Satoshi Dice -- Statistical Analysis

[Dabs]

Hi,

I got the latest numbers from dooglus post and tried the theoretical formula for consecutive losses in a row and came up with this.

bets     p-win   q-lose  loss-row
604294   0.5     0.5     18.20489587
1118230  0.48828 0.51172 19.71766168
244037   0.36621 0.63379 24.99911792
243386   0.24414 0.75586 39.27274907
94075    0.18311 0.81689 48.22841691
182495   0.12207 0.87793 76.89902593

So, those playing the 50% game can expect to lose 18 or 19 times in a row if they played that game since the beginning. Those playing the other games can expect to lose much more.

1. Let total number of times you want to make a bet on this game = "bets".
2. p is probability of winning the game you're playing, q is the probability of losing the same game, q = 1 - p
3. Then expected losses in a row = -log(bets*p + 1)/log(q)

Did I do this correctly?

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[organofcorti]

Hi,

I got the latest numbers from dooglus post and tried the theoretical formula for consecutive losses in a row and came up with this.

bets     p-win   q-lose  loss-row
604294   0.5     0.5     18.20489587
1118230  0.48828 0.51172 19.71766168
244037   0.36621 0.63379 24.99911792
243386   0.24414 0.75586 39.27274907
94075    0.18311 0.81689 48.22841691
182495   0.12207 0.87793 76.89902593

So, those playing the 50% game can expect to lose 18 or 19 times in a row if they played that game since the beginning. Those playing the other games can expect to lose much more.

1. Let total number of times you want to make a bet on this game = "bets".
2. p is probability of winning the game you're playing, q is the probability of losing the same game, q = 1 - p
3. Then expected losses in a row = -log(bets*p + 1)/log(q)

Did I do this correctly?

It looks fine, as long as you have the win/lose probabilities right.

You can also calculate the expected number of rolls before n losses in a row:

Code:

n = -log(bets*p + 1)/log(q)

n = expected losses in a row
bets = number of bets
p = probability of winning the game
q = 1 - p

So
-n*log(q) = log(bets*p + 1)
(1/q)^n = bets*p + 1 

Expected number of bets before n losses in a row = (q^(-n) - 1) / p

I've seen a few methods of proving this. The one I have to hand uses Markov chains and is a bit dense, and I can't find the other which is more inuitive to follow. If I find it I'll post it.

[dooglus]

I started producing a list of all the bets to find the longest winning and losing chains and found a problem:

SatoshiDice has at times in the past run low on confirmed funds in their hot wallet.  When this happens, they can easily pay out losing bets (since all they need to do that is the incoming bet itself), but they have to wait before they can pay out winning bets.  This results in large groups of consecutive bets with the same result.

I've only looked through a fraction of the bets and already found a chain of 319 losing "lessthan 32000" bets in a row, and also a chain of 287 winning "lessthan 32000" bets in a row.

This makes me think it's not worth continuing with this analysis, since it doesn't tell us anything other than that SatoshiDice sometimes bunches winning bets together.

Here's the progress so far.  In less than 400k bets I see all these chains:

$ awk '{print $3, $1}' allbets.txt | grep '^32000 ' | wc -l
389412

$ awk '{print $3, $1}' allbets.txt | grep '^32000 ' | uniq -c | sort -n | tail
    131 32000 W
    133 32000 W
    135 32000 W
    135 32000 W
    140 32000 W
    150 32000 W
    189 32000 W
    208 32000 W
    287 32000 W
    319 32000 L

[dooglus]

Total of 227 bets unaccounted for.

Results: 2013-Mar-14 03:27pm (up to block 225887)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |   100167 |       1 (0.00001) |   98586 |    1580 |    1164.40 |    1280.30 |   125.77 |   -115.90 | 109.954
 1dice1Qf4       2      0.00003 |     5218 |       0 (0.00000) |    4694 |     524 |      89.26 |       0.03 |    20.46 |     89.22 |   0.040
 1dice2pxm       4      0.00006 |     7672 |       1 (0.00014) |    7218 |     453 |     117.00 |     160.00 |    12.83 |    -43.00 | 136.758
 1dice2vQo       8      0.00012 |    12006 |       5 (0.00043) |   11536 |     465 |     225.43 |     431.98 |    10.08 |   -206.54 | 191.624
 1dice2WmR      16      0.00024 |    13691 |       1 (0.00008) |   13248 |     442 |     460.58 |       4.88 |    22.07 |    455.70 |   1.060
 1dice2xkj      32      0.00049 |    17634 |       6 (0.00035) |   17226 |     402 |     962.00 |     814.01 |     1.39 |    147.98 |  84.617
 1dice2zdo      64      0.00098 |    18908 |      20 (0.00108) |   18422 |     466 |    1381.03 |     573.04 |    55.81 |    807.99 |  41.494
 1dice37Ee     128      0.00195 |    19607 |      37 (0.00193) |   19112 |     458 |    2343.60 |    1557.71 |    48.39 |    785.89 |  66.467
 1dice3jkp     256      0.00391 |    24288 |     105 (0.00439) |   23798 |     385 |    4586.66 |    7357.31 |    13.20 |  -2770.64 | 160.407
 1dice4J1m     512      0.00781 |    33476 |     269 (0.00821) |   32506 |     701 |    5734.43 |    5676.18 |    10.04 |     58.24 |  98.984
 1dice5wwE    1000      0.01526 |   118489 |    1801 (0.01527) |  116165 |     523 |   36649.77 |   32115.98 |     2.07 |   4533.78 |  87.629
 1dice61SN    1500      0.02289 |    24604 |     570 (0.02351) |   23677 |     357 |    7659.72 |    8165.59 |    15.09 |   -505.86 | 106.604
 1dice6DPt    2000      0.03052 |    74504 |    2311 (0.03119) |   71795 |     398 |   37574.70 |   33693.51 |     9.37 |   3881.19 |  89.671
 1dice6gJg    3000      0.04578 |    28785 |    1312 (0.04628) |   27035 |     438 |    9268.01 |   10070.52 |    25.18 |   -802.50 | 108.659
 1dice6GV5    4000      0.06104 |    34724 |    2114 (0.06158) |   32218 |     392 |    7635.27 |    7429.59 |    31.35 |    205.68 |  97.306
 1dice6wBx    6000      0.09155 |    47311 |    4319 (0.09217) |   42542 |     450 |   16033.68 |   17762.94 |     7.31 |  -1729.25 | 110.785
 1dice6YgE    8000      0.12207 |   183640 |   22484 (0.12278) |  160646 |     510 |   91504.63 |   90361.03 |   100.47 |   1143.59 |  98.750
 1dice7EYz   12000      0.18311 |    94811 |   17289 (0.18340) |   76982 |     540 |  170640.56 |  172583.80 |  3314.90 |  -1943.23 | 101.139
 1dice7fUk   16000      0.24414 |   245006 |   59640 (0.24399) |  184801 |     565 |  366310.41 |  352426.39 |  2322.45 |  13884.01 |  96.210
 1dice7W2A   24000      0.36621 |   245693 |   90200 (0.36801) |  154900 |     593 |  583327.49 |  575041.86 |  1013.25 |   8285.62 |  98.580
 1dice8EMZ   32000      0.48828 |  1123259 |  547402 (0.48805) |  574205 |    1652 |  875003.41 |  857356.03 |  2924.98 |  17647.37 |  97.983
 1dice97EC   32768      0.50000 |   607685 |  303087 (0.49969) |  303458 |    1140 |  661647.32 |  645713.90 |  6521.25 |  15933.42 |  97.592
 1dice9wcM   48000      0.73242 |   342207 |  251049 (0.73498) |   90523 |     635 |  299745.67 |  292221.84 |  5455.28 |   7523.82 |  97.490
 1dicec9k7   52000      0.79346 |    75205 |   59307 (0.79408) |   15379 |     519 |   61646.26 |   60365.25 |  1187.57 |   1281.00 |  97.922
 1dicegEAr   56000      0.85449 |    63499 |   53911 (0.85676) |    9013 |     575 |   77787.59 |   77163.64 |   400.55 |    623.94 |  99.198
 1diceDCd2   60000      0.91553 |    98251 |   89515 (0.91626) |    8181 |     555 |   71019.90 |   70220.86 |     0.52 |    799.04 |  98.875
 1dice9wVt   64000      0.97656 |    16795 |   15364 (0.97960) |     320 |    1111 |   24062.03 |   23648.80 |   240.21 |    413.22 |  98.283
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  3562285 | 1469540           | 2076208 |   16537 |  772753.11 |  758256.04 |   263.26 |  14497.07 |  98.124
            big (bets >= 4 BTC) |   114850 |   52580           |   61978 |     292 | 2641827.81 | 2585941.06 | 23628.70 |  55886.75 |  97.885
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  3677135 | 1522120           | 2138186 |   16829 | 3414580.93 | 3344197.10 | 23891.96 |  70383.82 |  97.939
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      70383.82618517 BTC (2.061%)
Cumulative Fees Paid:        2878.06757500 BTC
SD Profit after fees:       67505.75861017 BTC (1.977%)
Pending Liabilities:           82.72401753 BTC
Final SD Profit:            67423.03459264 BTC (1.975%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 11540074  :  SatoshiDice Tx:  6771690  (58.7%)
Blockchain MB:   4956.9  :  SatoshiDice MB:   2783.8  (56.2%)

[Dabs]

Can I ask what shows up if you type the following?

$ awk '{print $3, $1}' allbets.txt | grep '^32000 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^32768 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^48000 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^52000 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^56000 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^60000 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^64000 ' | uniq -c | sort -n | tail

[dooglus]

Can I ask what shows up if you type the following?

$ awk '{print $3, $1}' allbets.txt | grep '^32000 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^32768 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^48000 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^52000 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^56000 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^60000 ' | uniq -c | sort -n | tail
$ awk '{print $3, $1}' allbets.txt | grep '^64000 ' | uniq -c | sort -n | tail

awk: cannot open allbets.txt (No such file or directory)

I'm regenerating the list such that I can sort it into the order that the bets were placed rather than payout order.  That should give better numbers I think.  It will take a few hours though.

Edit: the list of bets I'm generating has the block number and transaction number within the block, so I can sort it once it's done.  I just checked a few early entries to make sure the bets were being listed right, and it showed me:

32000 5020 L 178122-8 0.04
24000 5019 L 178122-8 0.04
12000 5018 L 178122-8 0.04

ie. the 8th transaction (counting from 0) in block 178122 contains 3 bets of 0.04 BTC.  I checked this against blockchain.info (http://blockchain.info/block-index/215305/0000000000000583451e3795919b1afbc6c6b96a0da71773015999a70da6aeb7) but found that these 3 bets were in the 9th transaction, and that there were bets in the 3rd transaction which show up in my list as being the 37th transaction.  So I was worried my code is listing the transactions in the wrong order.

It turns out though that my code lists the transactions in the same order as blockexplorer (http://blockexplorer.com/block/0000000000000583451e3795919b1afbc6c6b96a0da71773015999a70da6aeb7) so it's blockchain.info that's listing the transactions in an apparently random order.

It's only got as far as last October so far, but already found sequences of 30 and 26 wins in a row at lessthan 32768, and 23 losses in a row too:

$ grep '^32768 ' allbets.txt | sort -k2n | awk '{print $3}' | uniq -c | sort -n | tail -3
     23 L
     26 W
     30 W

Edit2: It's up to December 28th now, and I've improved the code that finds the longest sequences so it tells you which block and transaction number each sequence starts and ends at:

lessthan     1      0 wins (None        to None       )      0 losses (None        to None       )
lessthan     2      0 wins (None        to None       )      0 losses (None        to None       )
lessthan     4      1 wins (213426-111  to 213426-111 )   4293 losses (177365-68   to 213425-123 )
lessthan     8      1 wins (191198-55   to 191198-55  )   1676 losses (191205-145  to 202814-661 )
lessthan    16      1 wins (191139-261  to 191139-261 )   1582 losses (176832-53   to 191139-252 )
lessthan    32      1 wins (184331-26   to 184331-26  )   3363 losses (184331-33   to 191139-252 )
lessthan    64      1 wins (184331-26   to 184331-26  )   4209 losses (191139-273  to 209097-247 )
lessthan   128      1 wins (184218-167  to 184218-167 )   3165 losses (194000-15   to 206389-210 )
lessthan   256      2 wins (208181-71   to 208181-71  )   1297 losses (210373-648  to 214001-353 )
lessthan   512      1 wins (177492-65   to 177492-65  )    564 losses (206416-327  to 207020-196 )
lessthan  1000      2 wins (180131-98   to 180136-87  )    388 losses (185647-135  to 186200-55  )
lessthan  1500      2 wins (180806-572  to 180806-574 )    221 losses (186994-57   to 187443-156 )
lessthan  2000      3 wins (190605-433  to 190605-479 )    280 losses (192015-159  to 192877-145 )
lessthan  3000      3 wins (190605-433  to 190605-479 )    274 losses (196923-121  to 197196-178 )
lessthan  4000      3 wins (187645-74   to 187668-17  )    123 losses (191201-362  to 191339-143 )
lessthan  6000     25 wins (205973-153  to 205973-153 )     86 losses (187233-224  to 187273-126 )
lessthan  8000     21 wins (212274-43   to 212274-113 )     91 losses (197734-53   to 197745-364 )
lessthan 12000     12 wins (208332-49   to 208332-313 )     73 losses (208332-469  to 208335-22  )
lessthan 16000     18 wins (203664-170  to 203664-179 )     39 losses (204260-155  to 204260-306 )
lessthan 24000     14 wins (213616-75   to 213616-1053)     22 losses (201314-281  to 201319-67  )
lessthan 32000     34 wins (184344-956  to 184345-16  )     65 losses (184391-665  to 184391-739 )
lessthan 32768     30 wins (180866-367  to 180868-167 )     24 losses (213052-220  to 213052-475 )
lessthan 48000     68 wins (182535-247  to 182536-268 )     17 losses (189347-98   to 189347-126 )
lessthan 52000     59 wins (202481-127  to 202567-150 )     13 losses (209193-229  to 209193-229 )
lessthan 56000     56 wins (193592-338  to 193614-452 )     14 losses (209941-317  to 209945-15  )
lessthan 60000    158 wins (208494-103  to 208532-864 )     21 losses (208647-415  to 208647-458 )
lessthan 64000    439 wins (180744-103  to 181691-101 )      2 losses (177069-43   to 177087-37  )

That looks like a genuine run of 30 wins on lessthan 32768.  Isn't that incredibly unlikely?  Like a 1-in-a-billion chance?

Edit3: I see a problem.  It used to be that all the bets in a single transaction would get the same lucky number.  It's also possible to bet on the same address multiple times in a single transaction.  That means you can win the same bet twice in a single transaction, and I'm counting that as 2 in a row.  See the 'lessthan 256' above - it says "2 wins (208181-71   to 208181-71)".  That's because he bet on lessthan 256 twice in the same transaction, and both bets got the same lucky number:
  http://blockchain.info/tx-index/33164014/9
  http://blockchain.info/tx-index/33164014/19
or see lines 3 and 8 here.

OK, so it's finished making the list, and I've changed the script to ignore multiple bets in a single transaction in blocks earlier than block 213879 (when the rule changed).  Here's a list of the current losest winning and losing streaks per bet:

lessthan     1       1 wins (222877-119  to 222877-119 )   85965 losses (176831-34   to 222877-118 )
lessthan     2       0 wins (None        to None       )       0 losses (None        to None       )
lessthan     4       1 wins (213426-111  to 213426-111 )    4259 losses (177365-68   to 213425-123 )
lessthan     8       1 wins (191198-55   to 191198-55  )    4946 losses (202814-664  to 217110-578 )
lessthan    16       1 wins (191139-261  to 191139-261 )    1581 losses (176832-53   to 191139-252 )
lessthan    32       1 wins (184331-26   to 184331-26  )    6360 losses (196254-318  to 219048-260 )
lessthan    64       1 wins (184331-26   to 184331-26  )    4204 losses (191139-273  to 209097-247 )
lessthan   128       1 wins (184218-167  to 184218-167 )    3158 losses (194000-15   to 206389-210 )
lessthan   256       1 wins (179750-57   to 179750-57  )    1289 losses (210373-648  to 214001-353 )
lessthan   512       1 wins (177492-65   to 177492-65  )     564 losses (206416-327  to 207020-196 )
lessthan  1000       2 wins (180131-98   to 180136-87  )     566 losses (214383-45   to 214430-239 )
lessthan  1500       2 wins (180806-572  to 180806-574 )     303 losses (222782-200  to 222904-322 )
lessthan  2000       3 wins (190605-433  to 190605-479 )     280 losses (192015-159  to 192877-145 )
lessthan  3000       3 wins (190605-433  to 190605-479 )     274 losses (196923-121  to 197196-178 )
lessthan  4000       3 wins (187645-74   to 187668-17  )     123 losses (191201-362  to 191339-143 )
lessthan  6000       4 wins (199484-177  to 199512-23  )      96 losses (221597-329  to 221986-337 )
lessthan  8000       9 wins (192997-182  to 192997-232 )      91 losses (197734-53   to 197745-364 )
lessthan 12000      12 wins (208332-49   to 208332-313 )      73 losses (208332-469  to 208335-22  )
lessthan 16000       9 wins (184483-183  to 184483-294 )      42 losses (219440-228  to 219440-350 )
lessthan 24000      14 wins (213616-75   to 213616-1053)      22 losses (201314-281  to 201319-67  )
lessthan 32000      34 wins (184344-956  to 184345-16  )      65 losses (184391-665  to 184391-739 )
lessthan 32768      30 wins (180866-367  to 180868-167 )      26 losses (216081-852  to 216081-901 )
lessthan 48000      68 wins (182535-247  to 182536-268 )      17 losses (189347-98   to 189347-126 )
lessthan 52000      59 wins (202481-127  to 202567-150 )       9 losses (213719-227  to 213720-86  )
lessthan 56000      60 wins (224067-454  to 224072-192 )       5 losses (196994-197  to 197000-76  )
lessthan 60000     146 wins (213472-454  to 213513-36  )       4 losses (210367-580  to 210367-590 )
lessthan 64000     439 wins (180744-103  to 181691-101 )       2 losses (177069-43   to 177087-37  )

So the 30 wins in a row on lessthan 32768 was real.  Even more incredible is the run of 34 wins on the slightly harder lessthan 32000 game.

Edit76: I just noticed "65 losses (184391-665  to 184391-739" on the "lessthan 32000" game.  That's a huge number of losses in a row.  They're all in the same block, too.

Here's the list of them:

betnum R  block-tx# amount
------ -  --------- ------
383948 W 184391-663 1000000

383949 L 184391-665 7812500
383950 L 184391-666 1000000
383951 L 184391-667 3000000
383952 L 184391-668 1000000
383953 L 184391-669 3000000
383954 L 184391-670 15625000
383955 L 184391-672 15625000
383956 L 184391-674 3906250
383957 L 184391-675 3906250
383958 L 184391-676 3906250
383959 L 184391-677 3906250
383960 L 184391-679 3906250
383961 L 184391-680 15625000
383963 L 184391-683 7812500
383964 L 184391-684 1000000
383965 L 184391-685 1953125
383966 L 184391-686 1953125
383967 L 184391-687 1953125
383968 L 184391-688 1953125
383969 L 184391-689 1953125
383970 L 184391-690 1953125
383971 L 184391-691 1953125
383972 L 184391-692 1953125
383973 L 184391-693 1953125
383974 L 184391-694 1953125
383975 L 184391-695 1953125
383976 L 184391-696 1953125
383977 L 184391-697 1953125
383978 L 184391-698 3906250
383979 L 184391-699 3906250
383980 L 184391-700 3906250
383981 L 184391-701 3906250
383982 L 184391-702 3906250
383983 L 184391-703 3906250
383985 L 184391-705 3906250
383986 L 184391-706 1953125
383987 L 184391-707 3906250
383988 L 184391-708 3906250
383989 L 184391-709 7812500
383990 L 184391-710 7812500
383991 L 184391-711 7812500
383992 L 184391-713 1000000
383993 L 184391-714 1000000
383994 L 184391-715 1000000
383995 L 184391-716 976563
383996 L 184391-717 976563
383997 L 184391-718 976563
383998 L 184391-719 976563
383999 L 184391-721 3906250
384000 L 184391-722 976563
384001 L 184391-723 976563
384002 L 184391-724 1953125
384003 L 184391-725 976563
384004 L 184391-726 1000000
384005 L 184391-727 7000000
384006 L 184391-728 3000000
384007 L 184391-729 976563
384008 L 184391-730 976563
384009 L 184391-731 1953125
384010 L 184391-733 976563
384011 L 184391-735 1953125
384012 L 184391-736 1953125
384013 L 184391-737 1953125
384014 L 184391-738 1953125
384015 L 184391-739 1000000

384016 W 184391-740 1000000

[dooglus]

Total of 40 bets unaccounted for.

Results: 2013-Mar-15 01:02pm (up to block 225925)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |   100325 |       1 (0.00001) |   98744 |    1580 |    1166.63 |    1280.31 |   125.77 |   -113.67 | 109.744
 1dice1Qf4       2      0.00003 |     5225 |       0 (0.00000) |    4700 |     525 |      89.45 |       0.03 |    20.46 |     89.41 |   0.041
 1dice2pxm       4      0.00006 |     7675 |       1 (0.00014) |    7221 |     453 |     117.03 |     160.00 |    12.83 |    -42.97 | 136.723
 1dice2vQo       8      0.00012 |    12104 |       5 (0.00043) |   11634 |     465 |     228.46 |     431.99 |    10.08 |   -203.53 | 189.089
 1dice2WmR      16      0.00024 |    13743 |       1 (0.00008) |   13300 |     442 |     462.33 |       4.89 |    22.07 |    457.44 |   1.058
 1dice2xkj      32      0.00049 |    17787 |       7 (0.00040) |   17378 |     402 |     969.91 |     913.99 |     1.39 |     55.91 |  94.235
 1dice2zdo      64      0.00098 |    19438 |      23 (0.00121) |   18949 |     466 |    1425.97 |     743.16 |    55.81 |    682.80 |  52.116
 1dice37Ee     128      0.00195 |    19613 |      37 (0.00193) |   19118 |     458 |    2344.05 |    1557.71 |    48.39 |    786.33 |  66.454
 1dice3jkp     256      0.00391 |    24309 |     105 (0.00439) |   23819 |     385 |    4597.55 |    7357.37 |    13.20 |  -2759.81 | 160.028
 1dice4J1m     512      0.00781 |    33646 |     272 (0.00826) |   32673 |     701 |    5739.61 |    5683.71 |    10.04 |     55.90 |  99.026
 1dice5wwE    1000      0.01526 |   118708 |    1803 (0.01526) |  116382 |     523 |   36702.76 |   32138.86 |     2.07 |   4563.89 |  87.565
 1dice61SN    1500      0.02289 |    24614 |     570 (0.02350) |   23687 |     357 |    7661.34 |    8165.60 |    15.09 |   -504.26 | 106.582
 1dice6DPt    2000      0.03052 |    74604 |    2313 (0.03117) |   71893 |     398 |   37607.70 |   33701.03 |     9.37 |   3906.66 |  89.612
 1dice6gJg    3000      0.04578 |    28792 |    1313 (0.04631) |   27041 |     438 |    9298.04 |   10070.88 |    25.18 |   -772.83 | 108.312
 1dice6GV5    4000      0.06104 |    34745 |    2114 (0.06154) |   32239 |     392 |    7645.71 |    7429.64 |    31.35 |    216.06 |  97.174
 1dice6wBx    6000      0.09155 |    47340 |    4320 (0.09213) |   42570 |     450 |   16038.75 |   17764.57 |     7.31 |  -1725.82 | 110.760
 1dice6YgE    8000      0.12207 |   183960 |   22531 (0.12282) |  160919 |     510 |   91560.16 |   90418.14 |   100.47 |   1142.02 |  98.753
 1dice7EYz   12000      0.18311 |    95039 |   17324 (0.18332) |   77175 |     540 |  170736.10 |  172786.55 |  3314.90 |  -2050.45 | 101.201
 1dice7fUk   16000      0.24414 |   245491 |   59776 (0.24406) |  185150 |     565 |  366492.13 |  352670.49 |  2322.45 |  13821.63 |  96.229
 1dice7W2A   24000      0.36621 |   246028 |   90333 (0.36805) |  155101 |     594 |  583448.72 |  575210.45 |  1013.25 |   8238.27 |  98.588
 1dice8EMZ   32000      0.48828 |  1123886 |  547732 (0.48807) |  574502 |    1652 |  875668.99 |  858077.57 |  2924.98 |  17591.42 |  97.991
 1dice97EC   32768      0.50000 |   608690 |  303604 (0.49972) |  303944 |    1142 |  661993.44 |  646089.81 |  6521.25 |  15903.63 |  97.598
 1dice9wcM   48000      0.73242 |   342642 |  251385 (0.73503) |   90621 |     636 |  299847.86 |  292335.14 |  5455.28 |   7512.72 |  97.494
 1dicec9k7   52000      0.79346 |    75401 |   59475 (0.79426) |   15406 |     520 |   61668.45 |   60388.78 |  1187.58 |   1279.67 |  97.925
 1dicegEAr   56000      0.85449 |    63660 |   54048 (0.85675) |    9037 |     575 |   77808.70 |   77185.16 |   400.55 |    623.53 |  99.199
 1diceDCd2   60000      0.91553 |    98507 |   89750 (0.91627) |    8201 |     556 |   71064.66 |   70266.66 |     0.53 |    797.99 |  98.877
 1dice9wVt   64000      0.97656 |    16828 |   15395 (0.97957) |     321 |    1112 |   24067.48 |   23654.03 |   240.21 |    413.44 |  98.282
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  3567880 | 1471624           | 2079711 |   16545 |  773649.61 |  759350.66 |   263.28 |  14298.94 |  98.152
            big (bets >= 4 BTC) |   114920 |   52614           |   62014 |     292 | 2642802.50 | 2587135.98 | 23628.70 |  55666.51 |  97.894
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  3682800 | 1524238           | 2141725 |   16837 | 3416452.12 | 3346486.65 | 23891.99 |  69965.46 |  97.952
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      69965.46607793 BTC (2.048%)
Cumulative Fees Paid:        2883.76007500 BTC
SD Profit after fees:       67081.70600293 BTC (1.963%)
Pending Liabilities:          -64.47836550 BTC
Final SD Profit:            67146.18436843 BTC (1.965%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 11555723  :  SatoshiDice Tx:  6781108  (58.7%)
Blockchain MB:   4964.3  :  SatoshiDice MB:   2787.9  (56.2%)

[ThickAsThieves]

Thoughts on why profits are so low this month?

[Bugpowder]

Thoughts on why profits are so low this month?

https://bitcointalk.org/index.php?topic=80312.msg1515541#msg1515541

THIS ^

https://bitcointalk.org/index.php?topic=80312.msg1555528#msg1555528

But also see this ^

[Bugpowder]

The following addresses contributed approximately 40,000BTC to S.DICE's profits.

This is how much they have left.

Code:

                                      Remaining
15HJgkvj6roZQvNRC3pUJNKP2YgfEuD8wo      0BTC 
17sjYPaYJAvtwXM2q5ojzrCiYewnQMBi9y      0BTC
1A3z7M6GhpUejQ5eqgSyjVWRuezeepdKKV      0BTC   
1B5h9sf6xNLYGa3NBk48hwYbxyNZ22PRJk      0BTC   
1DBH7Xum2re7LXd8YNSe1uRznttsqeMXGK      0BTC
1Di6ux3CQBNXCZLD76BsnYWDo6XnFGzQah      0BTC
1EP4rM8hLZCRSWPNZDWJp9zdvmoWYkkgbQ      0BTC 
1MxgyKiKiHEemMUTJuq9NAbjmhKnUL5Ric      0BTC

Any questions?

Updated the stats.

I DO think there is another whale out there with at least 10k distributed across other addresses.  That guy uses a similar betting pattern to the first whale but much smaller bet sizes.

[dooglus]

I just noticed "65 losses (184391-665  to 184391-739" on the "lessthan 32000" game.  That's a huge number of losses in a row.  They're all in the same block, too.

I checked, and there really were 65 losing "lessthan 32000" bets in a row in this block: http://blockexplorer.com/b/184391.  Search for 25088, which is the winning bet before the losing streak starts, then pair up the txids in the first column with the bettx column in this (large, and so not inlined) collection of screenshots: https://i.imgur.com/GhH7b2H.png

[Uglux]

How crazy unlikely (or lucky?) is this? 0.000000000000000012219410750632388 %? Ain't it more likely to win "lessthan 1" two times in a row?

[dooglus]

How crazy unlikely (or lucky?) is this? 0.000000000000000012219410750632388 %? Ain't it more likely to win "lessthan 1" two times in a row?

I think it's about as unlikely as winning "lessthan 1" 3.9 times in a row:

>>> math.log((1 / (1-32000/65536.0)**65), 65536)
3.9267190562541083

I'm trying to think of an explanation for this.  There's no way it happened by pure chance, it's just too unlikely.

The miner of that block could have deliberately picked losing bets to mine.  If the results of the bets were published without any confirmations, like they used to always be some time ago, then that's possible.  I don't see why a miner would do that though.

It's possible that SatoshiDice's hot wallet was out of confirmed coins to pay out winners at the time, and so was only settling losing bets, but that shouldn't affect which bet transactions got mined.

So I'm at a loss to explain it.

How about the conspiracy theory answer: someone who knew the daily secret deliberately sent a bunch of losing bets to manipulate the stats.  But why would a SatoshiDice insider have any incentive to make it look like lots of small bets were losing?

[dooglus]

The downtime caused a flat-spot like I was expected when processing was down for the recent blockchain fork:

Total of 162 bets unaccounted for.

Results: 2013-Mar-16 09:50am (up to block 226194)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |   101071 |       1 (0.00001) |   99476 |    1594 |    1177.99 |    1280.37 |   126.79 |   -102.37 | 108.691
 1dice1Qf4       2      0.00003 |     5347 |       0 (0.00000) |    4821 |     526 |      91.05 |       0.04 |    20.47 |     91.00 |   0.049
 1dice2pxm       4      0.00006 |     7798 |       1 (0.00014) |    7343 |     454 |     118.40 |     160.01 |    12.84 |    -41.61 | 135.147
 1dice2vQo       8      0.00012 |    12735 |       5 (0.00041) |   12264 |     466 |     252.45 |     432.11 |    10.08 |   -179.65 | 171.163
 1dice2WmR      16      0.00024 |    14282 |       1 (0.00007) |   13839 |     442 |     490.35 |       5.03 |    22.07 |    485.32 |   1.026
 1dice2xkj      32      0.00049 |    19528 |       9 (0.00047) |   19117 |     402 |    1114.13 |    1396.44 |     1.39 |   -282.30 | 125.339
 1dice2zdo      64      0.00098 |    19951 |      24 (0.00123) |   19459 |     468 |    1471.20 |     803.35 |    55.82 |    667.84 |  54.605
 1dice37Ee     128      0.00195 |    19671 |      37 (0.00193) |   19174 |     460 |    2345.66 |    1557.72 |    48.39 |    787.93 |  66.409
 1dice3jkp     256      0.00391 |    24352 |     106 (0.00442) |   23861 |     385 |    4603.12 |    7359.89 |    13.20 |  -2756.76 | 159.889
 1dice4J1m     512      0.00781 |    33755 |     273 (0.00826) |   32781 |     701 |    5747.94 |    5685.00 |    10.04 |     62.94 |  98.905
 1dice5wwE    1000      0.01526 |   119626 |    1815 (0.01524) |  117287 |     524 |   36953.95 |   32275.08 |     2.07 |   4678.87 |  87.339
 1dice61SN    1500      0.02289 |    24632 |     571 (0.02352) |   23703 |     358 |    7677.79 |    8378.89 |    15.09 |   -701.10 | 109.132
 1dice6DPt    2000      0.03052 |    75090 |    2331 (0.03121) |   72361 |     398 |   37722.21 |   33752.49 |     9.37 |   3969.72 |  89.476
 1dice6gJg    3000      0.04578 |    28842 |    1313 (0.04623) |   27090 |     439 |    9348.47 |   10071.13 |    25.18 |   -722.66 | 107.730
 1dice6GV5    4000      0.06104 |    34770 |    2118 (0.06161) |   32260 |     392 |    7648.08 |    7439.57 |    31.35 |    208.51 |  97.274
 1dice6wBx    6000      0.09155 |    47496 |    4335 (0.09215) |   42710 |     451 |   16073.91 |   17885.47 |     7.31 |  -1811.56 | 111.270
 1dice6YgE    8000      0.12207 |   185629 |   22727 (0.12277) |  162391 |     511 |   91842.61 |   90660.50 |   100.48 |   1182.10 |  98.713
 1dice7EYz   12000      0.18311 |    95983 |   17479 (0.18314) |   77960 |     544 |  171317.94 |  173032.51 |  3314.91 |  -1714.56 | 101.001
 1dice7fUk   16000      0.24414 |   247531 |   60270 (0.24404) |  186695 |     566 |  367242.40 |  353354.86 |  2322.46 |  13887.53 |  96.218
 1dice7W2A   24000      0.36621 |   248563 |   91304 (0.36821) |  156664 |     595 |  583948.05 |  575680.26 |  1013.25 |   8267.78 |  98.584
 1dice8EMZ   32000      0.48828 |  1128608 |  549998 (0.48804) |  576950 |    1660 |  878694.15 |  861109.94 |  2925.00 |  17584.20 |  97.999
 1dice97EC   32768      0.50000 |   612187 |  305322 (0.49968) |  305719 |    1146 |  664053.35 |  648020.41 |  6521.27 |  16032.94 |  97.586
 1dice9wcM   48000      0.73242 |   344780 |  252951 (0.73503) |   91188 |     641 |  300301.08 |  292771.78 |  5455.30 |   7529.29 |  97.493
 1dicec9k7   52000      0.79346 |    75937 |   59909 (0.79438) |   15507 |     521 |   61780.20 |   60482.17 |  1187.58 |   1298.02 |  97.899
 1dicegEAr   56000      0.85449 |    64342 |   54633 (0.85679) |    9132 |     577 |   77992.86 |   77345.69 |   400.56 |    647.16 |  99.170
 1diceDCd2   60000      0.91553 |    99498 |   90652 (0.91622) |    8289 |     557 |   71359.32 |   70548.77 |     0.53 |    810.55 |  98.864
 1dice9wVt   64000      0.97656 |    16933 |   15491 (0.97970) |     321 |    1121 |   24078.74 |   23665.34 |   240.22 |    413.39 |  98.283
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  3593763 | 1480968           | 2096188 |   16607 |  777345.83 |  763239.69 |   264.46 |  14106.14 |  98.185
            big (bets >= 4 BTC) |   115174 |   52708           |   62174 |     292 | 2648101.66 | 2591915.27 | 23628.70 |  56186.39 |  97.878
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  3708937 | 1533676           | 2158362 |   16899 | 3425447.50 | 3355154.96 | 23893.16 |  70292.53 |  97.948
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      70292.53912493 BTC (2.052%)
Cumulative Fees Paid:        2909.98447500 BTC
SD Profit after fees:       67382.55464993 BTC (1.967%)
Pending Liabilities:          -52.54336004 BTC
Final SD Profit:            67435.09800997 BTC (1.969%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 11629962  :  SatoshiDice Tx:  6825397  (58.7%)
Blockchain MB:   4999.2  :  SatoshiDice MB:   2807.5  (56.2%)

[StarenseN]

The downtime caused a flat-spot like I was expected when processing was down for the recent blockchain fork:

Can you explain why it's only appearing now ?

[ThickAsThieves]

They had a planned downtime recently.

[StarenseN]

They had a planned downtime recently.

Ok I thought it was the downtime due to the fork alert.

[grau]

It seems the transaction format of SD changed. I do not see the usual dust.

[dooglus]

It seems the transaction format of SD changed. I do not see the usual dust.

They don't charge the 0.0005 BTC fee to losing payouts any more (as of about a week, I think) so the smallest payout now is 0.5% of the 0.01 BTC min bet, or 5000 satoshis.

[dooglus]

The list of longest sequences of wins and losses I posted yesterday had a mistake.  I wasn't counting any sequences which didn't finish yet.  Like the sequence of losing "lessthan 2" bets, which has been building since the start of the game.

Here's a correct list, as of now-ish:

lessthan     1     99531 bets       1 wins (222877-119  to 222877-119 )   85965 losses (176831-34   to 222877-118 )
lessthan     2      4762 bets       0 wins (None        to None       )    4762 losses (177355-25   to 226257-136 )
lessthan     4      7320 bets       1 wins (213426-111  to 213426-111 )    4259 losses (177365-68   to 213425-123 )
lessthan     8     12266 bets       1 wins (191198-55   to 191198-55  )    4946 losses (202814-664  to 217110-578 )
lessthan    16     13819 bets       1 wins (191139-261  to 191139-261 )   12237 losses (191139-273  to 226237-258 )
lessthan    32     19070 bets       1 wins (184331-26   to 184331-26  )    6360 losses (196254-318  to 219048-260 )
lessthan    64     19566 bets       1 wins (184331-26   to 184331-26  )    4204 losses (191139-273  to 209097-247 )
lessthan   128     19185 bets       1 wins (184218-167  to 184218-167 )    3158 losses (194000-15   to 206389-210 )
lessthan   256     23956 bets       1 wins (179750-57   to 179750-57  )    1289 losses (210373-648  to 214001-353 )
lessthan   512     32995 bets       1 wins (177492-65   to 177492-65  )     564 losses (206416-327  to 207020-196 )
lessthan  1000    119224 bets       2 wins (180131-98   to 180136-87  )     566 losses (214383-45   to 214430-239 )
lessthan  1500     24253 bets       2 wins (180806-572  to 180806-574 )     303 losses (222782-200  to 222904-322 )
lessthan  2000     74793 bets       3 wins (190605-433  to 190605-479 )     280 losses (192015-159  to 192877-145 )
lessthan  3000     28362 bets       3 wins (190605-433  to 190605-479 )     274 losses (196923-121  to 197196-178 )
lessthan  4000     34252 bets       3 wins (187645-74   to 187668-17  )     123 losses (191201-362  to 191339-143 )
lessthan  6000     46934 bets       4 wins (199484-177  to 199512-23  )      96 losses (221597-329  to 221986-337 )
lessthan  8000    185286 bets       9 wins (192997-182  to 192997-232 )      91 losses (197734-53   to 197745-364 )
lessthan 12000     95581 bets      12 wins (208332-49   to 208332-313 )      73 losses (208332-469  to 208335-22  )
lessthan 16000    247070 bets       9 wins (184483-183  to 184483-294 )      42 losses (219440-228  to 219440-350 )
lessthan 24000    248014 bets      14 wins (213616-75   to 213616-1053)      24 losses (225928-411  to 225937-147 )
lessthan 32000   1127422 bets      34 wins (184344-956  to 184345-16  )      65 losses (184391-665  to 184391-739 )
lessthan 32768    611382 bets      30 wins (180866-367  to 180868-167 )      26 losses (216081-852  to 216081-901 )
lessthan 48000    343930 bets      68 wins (182535-247  to 182536-268 )      17 losses (189347-98   to 189347-126 )
lessthan 52000     74960 bets      59 wins (202481-127  to 202567-150 )       9 losses (213719-227  to 213720-86  )
lessthan 56000     63223 bets      60 wins (224067-454  to 224072-192 )       5 losses (196994-197  to 197000-76  )
lessthan 60000     98374 bets     146 wins (213472-454  to 213513-36  )       4 losses (210367-580  to 210367-590 )
lessthan 64000     15488 bets     439 wins (180744-103  to 181691-101 )       2 losses (177069-43   to 177087-37  )

Note there are only 4762 "lessthan 2" losses shown, whereas the most recent daily stats showed there were 4821 losses on the same bet.  That's because I'm not counting two bets in the same transaction before Jan 3rd as being two bets when counting sequence length (since they always got the same lucky number), but am counting them as 2 bets in the daily stats.