card counting.

[evoorhees]

If it weren't for the big bets, SatoshiDice would be almost 4000 BTC up by now, but instead they're 500 BTC down.

Sounds like SatoshiDice is lazy and use big amounts for their statistics-skewing transactions masqueraded as real bets.</AlexJones>

It occurred to me that it was their way of taking a profit.  But if that's the case, why have they lowered the max bet and kept it low?  It doesn't make any sense to be decreasing the bet sizes as the profits grow.

Yeah, I wish the big bets had been paying out better for SatoshiDice, but we've been unlucky thus far. We lowered the max bet down to 5btc for a while to help curb the losses, and now have raised it back to 25btc.

As of today, SatoshiDice is back in the black after a fairly gruesome couple weeks. Needless to say, it is stressful running this site but hopefully the players are having fun!

[nibor]

Yeah, I wish the big bets had been paying out better for SatoshiDice, but we've been unlucky thus far. We lowered the max bet down to 5btc for a while to help curb the losses, and now have raised it back to 25btc.

As of today, SatoshiDice is back in the black after a fairly gruesome couple weeks. Needless to say, it is stressful running this site but hopefully the players are having fun!

Question is are you being actively scammed?
What have you learnt about zero-confirmation transactions and how safe they are?

We know there are theories as to how you could be scammed etc.. but would be interesting if they are actually occurring in the wild, and if there are any changes the bitcoin that could fix it or at least make it harder.

Having to wait 1-6 confirmations is one of bitcoins few weaknesses, so knowing if zero confirmation transactions were reasonably safe in the real world would be "news".

[Peter Todd]

Yeah, I wish the big bets had been paying out better for SatoshiDice, but we've been unlucky thus far. We lowered the max bet down to 5btc for a while to help curb the losses, and now have raised it back to 25btc.

As of today, SatoshiDice is back in the black after a fairly gruesome couple weeks. Needless to say, it is stressful running this site but hopefully the players are having fun!

Question is are you being actively scammed?
What have you learnt about zero-confirmation transactions and how safe they are?

Also, have you talked to zipconf? I dunno how exactly their service works - is it transaction or address based? - but it'd make for an interesting, high-visibility, high-risk test case. IE: maybe they'd give you a discount on the fees.

[k]

If it weren't for the big bets, SatoshiDice would be almost 4000 BTC up by now, but instead they're 500 BTC down.

Sounds like SatoshiDice is lazy and use big amounts for their statistics-skewing transactions masqueraded as real bets.</AlexJones>

It occurred to me that it was their way of taking a profit.  But if that's the case, why have they lowered the max bet and kept it low?  It doesn't make any sense to be decreasing the bet sizes as the profits grow.

Is this just a natural consequence of martingale type betting strategies? Players start with small bets, go on a losing run, doubling up each time, so there are string of profitable small bets for SatoshiDice and then player finally gets a winning (larger) bet, so those larger bets are less profitable from SatoshiDice's point of view.

[dooglus]

Is this just a natural consequence of martingale type betting strategies? Players start with small bets, go on a losing run, doubling up each time, so there are string of profitable small bets for SatoshiDice and then player finally gets a winning (larger) bet, so those larger bets are less profitable from SatoshiDice's point of view.

I don't think so.  The dice don't care whether your bet of 5 BTC is part of a martingale chain or not.  Each bet has the same (slightly negative) expectation no matter what your previous and next bets are.

[dooglus]

Small bets are very profitable.  Big bets are very expensive.

Since I wrote that, the effect has stopped.  Now the big bets are more profitable than the small bets.

Results: 2012-Jul-04 05:49pm (up to block 187572)

   Address   Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |    BTC In    |   BTC Out    |    Profit    |   RTP 
-----------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p        1      0.00002 |     6396 |      0 (0.00000) |   6139 |     257 |        22.41 |         0.01 |        22.39 |   0.086
 1dice1Qf4        2      0.00003 |      898 |      0 (0.00000) |    831 |      67 |         7.19 |         0.00 |         7.19 |   0.024
 1dice2pxm        4      0.00006 |     1412 |      0 (0.00000) |   1382 |      30 |        12.24 |         0.00 |        12.23 |   0.046
 1dice2vQo        8      0.00012 |     1152 |      0 (0.00000) |   1114 |      38 |        15.62 |         0.00 |        15.61 |   0.030
 1dice2WmR       16      0.00024 |     1370 |      0 (0.00000) |   1342 |      28 |        21.29 |         0.01 |        21.27 |   0.075
 1dice2xkj       32      0.00049 |     3110 |      1 (0.00032) |   3098 |      11 |        90.71 |       100.38 |        -9.66 | 110.653
 1dice2zdo       64      0.00098 |     4479 |      5 (0.00112) |   4457 |      17 |       177.61 |       110.74 |        66.87 |  62.351
 1dice37Ee      128      0.00195 |     5951 |     12 (0.00203) |   5892 |      47 |      1210.87 |      1142.21 |        68.65 |  94.330
 1dice3jkp      256      0.00391 |     4417 |     20 (0.00454) |   4385 |      12 |       462.00 |       330.69 |       131.31 |  71.577
 1dice4J1m      512      0.00781 |     5621 |     32 (0.00570) |   5584 |       5 |       769.83 |       330.67 |       439.16 |  42.953
 1dice5wwE     1000      0.01526 |     6882 |     95 (0.01381) |   6784 |       2 |      1428.24 |       746.85 |       681.38 |  52.292
 1dice61SN     1500      0.02289 |     5606 |    121 (0.02161) |   5479 |       6 |      2309.16 |      2539.37 |      -230.20 | 109.969
 1dice6DPt     2000      0.03052 |     5790 |    180 (0.03110) |   5607 |       3 |      1842.33 |      1740.24 |       102.09 |  94.459
 1dice6gJg     3000      0.04578 |     5849 |    294 (0.05033) |   5548 |       7 |      4171.64 |      5313.31 |     -1141.66 | 127.367
 1dice6GV5     4000      0.06104 |     5771 |    358 (0.06207) |   5410 |       3 |      1636.81 |      1443.86 |       192.95 |  88.212
 1dice6wBx     6000      0.09155 |     9881 |    922 (0.09335) |   8955 |       4 |      6467.88 |      6912.13 |      -444.24 | 106.868
 1dice6YgE     8000      0.12207 |    12435 |   1521 (0.12232) |  10914 |       0 |      3032.06 |      2616.39 |       415.66 |  86.291
 1dice7EYz    12000      0.18311 |    14937 |   2850 (0.19089) |  12080 |       5 |      6029.20 |      6374.06 |      -344.85 | 105.720
 1dice7fUk    16000      0.24414 |    36469 |   8837 (0.24236) |  27626 |       6 |      9217.75 |      8980.68 |       237.07 |  97.428
 1dice7W2A    24000      0.36621 |    24505 |   9036 (0.36921) |  15438 |      30 |     10984.14 |     11178.53 |      -194.39 | 101.770
 1dice8EMZ    32000      0.48828 |   275950 | 134351 (0.48708) | 141477 |     121 |     82125.09 |     83627.65 |     -1502.55 | 101.830
 1dice97EC    32768      0.50000 |   108253 |  54052 (0.49961) |  54137 |      64 |     37408.77 |     36644.39 |       764.37 |  97.957
 1dice9wcM    48000      0.73242 |    67184 |  49350 (0.73493) |  17799 |      35 |     38665.31 |     37241.58 |      1423.72 |  96.318
 1dice9wVt    64000      0.97656 |     5695 |   4598 (0.97457) |    120 |     976 |      4901.49 |      4709.70 |       191.79 |  96.087
-----------------------------------------------------------------------------------------------------------------------------------------
                                 |   620013 |
-----------------------------------------------------------------------------------------------------------------------------------------

Cumulative Wagers:             217238.77021334 BTC
Cumulative Rewards:            216310.81217506 BTC
Cumulative Fees Paid:             312.02222500 BTC
Cumulative Unreturned:              1.74000000 BTC
----
SD Profit on Completed Bets :       614.19581328 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  1810476  :  SatoshiDice Tx: 1156403  (63.9%)
Blockchain MB:  766.5  :  SatoshiDice Tx: 470.8  (61.4%)

[dooglus]

Results: 2012-Jul-05 12:41pm (up to block 187680)

   Address   Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |    BTC In    |   BTC Out    |    Profit    |   RTP 
-----------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p        1      0.00002 |     6453 |      0 (0.00000) |   6196 |     257 |        22.70 |         0.01 |        22.68 |   0.085
 1dice1Qf4        2      0.00003 |      901 |      0 (0.00000) |    834 |      67 |         7.23 |         0.00 |         7.22 |   0.024
 1dice2pxm        4      0.00006 |     1414 |      0 (0.00000) |   1384 |      30 |        12.30 |         0.00 |        12.30 |   0.046
 1dice2vQo        8      0.00012 |     1155 |      0 (0.00000) |   1117 |      38 |        15.78 |         0.00 |        15.77 |   0.030
 1dice2WmR       16      0.00024 |     1372 |      0 (0.00000) |   1344 |      28 |        21.50 |         0.01 |        21.48 |   0.076
 1dice2xkj       32      0.00049 |     3141 |      1 (0.00032) |   3129 |      11 |        91.02 |       100.38 |        -9.35 | 110.276
 1dice2zdo       64      0.00098 |     4520 |      5 (0.00111) |   4498 |      17 |       178.02 |       110.74 |        67.28 |  62.208
 1dice37Ee      128      0.00195 |     5953 |     12 (0.00203) |   5894 |      47 |      1211.08 |      1142.21 |        68.86 |  94.314
 1dice3jkp      256      0.00391 |     4419 |     20 (0.00454) |   4387 |      12 |       462.01 |       330.69 |       131.32 |  71.576
 1dice4J1m      512      0.00781 |     5622 |     32 (0.00570) |   5585 |       5 |       769.88 |       330.67 |       439.21 |  42.951
 1dice5wwE     1000      0.01526 |     6980 |     95 (0.01362) |   6882 |       2 |      1434.36 |       746.87 |       687.49 |  52.070
 1dice61SN     1500      0.02289 |     5722 |    125 (0.02187) |   5591 |       6 |      2312.58 |      2548.64 |      -236.06 | 110.208
 1dice6DPt     2000      0.03052 |     5841 |    180 (0.03083) |   5658 |       3 |      1849.04 |      1740.25 |       108.79 |  94.116
 1dice6gJg     3000      0.04578 |     5930 |    296 (0.04997) |   5627 |       7 |      4187.34 |      5317.57 |     -1130.22 | 126.991
 1dice6GV5     4000      0.06104 |     5838 |    365 (0.06255) |   5470 |       3 |      1643.96 |      1509.06 |       134.90 |  91.794
 1dice6wBx     6000      0.09155 |    10107 |    942 (0.09324) |   9161 |       4 |      6542.74 |      6934.11 |      -391.37 | 105.982
 1dice6YgE     8000      0.12207 |    12767 |   1558 (0.12203) |  11209 |       0 |      3051.56 |      2668.70 |       382.86 |  87.454
 1dice7EYz    12000      0.18311 |    14987 |   2859 (0.19085) |  12121 |       5 |      6048.12 |      6430.64 |      -382.52 | 106.325
 1dice7fUk    16000      0.24414 |    36604 |   8871 (0.24239) |  27727 |       6 |      9290.29 |      9018.05 |       272.24 |  97.070
 1dice7W2A    24000      0.36621 |    25173 |   9270 (0.36871) |  15872 |      30 |     11157.77 |     11382.89 |      -225.12 | 102.018
 1dice8EMZ    32000      0.48828 |   277183 | 134987 (0.48721) | 142074 |     121 |     82385.78 |     83902.06 |     -1516.27 | 101.840
 1dice97EC    32768      0.50000 |   109756 |  54795 (0.49954) |  54895 |      65 |     38539.38 |     37612.67 |       926.70 |  97.595
 1dice9wcM    48000      0.73242 |    67585 |  49649 (0.73500) |  17901 |      35 |     38852.41 |     37421.81 |      1430.60 |  96.318
 1dice9wVt    64000      0.97656 |     5695 |   4598 (0.97457) |    120 |     976 |      4901.49 |      4709.70 |       191.79 |  96.087
-----------------------------------------------------------------------------------------------------------------------------------------
                                 |   625118 |
-----------------------------------------------------------------------------------------------------------------------------------------

Cumulative Wagers:             219217.47210252 BTC
Cumulative Rewards:            218185.09823143 BTC
Cumulative Fees Paid:             314.58460000 BTC
Cumulative Unreturned:              1.76000000 BTC
----
SD Profit on Completed Bets :       716.02927109 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  1827797  :  SatoshiDice Tx: 1165307  (63.8%)
Blockchain MB:  773.9  :  SatoshiDice Tx: 474.7  (61.3%)

[Spekulatius]

Since I wrote that, the effect has stopped.  Now the big bets are more profitable than the small bets.

How is it even possible that such a large population of independant events (those bets up to 4 and those above 4) can differ so heavily from the mean (0 level)? Shouldn`t they even themselves out?

[gmaxwell]

How is it even possible that such a large population of independant events (those bets up to 4 and those above 4) can differ so heavily from the mean (0 level)? Shouldn`t they even themselves out?

I'm sure someone could give some figures on how often these results could be expected by chance.

Though since today seems to be the day for silly theories.

It was pointed out on IRC that you could do somewhat tidy laundering this way.


Identity X with dirty coins gambles until they lose Y coins.

Then using identity Y, they make more bets, and someone with knowledge of the MAC secret filters their candidate transactions  to help them win until they've won Y/2 (or whatever).

This would be pretty hard to distinguish, except for the weird effect would have on the odds, especially if they weren't careful about the distribution they drew the winning bets from... and it would be impossible to connect the parties beyond they were both participants at some point in the game.

It would also explain rapid, almost certainly bot-based, playing of a negative ev game, reasons for capping the total (make the distribution of bets more regular).  Plus elvis came down from a UFO and told me it was true.

[dooglus]

Results: 2012-Jul-06 03:22pm (up to block 187853)

   Address   Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |    BTC In    |   BTC Out    |    Profit    |   RTP 
-----------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p        1      0.00002 |     6757 |      0 (0.00000) |   6500 |     257 |        24.71 |         0.01 |        24.69 |   0.078
 1dice1Qf4        2      0.00003 |      911 |      0 (0.00000) |    843 |      68 |         7.26 |         0.00 |         7.26 |   0.024
 1dice2pxm        4      0.00006 |     1436 |      0 (0.00000) |   1406 |      30 |        12.45 |         0.00 |        12.44 |   0.045
 1dice2vQo        8      0.00012 |     1178 |      0 (0.00000) |   1140 |      38 |        15.94 |         0.00 |        15.94 |   0.030
 1dice2WmR       16      0.00024 |     1385 |      0 (0.00000) |   1357 |      28 |        21.54 |         0.01 |        21.53 |   0.076
 1dice2xkj       32      0.00049 |     3161 |      1 (0.00032) |   3149 |      11 |        91.22 |       100.38 |        -9.15 | 110.032
 1dice2zdo       64      0.00098 |     4536 |      5 (0.00111) |   4514 |      17 |       178.20 |       110.74 |        67.45 |  62.147
 1dice37Ee      128      0.00195 |     5973 |     12 (0.00202) |   5914 |      47 |      1212.23 |      1142.22 |        70.01 |  94.224
 1dice3jkp      256      0.00391 |     4433 |     21 (0.00475) |   4400 |      12 |       462.72 |       331.92 |       130.79 |  71.733
 1dice4J1m      512      0.00781 |     5651 |     33 (0.00584) |   5613 |       5 |       771.25 |       331.04 |       440.21 |  42.923
 1dice5wwE     1000      0.01526 |     7176 |     96 (0.01338) |   7077 |       2 |      1441.16 |       746.95 |       694.20 |  51.830
 1dice61SN     1500      0.02289 |     5744 |    127 (0.02213) |   5611 |       6 |      2315.04 |      2549.07 |      -234.03 | 110.109
 1dice6DPt     2000      0.03052 |     5938 |    181 (0.03050) |   5754 |       3 |      1857.41 |      1740.75 |       116.66 |  93.719
 1dice6gJg     3000      0.04578 |     6027 |    296 (0.04917) |   5724 |       7 |      4196.45 |      5317.58 |     -1121.13 | 126.716
 1dice6GV5     4000      0.06104 |     5902 |    366 (0.06204) |   5533 |       3 |      1671.65 |      1510.12 |       161.53 |  90.337
 1dice6wBx     6000      0.09155 |    10170 |    949 (0.09335) |   9217 |       4 |      6561.67 |      6935.97 |      -374.29 | 105.704
 1dice6YgE     8000      0.12207 |    14124 |   1731 (0.12257) |  12392 |       0 |      3263.58 |      2829.73 |       433.85 |  86.706
 1dice7EYz    12000      0.18311 |    15038 |   2869 (0.19087) |  12162 |       5 |      6196.77 |      6487.88 |      -291.11 | 104.698
 1dice7fUk    16000      0.24414 |    36902 |   8938 (0.24225) |  27958 |       6 |      9593.53 |      9106.52 |       487.01 |  94.924
 1dice7W2A    24000      0.36621 |    25612 |   9452 (0.36951) |  16128 |      31 |     11773.25 |     11840.04 |       -66.78 | 100.567
 1dice8EMZ    32000      0.48828 |   278761 | 135746 (0.48718) | 142891 |     121 |     83022.22 |     84420.19 |     -1397.97 | 101.684
 1dice97EC    32768      0.50000 |   111753 |  55834 (0.49991) |  55853 |      65 |     40377.40 |     39202.09 |      1175.30 |  97.089
 1dice9wcM    48000      0.73242 |    68104 |  50039 (0.73512) |  18030 |      35 |     39537.99 |     38150.71 |      1387.27 |  96.491
 1dice9wVt    64000      0.97656 |     5697 |   4598 (0.97457) |    120 |     978 |      4901.49 |      4709.70 |       191.79 |  96.087
-----------------------------------------------------------------------------------------------------------------------------------------
                                 |   632369 |
-----------------------------------------------------------------------------------------------------------------------------------------

Cumulative Wagers:             223736.59717931 BTC
Cumulative Rewards:            221791.09725092 BTC
Cumulative Fees Paid:             318.22992500 BTC
Cumulative Unreturned:              1.99700000 BTC
----
SD Profit on Completed Bets :      1625.27300339 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  1853276  :  SatoshiDice Tx: 1178231  (63.6%)
Blockchain MB:  784.7  :  SatoshiDice Tx: 479.9  (61.2%)

Note that the profit is almost up to what would be expected if the house had a 1% house edge all along:

[dooglus]

Results: 2012-Jul-07 09:05am (up to block 187978)

   Address   Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |    BTC In    |   BTC Out    |    Profit    |   RTP 
-----------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p        1      0.00002 |     6819 |      0 (0.00000) |   6559 |     260 |        25.13 |         0.01 |        25.12 |   0.076
 1dice1Qf4        2      0.00003 |      915 |      0 (0.00000) |    847 |      68 |         7.29 |         0.00 |         7.29 |   0.024
 1dice2pxm        4      0.00006 |     1439 |      0 (0.00000) |   1409 |      30 |        12.47 |         0.00 |        12.46 |   0.045
 1dice2vQo        8      0.00012 |     1196 |      0 (0.00000) |   1158 |      38 |        16.21 |         0.00 |        16.21 |   0.029
 1dice2WmR       16      0.00024 |     1388 |      0 (0.00000) |   1360 |      28 |        21.58 |         0.01 |        21.56 |   0.076
 1dice2xkj       32      0.00049 |     3166 |      1 (0.00032) |   3154 |      11 |        91.25 |       100.38 |        -9.12 | 109.995
 1dice2zdo       64      0.00098 |     4542 |      5 (0.00110) |   4520 |      17 |       178.28 |       110.74 |        67.53 |  62.119
 1dice37Ee      128      0.00195 |     5985 |     12 (0.00202) |   5926 |      47 |      1215.81 |      1142.23 |        73.57 |  93.948
 1dice3jkp      256      0.00391 |     4439 |     21 (0.00474) |   4406 |      12 |       462.85 |       331.92 |       130.92 |  71.713
 1dice4J1m      512      0.00781 |     5656 |     33 (0.00584) |   5618 |       5 |       771.31 |       331.04 |       440.26 |  42.920
 1dice5wwE     1000      0.01526 |     7191 |     96 (0.01335) |   7093 |       2 |      1441.33 |       746.95 |       694.37 |  51.824
 1dice61SN     1500      0.02289 |     5752 |    127 (0.02210) |   5619 |       6 |      2315.61 |      2549.07 |      -233.46 | 110.082
 1dice6DPt     2000      0.03052 |     5945 |    181 (0.03046) |   5761 |       3 |      1857.48 |      1740.75 |       116.72 |  93.716
 1dice6gJg     3000      0.04578 |     6055 |    297 (0.04911) |   5751 |       7 |      4203.69 |      5317.82 |     -1114.13 | 126.504
 1dice6GV5     4000      0.06104 |     5982 |    370 (0.06188) |   5609 |       3 |      1733.32 |      1571.74 |       161.58 |  90.678
 1dice6wBx     6000      0.09155 |    10248 |    958 (0.09353) |   9285 |       5 |      6565.86 |      6939.15 |      -373.28 | 105.685
 1dice6YgE     8000      0.12207 |    14375 |   1759 (0.12237) |  12616 |       0 |      3291.57 |      2847.10 |       444.47 |  86.497
 1dice7EYz    12000      0.18311 |    15133 |   2883 (0.19057) |  12245 |       5 |      6243.96 |      6529.52 |      -285.55 | 104.573
 1dice7fUk    16000      0.24414 |    37102 |   8983 (0.24216) |  28113 |       6 |      9764.16 |      9247.00 |       517.16 |  94.703
 1dice7W2A    24000      0.36621 |    25928 |   9566 (0.36939) |  16331 |      31 |     12103.49 |     12141.27 |       -37.77 | 100.312
 1dice8EMZ    32000      0.48828 |   279324 | 136015 (0.48716) | 143187 |     122 |     83123.96 |     84519.28 |     -1395.32 | 101.679
 1dice97EC    32768      0.50000 |   113221 |  56577 (0.50000) |  56578 |      66 |     40842.99 |     39642.50 |      1200.48 |  97.061
 1dice9wcM    48000      0.73242 |    68672 |  50451 (0.73505) |  18185 |      36 |     40387.04 |     38950.60 |      1436.44 |  96.443
 1dice9wVt    64000      0.97656 |     5696 |   4598 (0.97457) |    120 |     978 |      4901.49 |      4709.70 |       191.79 |  96.087
-----------------------------------------------------------------------------------------------------------------------------------------
                                 |   636169 | 272933           | 361450 |    1786 |
-----------------------------------------------------------------------------------------------------------------------------------------

Cumulative Wagers:             225807.47846859 BTC
Cumulative Rewards:            223696.39803905 BTC
Cumulative Fees Paid:             320.13880000 BTC
Cumulative Unreturned:              1.74000000 BTC
----
SD Profit on Completed Bets :      1789.20162954 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  1872304  :  SatoshiDice Tx: 1185253  (63.3%)
Blockchain MB:  792.1  :  SatoshiDice Tx: 482.9  (61.0%)

[dooglus]

Results: 2012-Jul-08 10:44am (up to block 188144)

   Address  Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP  
--------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |     6899 |      0 (0.00000) |   6638 |     261 |      25.99 |       0.01 |    15.79 |     25.97 |   0.074
 1dice1Qf4       2      0.00003 |      921 |      0 (0.00000) |    853 |      68 |       7.33 |       0.00 |     4.38 |      7.32 |   0.024
 1dice2pxm       4      0.00006 |     1449 |      0 (0.00000) |   1419 |      30 |      12.53 |       0.00 |     1.15 |     12.53 |   0.045
 1dice2vQo       8      0.00012 |     1212 |      0 (0.00000) |   1174 |      38 |      16.76 |       0.00 |     3.15 |     16.76 |   0.028
 1dice2WmR      16      0.00024 |     1396 |      0 (0.00000) |   1368 |      28 |      21.64 |       0.01 |     4.95 |     21.62 |   0.076
 1dice2xkj      32      0.00049 |     3172 |      1 (0.00032) |   3160 |      11 |      91.41 |     100.38 |     1.29 |     -8.96 | 109.804
 1dice2zdo      64      0.00098 |     4546 |      5 (0.00110) |   4524 |      17 |     178.33 |     110.74 |    55.64 |     67.58 |  62.103
 1dice37Ee     128      0.00195 |     5991 |     12 (0.00202) |   5932 |      47 |    1215.87 |    1142.23 |    39.25 |     73.64 |  93.943
 1dice3jkp     256      0.00391 |     4452 |     21 (0.00473) |   4419 |      12 |     463.24 |     331.92 |    11.11 |    131.31 |  71.653
 1dice4J1m     512      0.00781 |     5663 |     33 (0.00583) |   5625 |       5 |     771.42 |     331.04 |     9.35 |    440.37 |  42.914
 1dice5wwE    1000      0.01526 |     7264 |    100 (0.01377) |   7162 |       2 |    1446.34 |     760.87 |     1.80 |    685.47 |  52.607
 1dice61SN    1500      0.02289 |     5775 |    128 (0.02219) |   5641 |       6 |    2317.38 |    2553.29 |    15.00 |   -235.90 | 110.180
 1dice6DPt    2000      0.03052 |     6017 |    187 (0.03109) |   5827 |       3 |    1862.11 |    1748.66 |     9.24 |    113.45 |  93.907
 1dice6gJg    3000      0.04578 |     6104 |    299 (0.04904) |   5798 |       7 |    4206.99 |    5320.14 |    24.99 |  -1113.15 | 126.460
 1dice6GV5    4000      0.06104 |     6020 |    372 (0.06182) |   5645 |       3 |    1735.29 |    1574.19 |    31.20 |    161.10 |  90.716
 1dice6wBx    6000      0.09155 |    10500 |    984 (0.09376) |   9511 |       5 |    6587.95 |    6966.01 |     7.01 |   -378.06 | 105.739
 1dice6YgE    8000      0.12207 |    16923 |   2094 (0.12374) |  14829 |       0 |    3370.53 |    2994.28 |     0.00 |    376.24 |  88.837
 1dice7EYz   12000      0.18311 |    15164 |   2893 (0.19084) |  12266 |       5 |    6253.21 |    6575.03 |    14.50 |   -321.81 | 105.146
 1dice7fUk   16000      0.24414 |    37323 |   9033 (0.24206) |  28284 |       6 |    9919.56 |    9359.83 |    72.19 |    559.73 |  94.357
 1dice7W2A   24000      0.36621 |    26344 |   9720 (0.36940) |  16593 |      31 |   12143.53 |   12170.38 |   212.63 |    -26.84 | 100.221
 1dice8EMZ   32000      0.48828 |   280627 | 136684 (0.48728) | 143820 |     123 |   83830.59 |   85171.82 |  2173.21 |  -1341.23 | 101.600
 1dice97EC   32768      0.50000 |   113979 |  56965 (0.50007) |  56948 |      66 |   40978.94 |   39777.92 |   789.19 |   1201.02 |  97.069
 1dice9wcM   48000      0.73242 |    69221 |  50852 (0.73503) |  18332 |      37 |   40519.56 |   39081.22 |   442.88 |   1438.34 |  96.450
 1dice9wVt   64000      0.97656 |     5696 |   4598 (0.97457) |    120 |     978 |    4901.48 |    4709.70 |   287.60 |    191.78 |  96.087
--------------------------------------------------------------------------------------------------------------------------------------------
                                |   642658 | 274981           | 365888 |    1789 |  222878.09 |  220779.80 |  4227.58 |   2098.29 |  99.059
--------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:       2098.29516977 BTC (0.94%)
Cumulative Fees Paid:         323.39242500 BTC
SD Profit after fees:        1774.90274477 BTC (0.80%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  1895782  :  SatoshiDice Tx: 1197115  (63.1%)
Blockchain MB:  801.7  :  SatoshiDice Tx: 487.5  (60.8%)

[dooglus]

Results: 2012-Jul-09 11:18am (up to block 188313)

   Address  Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
--------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |     7091 |      0 (0.00000) |   6829 |     262 |      27.53 |       0.01 |    15.91 |     27.51 |   0.070
 1dice1Qf4       2      0.00003 |      923 |      0 (0.00000) |    854 |      69 |       7.33 |       0.00 |     5.38 |      7.33 |   0.024
 1dice2pxm       4      0.00006 |     1451 |      0 (0.00000) |   1421 |      30 |      12.54 |       0.00 |     1.15 |     12.54 |   0.045
 1dice2vQo       8      0.00012 |     1218 |      0 (0.00000) |   1180 |      38 |      16.91 |       0.00 |     3.15 |     16.90 |   0.028
 1dice2WmR      16      0.00024 |     1397 |      0 (0.00000) |   1369 |      28 |      21.65 |       0.01 |     4.95 |     21.63 |   0.076
 1dice2xkj      32      0.00049 |     3175 |      1 (0.00032) |   3163 |      11 |      91.44 |     100.38 |     1.29 |     -8.93 | 109.768
 1dice2zdo      64      0.00098 |     4552 |      5 (0.00110) |   4530 |      17 |     178.36 |     110.74 |    55.64 |     67.61 |  62.092
 1dice37Ee     128      0.00195 |     5997 |     12 (0.00202) |   5938 |      47 |    1217.43 |    1142.23 |    39.25 |     75.19 |  93.824
 1dice3jkp     256      0.00391 |     4477 |     21 (0.00470) |   4444 |      12 |     469.49 |     331.94 |    11.11 |    137.54 |  70.703
 1dice4J1m     512      0.00781 |     5668 |     33 (0.00583) |   5630 |       5 |     771.73 |     331.04 |     9.35 |    440.68 |  42.896
 1dice5wwE    1000      0.01526 |     7366 |    101 (0.01372) |   7263 |       2 |    1450.21 |     762.02 |     1.80 |    688.19 |  52.545
 1dice61SN    1500      0.02289 |     5813 |    128 (0.02204) |   5679 |       6 |    2323.46 |    2553.31 |    15.00 |   -229.84 | 109.892
 1dice6DPt    2000      0.03052 |     6023 |    187 (0.03106) |   5833 |       3 |    1863.43 |    1748.66 |     9.24 |    114.76 |  93.841
 1dice6gJg    3000      0.04578 |     6125 |    299 (0.04887) |   5819 |       7 |    4209.01 |    5320.14 |    24.99 |  -1111.13 | 126.399
 1dice6GV5    4000      0.06104 |     6202 |    390 (0.06291) |   5809 |       3 |    1794.16 |    1623.45 |    31.20 |    170.70 |  90.485
 1dice6wBx    6000      0.09155 |    10808 |   1010 (0.09349) |   9793 |       5 |    6600.32 |    6981.38 |     7.01 |   -381.06 | 105.773
 1dice6YgE    8000      0.12207 |    18189 |   2237 (0.12299) |  15952 |       0 |    3427.64 |    3040.84 |     0.00 |    386.80 |  88.715
 1dice7EYz   12000      0.18311 |    15279 |   2910 (0.19052) |  12364 |       5 |    6295.85 |    6612.47 |    14.50 |   -316.61 | 105.029
 1dice7fUk   16000      0.24414 |    37571 |   9088 (0.24193) |  28477 |       6 |   10048.75 |    9533.34 |    72.19 |    515.40 |  94.871
 1dice7W2A   24000      0.36621 |    27484 |  10137 (0.36925) |  17316 |      31 |   12330.85 |   12382.07 |   212.63 |    -51.21 | 100.415
 1dice8EMZ   32000      0.48828 |   282295 | 137505 (0.48731) | 144667 |     123 |   84284.83 |   85627.15 |  2173.21 |  -1342.32 | 101.593
 1dice97EC   32768      0.50000 |   115763 |  57860 (0.50010) |  57836 |      67 |   41394.01 |   40197.30 |   789.19 |   1196.70 |  97.109
 1dice9wcM   48000      0.73242 |    69458 |  51011 (0.73481) |  18410 |      37 |   40574.40 |   39130.62 |   442.88 |   1443.77 |  96.442
 1dice9wVt   64000      0.97656 |     5696 |   4598 (0.97457) |    120 |     978 |    4901.48 |    4709.70 |   287.60 |    191.78 |  96.087
--------------------------------------------------------------------------------------------------------------------------------------------
                                |   650021 | 277533           | 370696 |    1792 |  224312.92 |  222238.93 |  4228.71 |   2073.98 |  99.075
--------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:       2073.98498220 BTC (0.925%)
Cumulative Fees Paid:         327.08092500 BTC
SD Profit after fees:        1746.90405720 BTC (0.779%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  1921310  :  SatoshiDice Tx: 1209260  (62.9%)
Blockchain MB:  812.4  :  SatoshiDice Tx: 492.9  (60.7%)

[byronbb]

Pretty incredible to see over a million dollars wagered already.

[unk1911]

so today i was completely wiped out by the dice. i was playing the "1/8 bet" address:
lessthan 8000   1dice6YgEVBf88erBFra9BHf6ZMoyvG88    12.2070%   7.910x   3.000%   97.000%   0.0010   25.0000

after 75 consecutive losses i was wiped out, because i was placing relatively large bets. i have decided not to play this game any more. 
i must be very  unlucky or because if i'm not mistaken, the probability of getting 75 consecutive losses on a 12.20% dice  are  1/(7/8)^75 .   so basically this occurs once in every 22,356 turns, assuming a house edge of 0%.  if the house has an edge of 3%, the occurrence is slightly more frequent 1/(0.87875^75) =   once every 16,221 turns... still, i must be one unlucky bastard...

[dooglus]

so today i was completely wiped out by the dice. i was playing the "1/8 bet" address:
lessthan 8000   1dice6YgEVBf88erBFra9BHf6ZMoyvG88    12.2070%   7.910x   3.000%   97.000%   0.0010   25.0000

after 75 consecutive losses i was wiped out, because i was placing relatively large bets. i have decided not to play this game any more.  
i must be very  unlucky or because if i'm not mistaken, the probability of getting 75 consecutive losses on a 12.20% dice  are  1/(7/8)^75 .   so basically this occurs once in every 22,356 turns, assuming a house edge of 0%.  if the house has an edge of 3%, the occurrence is slightly more frequent 1/(0.87875^75) =   once every 16,221 turns... still, i must be one unlucky bastard...

The house edge is determined by the payout when you win.  The chance of winning is always the same - it picks a number between 0 and 65535 and you win if the number is less than 8000.  Your calculation is off a little because 1 - 8000/65536 isn't 7/8, it's a little more than that.

I make it a one-in-17399 chance of losing all 75 bets, so still really unlucky.  But then again 1-in-17k shots do happen.  About once every 17k bets.  And there have been over 600k bets.

 >>> 1 / ((1 - 8000/65536.0) ** 75)
  17398.822919111808

Here's the same for losing a 50/50 (less than 32768) bet 3 times in a row to sanity-check the calculation:

 >>> 1 / ((1 - 32768/65536.0) ** 3)
  8.0

and as you would expect, that's a 1-in-8 chance.

What's puzzling me is the payout for the SatoshiDice bets.  A 0% house edge would pay out 65536/8000 = 8.192x.  And so a 3% house edge should pay out 3% less than that, or 7.94624x.  So why does the SD website say it pays out 7.910x?  7.910 * 8000/65536 is 0.965576171875, ie. a house edge of 3.44%.

Not that it makes any difference to you, since you only get the payout if you win a bet...

[dooglus]

What's puzzling me is the payout for the SatoshiDice bets.  A 0% house edge would pay out 65536/8000 = 8.192x.  And so a 3% house edge should pay out 3% less than that, or 7.94624x.  So why does the SD website say it pays out 7.910x?  7.910 * 8000/65536 is 0.965576171875, ie. a house edge of 3.44%.

Here's an example of a recent 1 BTC bet winning at "lessthan 8000".

The 1 BTC bet was paid out 7.90977999 BTC, which would have been 7.91027999 before the 0.0005 BTC transaction fee was removed.

This one is a losing 1 BTC bet.  The player was returned 0.0045 BTC (0.005 BTC including the fee), or 0.5%.  So the expected return from a 1 BTC bet is:

7.91027999 * 8000/65536 + 0.005 * (65536-8000)/65536

which is very close to 0.97 BTC.

So the house edge is 3.0% if you include the amount which is returned when you lose!

I was thinking the house edge wasn't including the returned amount, because the site used to say something like "house edge 1%" and "when you lose we return half the house edge to you".  But that's changed now.