Satoshi Dice -- Statistical Analysis

[dooglus]

Variance, eh?

Nice recovery just as the month's about to end...

Total of 16 bets unaccounted for.

Results: 2013-Jan-31 11:32am (up to block 218965)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP  
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    77415 |       0 (0.00000) |   76121 |    1294 |     797.55 |       0.01 |   104.64 |    797.53 |   0.002
 1dice1Qf4       2      0.00003 |     3824 |       0 (0.00000) |    3325 |     499 |      62.95 |       0.01 |    17.04 |     62.94 |   0.020
 1dice2pxm       4      0.00006 |     6062 |       1 (0.00018) |    5640 |     421 |      88.41 |     159.97 |     8.46 |    -71.56 | 180.939
 1dice2vQo       8      0.00012 |     8660 |       3 (0.00036) |    8231 |     426 |     131.05 |     176.01 |    10.03 |    -44.95 | 134.301
 1dice2WmR      16      0.00024 |    10544 |       1 (0.00010) |   10131 |     412 |     313.59 |       4.56 |    18.66 |    309.02 |   1.456
 1dice2xkj      32      0.00049 |    11712 |       3 (0.00027) |   11315 |     394 |     626.52 |     303.62 |     1.36 |    322.89 |  48.463
 1dice2zdo      64      0.00098 |    14508 |      14 (0.00099) |   14072 |     422 |     920.39 |     230.74 |    55.73 |    689.64 |  25.071
 1dice37Ee     128      0.00195 |    16543 |      32 (0.00199) |   16079 |     432 |    1983.06 |    1416.66 |    48.32 |    566.39 |  71.438
 1dice3jkp     256      0.00391 |    18259 |      83 (0.00464) |   17798 |     378 |    2275.21 |    3651.88 |    13.17 |  -1376.67 | 160.507
 1dice4J1m     512      0.00781 |    27139 |     204 (0.00771) |   26251 |     684 |    4465.82 |    4158.96 |     9.98 |    306.86 |  93.129
 1dice5wwE    1000      0.01526 |    87191 |    1331 (0.01534) |   85411 |     449 |   23186.31 |   19657.87 |     1.95 |   3528.43 |  84.782
 1dice61SN    1500      0.02289 |    20409 |     476 (0.02373) |   19582 |     351 |    6534.61 |    6608.00 |    15.07 |    -73.39 | 101.123
 1dice6DPt    2000      0.03052 |    51950 |    1595 (0.03093) |   49969 |     386 |   25838.70 |   23126.99 |     9.32 |   2711.71 |  89.505
 1dice6gJg    3000      0.04578 |    23709 |    1080 (0.04637) |   22211 |     418 |    8622.55 |    9770.89 |    25.11 |  -1148.34 | 113.318
 1dice6GV5    4000      0.06104 |    29342 |    1778 (0.06137) |   27193 |     371 |    6679.21 |    6308.35 |    31.29 |    370.86 |  94.448
 1dice6wBx    6000      0.09155 |    36526 |    3389 (0.09381) |   32738 |     399 |   14199.04 |   15917.82 |     7.15 |  -1718.77 | 112.105
 1dice6YgE    8000      0.12207 |   146457 |   17982 (0.12316) |  128021 |     454 |   72635.57 |   72942.95 |   100.24 |   -307.37 | 100.423
 1dice7EYz   12000      0.18311 |    60200 |   11009 (0.18424) |   48744 |     447 |  145406.48 |  148966.51 |  3314.67 |  -3560.02 | 102.448
 1dice7fUk   16000      0.24414 |   179703 |   43694 (0.24380) |  135529 |     480 |  332317.06 |  319177.29 |  2056.09 |  13139.76 |  96.046
 1dice7W2A   24000      0.36621 |   176502 |   64752 (0.36795) |  111229 |     521 |  529202.23 |  525722.60 |  1012.97 |   3479.63 |  99.342
 1dice8EMZ   32000      0.48828 |   929539 |  453083 (0.48817) |  475035 |    1421 |  752558.98 |  735657.23 |  2924.16 |  16901.75 |  97.754
 1dice97EC   32768      0.50000 |   425912 |  212260 (0.49940) |  212771 |     881 |  573438.12 |  561459.76 |  5720.41 |  11978.35 |  97.911
 1dice9wcM   48000      0.73242 |   271951 |  199617 (0.73547) |   71799 |     535 |  263250.74 |  257470.07 |  5454.88 |   5780.67 |  97.804
 1dicec9k7   52000      0.79346 |    54270 |   42741 (0.79385) |   11099 |     430 |   55397.36 |   54229.66 |  1187.20 |   1167.70 |  97.892
 1dicegEAr   56000      0.85449 |    40270 |   34073 (0.85619) |    5723 |     474 |   60871.21 |   60349.67 |   400.24 |    521.53 |  99.143
 1diceDCd2   60000      0.91553 |    54469 |   49474 (0.91585) |    4546 |     449 |   56721.75 |   56317.52 |     0.22 |    404.22 |  99.287
 1dice9wVt   64000      0.97656 |    13169 |   12152 (0.98063) |     240 |     777 |   22471.60 |   22076.80 |   239.70 |    394.79 |  98.243
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  2698994 | 1104976           | 1579702 |   14316 |  617222.65 |  604210.49 |   225.48 |  13012.15 |  97.892
            big (bets >= 4 BTC) |    97241 |   45851           |   51101 |     289 | 2343773.53 | 2301652.04 | 22562.70 |  42121.49 |  98.203
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  2796235 | 1150827           | 1630803 |   14605 | 2960996.19 | 2905862.54 | 22788.19 |  55133.64 |  98.138
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      55133.64999467 BTC (1.862%)
Cumulative Fees Paid:        1994.43637500 BTC
SD Profit after fees:       53139.21361967 BTC (1.795%)
Pending Liabilities:           -0.45667668 BTC
Final SD Profit:            53139.67029635 BTC (1.795%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  9101422  :  SatoshiDice Tx:  5147181  (56.6%)
Blockchain MB:   3885.0  :  SatoshiDice MB:   2113.9  (54.4%)

[1714065317]

1714065317

[dooglus]

Here's a summary of the recent big bets.  I wanted to see how s.dice made its money back.  The first line says "there were 17 winning bets of 10 BTC on lessthan 12000 and 125 losing bets with the same stake and target, making a net loss (for the player) for 506 BTC":

              wins                                                           losses
-------------------------------------------------  --------------------------------------------
count target  stake     profit      total profit   count target  stake    profit   total profit        net profit
-------------------------------------------------  --------------------------------------------     --------------
   17 <12000     10     43.35211333  736.98592661    125 <12000     10     -9.9505 -1243.8125        -506.82657339
    2 <12000     20     86.70472666  173.40945332      8 <12000     20    -19.9005  -159.204           14.20545332

   32 <16000     10     30.02646000  960.84672        77 <16000     10     -9.9505  -766.1885         194.65822
   14 <16000     50    150.13430000 2101.8802         30 <16000     50    -49.7505 -1492.515          609.3652

   18 <24000    100    167.01256666 3006.22619988     39 <24000    100    -99.5005 -3880.5195        -874.29330012
   19 <24000    150    250.51910000 4759.8629         52 <24000    150   -149.2505 -7761.026        -3001.1631
    2 <24000    200    334.02563333  668.05126666      6 <24000    200   -199.0005 -1194.003         -525.95173334
    2 <24000    250    417.53216666  835.06433332     19 <24000    250   -248.7505 -4726.2595       -3891.19516668

   84 <32000    100    100.38430000 8432.2812         72 <32000    100    -99.5005 -7164.036         1268.2452
   74 <32768    100     95.69950000 7081.763          82 <32768    100    -99.5005 -8159.041        -1077.278
-------------------------------------------------  --------------------------------------------     --------------
                                   28756.37119979                      -36546.605                   -7790.23380021
-------------------------------------------------  --------------------------------------------     --------------

The majority of the losses were on the lessthan 24000 bets.  Here are graphs of the probabilities of the number of wins for 3 cases.  In all 3 cases the actual number of wins is pretty far left on the graph:

stake 150 BTC, target <24000,  71 bets, 19 wins,  52 losses:



stake 250 BTC, target <24000,  21 bets,  2 wins,  19 losses:



stake (all 4 stakes), target <24000, 157 bets, 41 wins, 116 losses:



Incidentally, how's the font look in the table inside the 'quote' above?  It's much easier to read than the one I usually use, but does it show up well for you too?

[ingrownpocket]

Thanks for the graphs dooglus.

The guy really had a run of bad luck there  


BTW, both fonts:

New: asdsadasdad23101010 ... ?!"#%#$

Old: asdsadasdad23101010 ... ?!"#%#$

I prefer the old one. Not that there is much difference.

[m_yaw]

can anyone make an educated guess about s.dice's profits this month (if any)?

[ingrownpocket]

can anyone make an educated guess about s.dice's profits this month (if any)?

December 31, 2012
Final SD Profit:            33274.25422617 BTC (1.879%)

January 01, 2013
Final SD Profit:            43115.08527065 BTC (2.342%)

Today
Final SD Profit:            53139.67029635 BTC (1.795%)

[Kryptox]

Thank you dooglus for explaining this so clearly!  I didn't realize SD allows you to split a single transaction into multiple bets now.  From what I understand, there was an update to the Bitcoin network not too long ago that doesn't actually allow you to use the exact same transaction ID twice.

It's not splitting a transaction into multiple transactions.  It's putting multiple bets into a single transaction.  If you're using the reference (satoshi) client, go to the 'send coins' tab and then click 'add recipient' a few times. That way you can send bets to many different satoshidice addresses in a single transaction.  You can't send multiple bets to the same address using the standard client, but apparently can with some of the other clients.

Right, I realized this shortly after my response.  I don't actually play SD - I think I've maybe placed 2 or 3 minimum bets in the past but I'm finding the math behind it quite interesting, along with how they are relying on a hash to spit out a lucky number.  I suppose it's probably the best way to make the game provable for now.

I just happened to come across some of your posts on stackexchange.  Really enjoy reading your posts.

I read an interesting article regarding sha256 statistical patterns by Femtosecond, as well as a few other authors.  From what I gathered, SD could actually create an even larger edge for themselves by being selective in the hashes they decide to use.  Conversely, players could also be selective in choosing the transaction ID's they decide to actually submit to give themselves the edge, including possibly sending transactions ID's that hash out identically to previously calculated hashes.  That's my understanding anyway, and I'm not sure how that applies to hmac sha512 but I'd guess it would be similar.

I might just start playing SD!

[m_yaw]

"if any": in the latest chart the black line hasn't caught up to the red line yet.

I always thought the 50.000 number is all-time profit not this month's profit.

[ingrownpocket]

I always thought the 50.000 number is all-time profit not this month's profit.

You were right, the 'Final SD Profit' is the all-time profit.

[FTWbitcoinFTW]

can anyone make an educated guess about s.dice's profits this month (if any)?

About 20K BTC

[dooglus]

I prefer the old one. Not that there is much difference.

I was talking about the difference between these two:

New: asdsadasdad23101010 ... ?!"#%#$

Old: asdsadasdad23101010 ... ?!"#%#$

For me, the first one is much clearer.  The 2nd looks kind of grey, not black.  Here's a screenshot of how they look to me:

[dooglus]

"if any": in the latest chart the black line hasn't caught up to the red line yet.

The red line is the expected profit, based on the bet volume so far.  The black line is the actual profit.  As you say, the black line didn't catch the red line yet, but that just means the overall profit isn't quite 1.9% of turnover (it's 1.86% of turnover).  So the site is performing a little worse than expected, but it's still doing amazingly well, and making huge profits.

(Note, the house edge hasn't always been 1.9%; it has changed a couple of times in the past.  And also note that the red line is the expected profit after transaction fees are taken into account, so a little less than 1.9% of turnover).

[ingrownpocket]

[2112]

http://imageshack.us/photo/my-images/825/snaph.png/

Lets see if my reply with imageshack link works. Well, it appears to be working for now. Both fonts are quite readable on my end. The forum software prepends some proxy by anonymouse; but when I save and compare the images they are identical.

[dooglus]

http://imageshack.us/photo/my-images/825/snaph.png/

Lets see if my reply with imageshack link works. Well, it appears to be working for now. Both fonts are quite readable on my end. The forum software prepends some proxy by anonymouse; but when I save and compare the images they are identical.

Thanks for that.

[dooglus]

Two things:

1) The black line very nearly caught the red line.

2) I never noticed before how the graph sometimes goes back in time, due to the way that some blocks have an older timestamp than the preceding block.

[dserrano5]

New: asdsadasdad23101010 ... ?!"#%#$

Old: asdsadasdad23101010 ... ?!"#%#$

For me, the first one is much clearer.  The 2nd looks kind of grey, not black.

Same here. First one has way more contrast.

[Herbert]

2) I never noticed before how the graph sometimes goes back in time, due to the way that some blocks have an older timestamp than the preceding block.

This looks funny.

[smickles]

<snip>

Incidentally, how's the font look in the table inside the 'quote' above?  It's much easier to read than the one I usually use, but does it show up well for you too?

It comes out as 'Source Code Pro' for me, so it looks like the best font out there

[dooglus]

Total of 31 bets unaccounted for.

Results: 2013-Feb-01 12:33pm (up to block 219132)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP  
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    77686 |       0 (0.00000) |   76382 |    1304 |     801.28 |       0.01 |   105.50 |    801.26 |   0.002
 1dice1Qf4       2      0.00003 |     3837 |       0 (0.00000) |    3337 |     500 |      63.41 |       0.01 |    17.22 |     63.39 |   0.020
 1dice2pxm       4      0.00006 |     6081 |       1 (0.00018) |    5658 |     422 |      89.79 |     159.98 |     8.46 |    -70.18 | 178.167
 1dice2vQo       8      0.00012 |     8680 |       3 (0.00036) |    8251 |     426 |     132.41 |     176.01 |    10.03 |    -43.60 | 132.927
 1dice2WmR      16      0.00024 |    10611 |       1 (0.00010) |   10196 |     414 |     315.98 |       4.56 |    20.03 |    311.41 |   1.445
 1dice2xkj      32      0.00049 |    12030 |       4 (0.00034) |   11632 |     394 |     641.94 |     383.59 |     1.36 |    258.35 |  59.755
 1dice2zdo      64      0.00098 |    15025 |      14 (0.00096) |   14586 |     425 |     948.20 |     230.75 |    55.73 |    717.45 |  24.336
 1dice37Ee     128      0.00195 |    16716 |      32 (0.00197) |   16252 |     432 |    2001.85 |    1416.70 |    48.32 |    585.14 |  70.770
 1dice3jkp     256      0.00391 |    18503 |      84 (0.00463) |   18041 |     378 |    2305.66 |    3683.16 |    13.17 |  -1377.49 | 159.744
 1dice4J1m     512      0.00781 |    27301 |     206 (0.00774) |   26411 |     684 |    4491.67 |    4210.26 |     9.98 |    281.40 |  93.735
 1dice5wwE    1000      0.01526 |    87951 |    1353 (0.01546) |   86145 |     453 |   23263.64 |   19774.85 |     1.95 |   3488.78 |  85.003
 1dice61SN    1500      0.02289 |    20552 |     480 (0.02376) |   19721 |     351 |    6566.44 |    6619.64 |    15.07 |    -53.20 | 100.810
 1dice6DPt    2000      0.03052 |    52654 |    1621 (0.03101) |   50647 |     386 |   25912.96 |   23376.42 |     9.32 |   2536.53 |  90.211
 1dice6gJg    3000      0.04578 |    23733 |    1081 (0.04637) |   22234 |     418 |    8648.93 |    9898.95 |    25.11 |  -1250.01 | 114.453
 1dice6GV5    4000      0.06104 |    29368 |    1781 (0.06142) |   27215 |     372 |    6723.72 |    6385.15 |    31.29 |    338.56 |  94.965
 1dice6wBx    6000      0.09155 |    36697 |    3407 (0.09387) |   32889 |     401 |   14238.54 |   15933.48 |     7.16 |  -1694.93 | 111.904
 1dice6YgE    8000      0.12207 |   150188 |   18489 (0.12348) |  131245 |     454 |   72932.01 |   73228.80 |   100.24 |   -296.78 | 100.407
 1dice7EYz   12000      0.18311 |    60682 |   11109 (0.18444) |   49122 |     451 |  145717.37 |  149202.78 |  3314.67 |  -3485.40 | 102.392
 1dice7fUk   16000      0.24414 |   180562 |   43902 (0.24379) |  136179 |     481 |  332925.52 |  319549.93 |  2056.10 |  13375.59 |  95.982
 1dice7W2A   24000      0.36621 |   178590 |   65516 (0.36793) |  112552 |     522 |  532287.03 |  528557.90 |  1012.97 |   3729.13 |  99.299
 1dice8EMZ   32000      0.48828 |   933519 |  454985 (0.48813) |  477110 |    1424 |  756264.91 |  739164.60 |  2924.17 |  17100.30 |  97.739
 1dice97EC   32768      0.50000 |   430481 |  214555 (0.49943) |  215045 |     881 |  577639.13 |  565285.22 |  5720.41 |  12353.91 |  97.861
 1dice9wcM   48000      0.73242 |   273491 |  200745 (0.73545) |   72210 |     536 |  263973.73 |  258206.22 |  5454.88 |   5767.51 |  97.815
 1dicec9k7   52000      0.79346 |    54840 |   43202 (0.79402) |   11207 |     431 |   55597.01 |   54391.49 |  1187.21 |   1205.52 |  97.832
 1dicegEAr   56000      0.85449 |    40507 |   34282 (0.85634) |    5751 |     474 |   63313.52 |   62853.37 |   400.24 |    460.14 |  99.273
 1diceDCd2   60000      0.91553 |    55066 |   50016 (0.91579) |    4599 |     451 |   57196.81 |   56789.54 |     0.22 |    407.26 |  99.288
 1dice9wVt   64000      0.97656 |    13215 |   12194 (0.98054) |     242 |     779 |   22516.74 |   22121.09 |   239.71 |    395.64 |  98.243
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  2720881 | 1112988           | 1593538 |   14355 |  621011.82 |  608073.42 |   227.95 |  12938.40 |  97.917
            big (bets >= 4 BTC) |    97685 |   46075           |   51321 |     289 | 2356498.53 | 2313531.16 | 22562.70 |  42967.36 |  98.177
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  2818566 | 1159063           | 1644859 |   14644 | 2977510.35 | 2921604.58 | 22790.65 |  55905.76 |  98.122
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      55905.76815102 BTC (1.878%)
Cumulative Fees Paid:        2016.81227500 BTC
SD Profit after fees:       53888.95587602 BTC (1.810%)
Pending Liabilities:          412.22806110 BTC
Final SD Profit:            53476.72781492 BTC (1.796%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  9164276  :  SatoshiDice Tx:  5187972  (56.6%)
Blockchain MB:   3911.8  :  SatoshiDice MB:   2130.4  (54.5%)

[Bowjob]

Looks like we spooked the whale!