Satoshi Dice -- Statistical Analysis

[Picklee]

It's complicated by the fact that with 1 trial, there is a 0% chance that the house will take within 1.89 to 1.91 percent.

The chance is not 0%, but it is very small, perhaps <<0.001%.

Markov chains are more useful when there's a relationship between the states of the system.  In this case, it would be more like "losing 3 in a row changes your chances of winning the next one".  Since we don't have that, you can use regular IID statistics.   

It seems to me that SD could be modelled as a markov chain since the game is stochastic and has a markov property; that is, the outcome of trial B is not dependent on the outcome of trial A (I'm not sure if that's what you meant?). Although the probability of consecutive lessthan1 "successes" is very remote, it is still possible and a probability is associated with it. Given infinite number of trials, its bound to happen and there is no "losing 3 in a row changes your chance of winning the next one" for the markov model because the game has a markov property (or maybe it doesn't?). Maybe I'm misunderstanding the application of markov models, so please correct any errors I've made.

[1714218804]

1714218804

[etotheipi]

It's complicated by the fact that with 1 trial, there is a 0% chance that the house will take within 1.89 to 1.91 percent.

The chance is not 0%, but it is very small, perhaps <<0.001%.

Markov chains are more useful when there's a relationship between the states of the system.  In this case, it would be more like "losing 3 in a row changes your chances of winning the next one".  Since we don't have that, you can use regular IID statistics.   

It seems to me that SD could be modelled as a markov chain since the game is stochastic and has a markov property; that is, the outcome of trial B is not dependent on the outcome of trial A (I'm not sure if that's what you meant?). Although the probability of consecutive lessthan1 "successes" is very remote, it is still possible and a probability is associated with it. Given infinite number of trials, its bound to happen and there is no "losing 3 in a row changes your chance of winning the next one" for the markov model because the game has a markov property (or maybe it doesn't?). Maybe I'm misunderstanding the application of markov models, so please correct any errors I've made.

There's nothing stopping you from using Markov chains to model this problem and get a correct answer.  But it would be like using calculus to compute the area of a square.  It works,  but there's simpler ways to do it.

[dooglus]

It's complicated by the fact that with 1 trial, there is a 0% chance that the house will take within 1.89 to 1.91 percent.

The chance is not 0%, but it is very small, perhaps <<0.001%.

I think you may have misunderstood.  If after 1 bet the house has a profit, it's a 99.5% profit (0.5% is returned to the player).  It's never a 1.9% profit.

Total of 47 bets unaccounted for.

Results: 2013-Apr-03 11:51am (up to block 229527)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |   117399 |       3 (0.00003) |  115561 |    1835 |    1418.85 |    3841.57 |   141.67 |  -2422.71 | 270.751
 1dice1Qf4       2      0.00003 |     6851 |       0 (0.00000) |    6299 |     552 |     111.13 |       0.14 |    22.23 |    110.99 |   0.131
 1dice2pxm       4      0.00006 |     8885 |       1 (0.00012) |    8413 |     471 |     136.37 |     160.10 |    14.54 |    -23.73 | 117.403
 1dice2vQo       8      0.00012 |    15522 |       5 (0.00033) |   15028 |     489 |     304.80 |     432.37 |    10.11 |   -127.57 | 141.856
 1dice2WmR      16      0.00024 |    16464 |       1 (0.00006) |   16000 |     463 |     566.01 |       5.40 |    22.13 |    560.60 |   0.956
 1dice2xkj      32      0.00049 |    23419 |      11 (0.00048) |   22992 |     416 |    1367.75 |    1537.62 |     1.45 |   -169.87 | 112.420
 1dice2zdo      64      0.00098 |    26231 |      32 (0.00124) |   25703 |     496 |    1922.80 |    1521.20 |    55.91 |    401.60 |  79.114
 1dice37Ee     128      0.00195 |    20749 |      38 (0.00187) |   20241 |     470 |    2379.58 |    1562.89 |    48.42 |    816.68 |  65.679
 1dice3jkp     256      0.00391 |    25893 |     113 (0.00443) |   25375 |     405 |    5996.58 |    8653.62 |    13.25 |  -2657.04 | 144.309
 1dice4J1m     512      0.00781 |    37032 |     296 (0.00815) |   36007 |     729 |    8286.23 |    6899.00 |    10.13 |   1387.22 |  83.259
 1dice5wwE    1000      0.01526 |   130886 |    1973 (0.01514) |  128348 |     565 |   40990.30 |   36083.16 |     2.22 |   4907.14 |  88.029
 1dice61SN    1500      0.02289 |    25466 |     581 (0.02315) |   24520 |     365 |    7961.39 |    8558.13 |    15.12 |   -596.73 | 107.495
 1dice6DPt    2000      0.03052 |    84015 |    2570 (0.03074) |   81042 |     403 |   40958.39 |   36633.46 |     9.39 |   4324.92 |  89.441
 1dice6gJg    3000      0.04578 |    30057 |    1367 (0.04621) |   28217 |     473 |    9808.39 |   10627.78 |    25.34 |   -819.38 | 108.354
 1dice6GV5    4000      0.06104 |    36081 |    2216 (0.06211) |   33462 |     403 |    7723.23 |    7513.56 |    31.39 |    209.66 |  97.285
 1dice6wBx    6000      0.09155 |    50262 |    4569 (0.09179) |   45206 |     487 |   16789.73 |   18399.76 |     7.43 |  -1610.02 | 109.589
 1dice6YgE    8000      0.12207 |   196469 |   24023 (0.12261) |  171903 |     543 |   96113.87 |   94971.36 |   100.62 |   1142.50 |  98.811
 1dice7EYz   12000      0.18311 |   104377 |   18973 (0.18280) |   84819 |     585 |  175335.89 |  176243.30 |  3315.05 |   -907.40 | 100.518
 1dice7fUk   16000      0.24414 |   270168 |   65844 (0.24426) |  203719 |     605 |  372802.77 |  358817.24 |  2322.58 |  13985.52 |  96.249
 1dice7W2A   24000      0.36621 |   263772 |   96786 (0.36779) |  166368 |     618 |  590251.02 |  582124.88 |  1013.34 |   8126.13 |  98.623
 1dice8EMZ   32000      0.48828 |  1167655 |  569067 (0.48810) |  596824 |    1764 |  903486.61 |  885558.38 |  2925.34 |  17928.23 |  98.016
 1dice97EC   32768      0.50000 |   652546 |  325402 (0.49966) |  325839 |    1305 |  679635.59 |  662940.30 |  6521.88 |  16695.28 |  97.543
 1dice9wcM   48000      0.73242 |   371003 |  272221 (0.73522) |   98039 |     743 |  307390.07 |  300293.47 |  6172.23 |   7096.60 |  97.691
 1dicec9k7   52000      0.79346 |    83238 |   65666 (0.79445) |   16990 |     582 |   64156.04 |   62745.47 |  1187.78 |   1410.56 |  97.801
 1dicegEAr   56000      0.85449 |    74192 |   63010 (0.85675) |   10535 |     647 |   81314.33 |   80528.56 |   400.81 |    785.76 |  99.034
 1diceDCd2   60000      0.91553 |   116106 |  105780 (0.91625) |    9669 |     657 |   74182.51 |   73131.53 |     0.97 |   1050.97 |  98.583
 1dice9wVt   64000      0.97656 |    19248 |   17566 (0.97964) |     365 |    1317 |   24733.69 |   24319.01 |   240.51 |    414.67 |  98.323
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  3854007 | 1583822           | 2252090 |   18095 |  811433.98 |  797411.52 |   286.73 |  14022.46 |  98.272
            big (bets >= 4 BTC) |   119979 |   54292           |   65394 |     293 | 2704690.03 | 2646691.88 | 24345.21 |  57998.15 |  97.856
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  3973986 | 1638114           | 2317484 |   18388 | 3516124.02 | 3444103.40 | 24631.95 |  72020.61 |  97.952
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      72020.61453961 BTC (2.048%)
Cumulative Fees Paid:        3184.91817500 BTC
SD Profit after fees:       68835.69636461 BTC (1.958%)
Pending Liabilities:           -0.52469045 BTC
Final SD Profit:            68836.22105506 BTC (1.958%)
Profit This Month:            993.29448744 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 12577501  :  SatoshiDice Tx:  7301854  (58.1%)
Blockchain MB:   5452.9  :  SatoshiDice MB:   3009.1  (55.2%)

[fredtrader]

Is there any way to get exact numbers on total bets and total profit on a month by month basis? It is useful so we can see in exact numbers rather than a graph how the site has been growing.

[StarenseN]

Is there any way to get exact numbers on total bets and total profit on a month by month basis? It is useful so we can see in exact numbers rather than a graph how the site has been growing.

fred, look after the orange line. It's the EV line. Multiplie it by (1/0.019) and you have the volume of bet.

[fredtrader]

Is there any way to get exact numbers on total bets and total profit on a month by month basis? It is useful so we can see in exact numbers rather than a graph how the site has been growing.

fred, look after the orange line. It's the EV line. Multiplie it by (1/0.019) and you have the volume of bet.

It only appears as a line, I can't get the exact numbers for each whole month, I wanted to do a month by month comparison of turnover and profit.

[MeatPopsicle]

Looks like 1PVkEnfTXD5uHeWZSGeXqGdTZ44KAeZsgV is the new guy to watch, doing mass 20x bet txns all over the board.

[nimda]

It's complicated by the fact that with 1 trial, there is a 0% chance that the house will take within 1.89 to 1.91 percent.

The chance is not 0%, but it is very small, perhaps <<0.001%.

Wrong. Let's say you bet 2 BTC once on the 50/48.1 address. There are only two options:
The house gains 2 BTC (100%)
The house loses nearly 2 BTC (98.1%)

[StarenseN]

Is there any way to get exact numbers on total bets and total profit on a month by month basis? It is useful so we can see in exact numbers rather than a graph how the site has been growing.

fred, look after the orange line. It's the EV line. Multiplie it by (1/0.019) and you have the volume of bet.

It only appears as a line, I can't get the exact numbers for each whole month, I wanted to do a month by month comparison of turnover and profit.

Check the other image in the topic

[Zaih]

You seem very into tracking Satoshi, Doog 

I assume you own a large percentage of it?

[bb113]

It's complicated by the fact that with 1 trial, there is a 0% chance that the house will take within 1.89 to 1.91 percent.

The chance is not 0%, but it is very small, perhaps <<0.001%.

Markov chains are more useful when there's a relationship between the states of the system.  In this case, it would be more like "losing 3 in a row changes your chances of winning the next one".  Since we don't have that, you can use regular IID statistics.  

It seems to me that SD could be modelled as a markov chain since the game is stochastic and has a markov property; that is, the outcome of trial B is not dependent on the outcome of trial A (I'm not sure if that's what you meant?). Although the probability of consecutive lessthan1 "successes" is very remote, it is still possible and a probability is associated with it. Given infinite number of trials, its bound to happen and there is no "losing 3 in a row changes your chance of winning the next one" for the markov model because the game has a markov property (or maybe it doesn't?). Maybe I'm misunderstanding the application of markov models, so please correct any errors I've made.

There's nothing stopping you from using Markov chains to model this problem and get a correct answer.  But it would be like using calculus to compute the area of a square.  It works,  but there's simpler ways to do it.

I think this is somewhat a matter of taste. The MCMC method is more intuitive (at least to me, who is no math whiz), and it is easier to modify for input parameters for testing alternative hypotheses (satoshi dice does not work as claimed in some specific way that may be due to interactions between parameters). There is also a psychological factor in that you are more encouraged to go "outside the box" and mess around. And of course, you always get a nice approximation of the actual distribution, even if it is not normal. The tradeoff is cpu time and expenses. It is less limiting when you want to test other assumptions though, IMO.

edit: I thought of another way of putting it. MCMC slowly gives you an answer about the supposed 'square' you are actually measuring, while your method quickly gives an answer about perfect squares. Which is the better approach depends on how perfect the square is you are trying to measure.

[dooglus]

You seem very into tracking Satoshi, Doog 

I assume you own a large percentage of it?

You'd think so wouldn't you, but no.

I just somehow found myself running the script each day.

[RationalSpeculator]

Hi dooglus,

Is it possible to find the 'btc bet total' from your graphs? (for month of march)

For February this was 344,973 btc, for January this was 1,198,694 btc

[Dice]

Can we somehow get daily/weekly automated emails based on results?

Regards

[Carnth]

Can we somehow get daily/weekly automated emails based on results?

Regards

This may help

[Picklee]

The chance is not 0%, but it is very small, perhaps <<0.001%.

I think you may have misunderstood.  If after 1 bet the house has a profit, it's a 99.5% profit (0.5% is returned to the player).  It's never a 1.9% profit.

Yup, I stand corrected.

[dooglus]

SatoshiDice is having exceptional luck so far this month.  Expected profits are around 200 BTC, and actual profits are over 1600 BTC!

Total of 201 bets unaccounted for.

Results: 2013-Apr-04 12:40pm (up to block 229689)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |   117958 |       3 (0.00003) |  116112 |    1843 |    1431.33 |    3841.63 |   142.11 |  -2410.30 | 268.395
 1dice1Qf4       2      0.00003 |     6889 |       0 (0.00000) |    6337 |     552 |     111.64 |       0.14 |    22.23 |    111.49 |   0.132
 1dice2pxm       4      0.00006 |     9020 |       1 (0.00012) |    8548 |     471 |     137.91 |     160.11 |    14.54 |    -22.19 | 116.096
 1dice2vQo       8      0.00012 |    17450 |       5 (0.00029) |   16955 |     490 |     353.55 |     432.62 |    10.11 |    -79.06 | 122.364
 1dice2WmR      16      0.00024 |    17498 |       1 (0.00006) |   17034 |     463 |     599.80 |       5.57 |    22.13 |    594.22 |   0.930
 1dice2xkj      32      0.00049 |    24422 |      11 (0.00046) |   23994 |     417 |    1409.15 |    1537.83 |     1.45 |   -128.68 | 109.132
 1dice2zdo      64      0.00098 |    27364 |      34 (0.00127) |   26833 |     497 |    1993.01 |    1659.47 |    55.91 |    333.53 |  83.265
 1dice37Ee     128      0.00195 |    20821 |      38 (0.00187) |   20312 |     471 |    2386.04 |    1562.92 |    48.42 |    823.11 |  65.503
 1dice3jkp     256      0.00391 |    25924 |     113 (0.00443) |   25406 |     405 |    5997.93 |    8653.63 |    13.25 |  -2655.69 | 144.277
 1dice4J1m     512      0.00781 |    37099 |     297 (0.00817) |   36071 |     731 |    8298.28 |    6905.30 |    10.13 |   1392.97 |  83.214
 1dice5wwE    1000      0.01526 |   131893 |    1992 (0.01517) |  129335 |     566 |   41104.91 |   36209.87 |     2.23 |   4895.04 |  88.091
 1dice61SN    1500      0.02289 |    25488 |     581 (0.02313) |   24541 |     366 |    7961.98 |    8558.13 |    15.12 |   -596.14 | 107.487
 1dice6DPt    2000      0.03052 |    84207 |    2574 (0.03071) |   81230 |     403 |   40975.70 |   36645.55 |     9.39 |   4330.14 |  89.432
 1dice6gJg    3000      0.04578 |    30115 |    1374 (0.04635) |   28268 |     473 |    9809.93 |   10632.30 |    25.34 |   -822.37 | 108.383
 1dice6GV5    4000      0.06104 |    36154 |    2219 (0.06207) |   33531 |     404 |    7724.85 |    7514.26 |    31.39 |    210.58 |  97.274
 1dice6wBx    6000      0.09155 |    50456 |    4586 (0.09178) |   45383 |     487 |   16795.17 |   18404.97 |     7.43 |  -1609.80 | 109.585
 1dice6YgE    8000      0.12207 |   197043 |   24108 (0.12269) |  172391 |     544 |   96176.00 |   95048.21 |   100.62 |   1127.79 |  98.827
 1dice7EYz   12000      0.18311 |   105178 |   19124 (0.18285) |   85464 |     590 |  175395.16 |  176302.41 |  3315.06 |   -907.25 | 100.517
 1dice7fUk   16000      0.24414 |   270883 |   66014 (0.24425) |  204261 |     608 |  372857.06 |  358877.32 |  2322.59 |  13979.73 |  96.251
 1dice7W2A   24000      0.36621 |   264529 |   97049 (0.36774) |  166861 |     619 |  590327.30 |  582188.32 |  1013.34 |   8138.98 |  98.621
 1dice8EMZ   32000      0.48828 |  1169800 |  570126 (0.48811) |  597905 |    1769 |  904870.29 |  886518.00 |  2925.36 |  18352.28 |  97.972
 1dice97EC   32768      0.50000 |   654644 |  326440 (0.49965) |  326892 |    1312 |  680539.51 |  663693.85 |  6521.91 |  16845.65 |  97.525
 1dice9wcM   48000      0.73242 |   372494 |  273298 (0.73518) |   98446 |     750 |  307550.70 |  300442.90 |  6172.24 |   7107.80 |  97.689
 1dicec9k7   52000      0.79346 |    83677 |   66005 (0.79437) |   17086 |     586 |   64253.38 |   62847.29 |  1187.79 |   1406.08 |  97.812
 1dicegEAr   56000      0.85449 |    74647 |   63390 (0.85663) |   10609 |     648 |   81412.21 |   80627.38 |   400.81 |    784.82 |  99.036
 1diceDCd2   60000      0.91553 |   116887 |  106487 (0.91621) |    9739 |     661 |   74306.24 |   73250.57 |     1.00 |   1055.66 |  98.579
 1dice9wVt   64000      0.97656 |    19348 |   17660 (0.97970) |     366 |    1322 |   24742.30 |   24326.97 |   240.52 |    415.33 |  98.321
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  3871787 | 1589180           | 2264452 |   18155 |  813189.74 |  799072.68 |   287.34 |  14117.06 |  98.264
            big (bets >= 4 BTC) |   120101 |   54350           |   65458 |     293 | 2706331.71 | 2647774.98 | 24345.21 |  58556.72 |  97.836
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  3991888 | 1643530           | 2329910 |   18448 | 3519521.46 | 3446847.67 | 24632.55 |  72673.78 |  97.935
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      72673.78974060 BTC (2.065%)
Cumulative Fees Paid:        3203.77317500 BTC
SD Profit after fees:       69470.01656560 BTC (1.974%)
Pending Liabilities:          -11.95017954 BTC
Final SD Profit:            69481.96674514 BTC (1.974%)
Profit This Month:           1639.04017752 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 12647052  :  SatoshiDice Tx:  7331948  (58.0%)
Blockchain MB:   5486.8  :  SatoshiDice MB:   3021.7  (55.1%)

[dooglus]

Overnight profits were mostly from this big spender:

Thu Apr  4 00:40:22 2013 <32000 229564 331d45940bdde2a7:0  1LuVKtWeLTVKcS5NPBNsFA7ygjWXRRqeLz BET   100.00000000 WIN    100.38480000
Thu Apr  4 00:40:22 2013 <32000 229564 0d115449e1ae00ea:0  1LuVKtWeLTVKcS5NPBNsFA7ygjWXRRqeLz BET   200.00000000 LOSE  -199.00000000
Thu Apr  4 00:55:19 2013 <32000 229565 3ebdacdf74f89d9a:0  1LuVKtWeLTVKcS5NPBNsFA7ygjWXRRqeLz BET   200.00000000 LOSE  -199.00000000
Thu Apr  4 00:57:14 2013 <32000 229566 943b01852c37b190:0  1LuVKtWeLTVKcS5NPBNsFA7ygjWXRRqeLz BET   100.00000000 LOSE   -99.50000000

[BTCdude007]

SD is a profit generating monster...amazing! Already $215K profit in just 4 days.

I am eagerly awaiting the March report to see if the total BTC bet as well as average BTC per bet decreased due to the
price going from ~32 to ~92. I expect BTC per bet to decrease but total BTC bet to not go down due to increased userbase.

[fredtrader]

SD is a profit generating monster...amazing! Already $215K profit in just 4 days.

I am eagerly awaiting the March report to see if the total BTC bet as well as average BTC per bet decreased due to the
price going from ~32 to ~92. I expect BTC per bet to decrease but total BTC bet to not go down due to increased userbase.

I wish exact numbers were posted for BTC per bet and total BTC bet each month, but from the graph alone it looks like BTC profits and BTC wagered is going down while the same numbers measured in USD is going up. If someone has the data for each month I wouldn't mind making a nice table along with USD conversions each time, I think the SDICE shares will benefit from more information on their profits.