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Author Topic: Satoshi Dice -- Statistical Analysis  (Read 177315 times)
organofcorti
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May 31, 2013, 04:05:01 AM
 #1421

are you able to tell if the amount being bet on satoshidice has declined since they closed their operations to americans?

Look at the slope of the red line.  When it's steep, lots is being bet.  When it's flat, nothing is being bet.

I wouldn't believe dooglus. That's clearly a sock puppet account Grin (you've just been waiting for that, huh?)

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May 31, 2013, 04:12:31 AM
 #1422

are you able to tell if the amount being bet on satoshidice has declined since they closed their operations to americans?

Look at the slope of the red line.  When it's steep, lots is being bet.  When it's flat, nothing is being bet.

looks like i needed to be on my laptop instead of my phone to see that. i'm guess that number is just the expected 1.9% edge on the bets placed each day?
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May 31, 2013, 04:29:39 AM
 #1423

I wouldn't believe dooglus. That's clearly a sock puppet account Grin (you've just been waiting for that, huh?)

Heh.  I found them here: https://bitcointalk.org/index.php?topic=218231.msg2324967#msg2324967

Also, I just remembered and used something you taught me about a year ago: https://bitcointalk.org/index.php?topic=191176.msg2325281#msg2325281

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May 31, 2013, 05:09:33 AM
 #1424

I wouldn't believe dooglus. That's clearly a sock puppet account Grin (you've just been waiting for that, huh?)

Heh.  I found them here: https://bitcointalk.org/index.php?topic=218231.msg2324967#msg2324967

Also, I just remembered and used something you taught me about a year ago: https://bitcointalk.org/index.php?topic=191176.msg2325281#msg2325281

Those were the days! I think it was more of a collaborative effort than anything else, though Wink

Now If I could just find the post where I derived the expected number of losses in a row as -log(bets*p + 1)/log(q). Where the hell did I leave that thing? Or maybe you derived it?


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May 31, 2013, 01:33:02 PM
 #1425

are you able to tell if the amount being bet on satoshidice has declined since they closed their operations to americans?

if desired here are the graphs of change of bets, change of TX and MB % on the blockchain in full or 2013 only. they probably have errors and they are based on dooglus' data from this thread (many thanks).

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May 31, 2013, 02:54:37 PM
 #1426

are you able to tell if the amount being bet on satoshidice has declined since they closed their operations to americans?

The betting volume has increased since closing to US bettors.
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May 31, 2013, 03:27:56 PM
 #1427

are you able to tell if the amount being bet on satoshidice has declined since they closed their operations to americans?

The betting volume has increased since closing to US bettors.


He is using gorilla marketing tactics. Free media attention by blocking his site in the US.

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May 31, 2013, 03:28:25 PM
 #1428

are you able to tell if the amount being bet on satoshidice has declined since they closed their operations to americans?

if desired here are the graphs of change of bets, change of TX and MB % on the blockchain in full or 2013 only. they probably have errors and they are based on dooglus' data from this thread (many thanks).

Thank you so much for sharing your work Smiley

It's very interesting to see your graph about avg bets per day since inception.

It looks like we hit a double bottom now, and if the past repeats it can go up from here a lot. Smiley


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May 31, 2013, 03:31:18 PM
 #1429

are you able to tell if the amount being bet on satoshidice has declined since they closed their operations to americans?

The betting volume has increased since closing to US bettors.


He is using gorilla marketing tactics. Free media attention by blocking his site in the US.

I'm not sure. Swiss banks have also started refusing US citizens and I don't think this is guerrilla marketing nor does it add to the bottom line. They lose business but also take less legal risk. I think the same applies here.

Though I agree some US citizens will be motivated to gamble more with SatoshiDice now that it's forbidden, many more I think will go for the easy solution and just switch gambling website.

Ie: I think if US citizens were not refused, the growth would have been stronger.
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May 31, 2013, 03:37:26 PM
 #1430

He is using gorilla marketing tactics. Free media attention by blocking his site in the US.

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May 31, 2013, 05:17:32 PM
 #1431

If I'm looking at the profit for may right, before expenses are taken out, each share in SD will receive about 5 satoshis, right? After paying for system admin and hosting, it's well negative. Right?

          WTF!     Don't Click Here              
          .      .            .            .        .            .            .          .        .     .               .            .             .            .            .           .            .     .               .         .              .           .            .            .            .     .      .     .    .     .          .            .          .            .            .           .              .     .            .            .           .            .               .         .            .     .            .            .             .            .              .            .            .      .            .            .            .            .            .            .             .          .
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May 31, 2013, 05:25:04 PM
 #1432

If I'm looking at the profit for may right, before expenses are taken out, each share in SD will receive about 5 satoshis, right? After paying for system admin and hosting, it's well negative. Right?

That's correct.
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May 31, 2013, 05:36:20 PM
 #1433

If I'm looking at the profit for may right, before expenses are taken out, each share in SD will receive about 5 satoshis, right? After paying for system admin and hosting, it's well negative. Right?

That's correct.

And losses are forwarded to the next month as well, right?

          WTF!     Don't Click Here              
          .      .            .            .        .            .            .          .        .     .               .            .             .            .            .           .            .     .               .         .              .           .            .            .            .     .      .     .    .     .          .            .          .            .            .           .              .     .            .            .           .            .               .         .            .     .            .            .             .            .              .            .            .      .            .            .            .            .            .            .             .          .
RationalSpeculator
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May 31, 2013, 06:19:04 PM
 #1434

If I'm looking at the profit for may right, before expenses are taken out, each share in SD will receive about 5 satoshis, right? After paying for system admin and hosting, it's well negative. Right?

That's correct.

And losses are forwarded to the next month as well, right?

Indeed, as I understand it if the month ends at a loss it is prefinanced by the largest stockholder and forwarded to the next month where the large shareholder will first recoup their loss only after which remaining profits will be distributed.
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May 31, 2013, 07:21:02 PM
 #1435

I wouldn't believe dooglus. That's clearly a sock puppet account Grin (you've just been waiting for that, huh?)

Heh.  I found them here: https://bitcointalk.org/index.php?topic=218231.msg2324967#msg2324967

Also, I just remembered and used something you taught me about a year ago: https://bitcointalk.org/index.php?topic=191176.msg2325281#msg2325281

Those were the days! I think it was more of a collaborative effort than anything else, though Wink

Now If I could just find the post where I derived the expected number of losses in a row as -log(bets*p + 1)/log(q). Where the hell did I leave that thing? Or maybe you derived it?
Please define "expected number of losses in a row." Are you using mean, median, or mode; are you ignoring wins in a row, etc.

I recommend asking me for a signature from my GPG key before doing a trade. I will NEVER deny such a request.
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May 31, 2013, 10:00:41 PM
 #1436

If I'm looking at the profit for may right, before expenses are taken out, each share in SD will receive about 5 satoshis, right? After paying for system admin and hosting, it's well negative. Right?

Wasn't it still May when you posted that?  I think it's still May now for another hour maybe, server time.

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May 31, 2013, 10:27:19 PM
 #1437

Quote
Fri May 31 03:32:26 2013 <32768 238801 5b7a993cc26d3571:2  14j73fVVomPRpfzxb9DmYQQy7sFZj626a8 BET   100.00000000 WIN     95.70000000
Fri May 31 03:42:40 2013 <32768 238802 9957fb4afd02c40b:2  14j73fVVomPRpfzxb9DmYQQy7sFZj626a8 BET   100.00000000 LOSE   -99.50000000
Fri May 31 03:58:04 2013 <32768 238803 01fcefd94ef5a333:2  14j73fVVomPRpfzxb9DmYQQy7sFZj626a8 BET   150.00000000 WIN    143.55000000
Fri May 31 04:27:50 2013 <32768 238805 0148217af38a4240:0  1MnUw7R9Rj7RqTaZqL9RQSAcpdEqixRrLw BET   100.00000000 LOSE   -99.50000000
Fri May 31 04:55:56 2013 <32768 238808 b037b30196ead4e9:2  14j73fVVomPRpfzxb9DmYQQy7sFZj626a8 BET   100.00000000 LOSE   -99.50000000
Fri May 31 06:33:26 2013 <32768 238816 529880c6bc107319:2  14j73fVVomPRpfzxb9DmYQQy7sFZj626a8 BET   100.00000000 LOSE   -99.50000000
Fri May 31 06:38:45 2013 <32768 238817 ec59541b8aa2ab59:2  14j73fVVomPRpfzxb9DmYQQy7sFZj626a8 BET   200.00000000 WIN    191.40000000
Fri May 31 07:08:19 2013 <32768 238819 e7aa97061a251ea3:0  1MnUw7R9Rj7RqTaZqL9RQSAcpdEqixRrLw BET   100.00000000 LOSE   -99.50000000
Fri May 31 07:10:53 2013 <32768 238821 e9c88f618da46fd0:2  14j73fVVomPRpfzxb9DmYQQy7sFZj626a8 BET   100.00000000 LOSE   -99.50000000
Fri May 31 07:18:38 2013 <32768 238824 515a73db982f864d:2  14j73fVVomPRpfzxb9DmYQQy7sFZj626a8 BET   200.00000000 WIN    191.40000000
Fri May 31 14:20:31 2013 <32768 238884 d0f63bf9cf85e456:2  14j73fVVomPRpfzxb9DmYQQy7sFZj626a8 BET   200.00000000 WIN    191.40000000
Fri May 31 14:56:35 2013 <32768 238888 b424885c320016fa:2  14j73fVVomPRpfzxb9DmYQQy7sFZj626a8 BET   100.00000000 WIN     95.70000000

Quote
Total of 220 bets unaccounted for.

Results: 2013-May-31 03:26pm (up to block 238941)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
----------------------------------------------------------------------------------------------------------------------------------------------
1dice9wVt   64000      0.97656 |    24352 |   22003 (0.97861) |     481 |    1868 |   25710.59 |   25269.45 |   241.37 |    441.14 |  98.284
1diceDCd2   60000      0.91553 |   158248 |  143981 (0.91565) |   13263 |    1004 |   81850.21 |   80617.15 |     2.59 |   1233.05 |  98.494
1dicegEAr   56000      0.85449 |   100520 |   85416 (0.85675) |   14282 |     822 |   87532.07 |   86678.51 |   401.43 |    853.55 |  99.025
1dicec9k7   52000      0.79346 |   105661 |   83277 (0.79377) |   21636 |     748 |   70581.53 |   68747.34 |  1188.33 |   1834.19 |  97.401
1dice9wcM   48000      0.73242 |   458566 |  336246 (0.73492) |  121282 |    1038 |  322390.92 |  314638.92 |  6173.51 |   7751.99 |  97.595
1dice97EC   32768      0.50000 |   815948 |  406789 (0.49971) |  407269 |    1890 |  756030.92 |  737295.68 |  6524.21 |  18735.24 |  97.522
1dice8EMZ   32000      0.48828 |  1333540 |  649790 (0.48803) |  681655 |    2095 |  947902.25 |  928447.09 |  2926.75 |  19455.16 |  97.948
1dice7W2A   24000      0.36621 |   313922 |  115020 (0.36726) |  198166 |     736 |  601354.16 |  592641.45 |  1013.89 |   8712.71 |  98.551
1dice7fUk   16000      0.24414 |   328246 |   79918 (0.24407) |  247518 |     810 |  395547.59 |  380224.41 |  2323.45 |  15323.17 |  96.126
1dice7EYz   12000      0.18311 |   136349 |   24897 (0.18352) |  110764 |     688 |  184387.50 |  185436.05 |  3315.49 |  -1048.54 | 100.569
1dice6YgE    8000      0.12207 |   241619 |   29585 (0.12278) |  211375 |     659 |  116660.02 |  115811.11 |   101.17 |    848.91 |  99.272
1dice6wBx    6000      0.09155 |    65363 |    5934 (0.09158) |   58862 |     567 |   18024.55 |   19647.05 |     7.72 |  -1622.49 | 109.002
1dice6GV5    4000      0.06104 |    40878 |    2508 (0.06200) |   37944 |     426 |    8076.94 |    7992.81 |    31.48 |     84.13 |  98.958
1dice6gJg    3000      0.04578 |    33348 |    1523 (0.04638) |   31311 |     514 |   10232.07 |   11239.18 |    25.48 |  -1007.10 | 109.843
1dice6DPt    2000      0.03052 |   108116 |    3287 (0.03054) |  104354 |     475 |   55020.21 |   52051.82 |     9.68 |   2968.39 |  94.605
1dice61SN    1500      0.02289 |    28326 |     655 (0.02346) |   27266 |     405 |    8141.02 |    8728.21 |    15.24 |   -587.19 | 107.213
1dice5wwE    1000      0.01526 |   166847 |    2582 (0.01554) |  163563 |     702 |   49618.80 |   46865.54 |     2.74 |   2753.25 |  94.451
1dice4J1m     512      0.00781 |    41944 |     331 (0.00805) |   40812 |     801 |    8540.21 |    6982.35 |    10.38 |   1557.86 |  81.759
1dice3jkp     256      0.00391 |    28205 |     118 (0.00425) |   27652 |     435 |    6132.04 |    8667.29 |    13.33 |  -2535.24 | 141.344
1dice37Ee     128      0.00195 |    23486 |      43 (0.00187) |   22908 |     535 |    2462.38 |    1598.31 |    48.60 |    864.07 |  64.909
1dice2zdo      64      0.00098 |    31750 |      35 (0.00112) |   31155 |     560 |    2216.39 |    1740.54 |   117.14 |    475.84 |  78.531
1dice2xkj      32      0.00049 |    31408 |      14 (0.00045) |   30931 |     463 |    1689.59 |    1851.06 |     1.62 |   -161.46 | 109.557
1dice2WmR      16      0.00024 |    25420 |       5 (0.00020) |   24913 |     502 |     895.00 |     606.71 |    22.24 |    288.29 |  67.788
1dice2vQo       8      0.00012 |    26041 |       5 (0.00020) |   25479 |     557 |     622.63 |     433.96 |    14.67 |    188.66 |  69.699
1dice2pxm       4      0.00006 |    15243 |       2 (0.00014) |   14691 |     550 |     219.64 |     320.43 |    18.54 |   -100.78 | 145.888
1dice1Qf4       2      0.00003 |    13573 |       0 (0.00000) |   12972 |     601 |     189.93 |       0.54 |    30.50 |    189.39 |   0.285
1dice1e6p       1      0.00002 |   153008 |       3 (0.00002) |  150349 |    2656 |    1963.28 |    3844.33 |   181.83 |  -1881.05 | 195.812
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  4719575 | 1936174           | 2760588 |   22813 |  909803.49 |  893832.81 |   357.28 |  15970.68 |  98.245
            big (bets >= 4 BTC) |   130352 |   57793           |   72265 |     294 | 2854189.08 | 2794544.58 | 24406.21 |  59644.50 |  97.910
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  4849927 | 1993967           | 2832853 |   23107 | 3763992.58 | 3688377.40 | 24763.49 |  75615.18 |  97.991
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      75615.18930502 BTC (2.009%)
Cumulative Fees Paid:        4103.81857500 BTC
SD Profit after fees:       71511.37073002 BTC (1.900%)
Pending Liabilities:           11.78571482 BTC
Final SD Profit:            71499.58501520 BTC (1.900%)
Profit This Month:           -103.82332942 BTC
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 15861501  :  SatoshiDice Tx:  8912717  (56.2%)
Blockchain MB:   6980.2  :  SatoshiDice MB:   3676.2  (52.7%)




organofcorti
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May 31, 2013, 11:49:56 PM
 #1438

I wouldn't believe dooglus. That's clearly a sock puppet account Grin (you've just been waiting for that, huh?)

Heh.  I found them here: https://bitcointalk.org/index.php?topic=218231.msg2324967#msg2324967

Also, I just remembered and used something you taught me about a year ago: https://bitcointalk.org/index.php?topic=191176.msg2325281#msg2325281

Those were the days! I think it was more of a collaborative effort than anything else, though Wink

Now If I could just find the post where I derived the expected number of losses in a row as -log(bets*p + 1)/log(q). Where the hell did I leave that thing? Or maybe you derived it?
Please define "expected number of losses in a row." Are you using mean, median, or mode; are you ignoring wins in a row, etc.

I'm using "expected" in the statistical sense, and "in a row" in the usual sense. So the derivation is for mean number of losses in a row for a game with a win probability of 'p', loss probability 'q' (q=1-p), and number of bets, 'bets'.

As for ignoring "losses in a row", of course. Expected losses in a row can of course be derived the same way by redefining p and q.

Edit: That should be "expected longest number of wins in a row".

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June 01, 2013, 12:10:55 AM
 #1439

OK, just making sure. Hmm... I believe the longest expected loss run is actually -log(np)/log(q). This follows from the statements made at http://mathworld.wolfram.com/Run.html.

Edit: I believe I see where the 1 comes from... and yet it doesn't seem to work.
-log(1*1/2 + 1)/log(1/2) is about 0.5849625007211561814537389439478165087598144076924810, not 0.5 as intuition would suggest. Does the formula converge towards "correctness?"

I recommend asking me for a signature from my GPG key before doing a trade. I will NEVER deny such a request.
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June 01, 2013, 10:29:48 AM
 #1440

OK, just making sure. Hmm... I believe the longest expected loss run is actually -log(np)/log(q). This follows from the statements made at http://mathworld.wolfram.com/Run.html.


I've confused "expected length of a run" and "expected longest run", and probably confused you too.

I can derive the "expected length of a run":

Expected length of a run

For a series of Bernoulli trials where:

P(win) = p
P(loss) = 1 - p

the probability of k of losses before a win is the probability of k - 1 losses multiplied by the probability of 1 win:

P(X = k) = (1 - p)^(k-1) * p

From this the expected number of losses before a win can be derived.

E(X) = sum(n = 1 to n = k)  [ n * (1 - p)^(n - 1) * p ]

= p * sum(n=1 to n=k) [ n * (1 - p)^(n - 1)]

The derivative of a geometric progression sum(n=1 to k) n * x^ (n - 1) = 1/(1 - x)^2, so substituting (1 - p) for x:

p * sum(n=1 to n=k) [ n * (1 - p)^(n - 1)] = p * 1 / (1 - ( 1 - p))^2

 = p / p^2 = 1/p

So the expected number of losses before a win is 1 / p

This holds true for the number of runs in a win, by redefining

P(loss) = p
P(win) = 1 - p


Expected longest run

I'm pretty sure I didn't derive this one. Maybe it was dooglus.
* organofcorti attempts to shift the blame

Edit: I believe I see where the 1 comes from... and yet it doesn't seem to work.
-log(1*1/2 + 1)/log(1/2) is about 0.5849625007211561814537389439478165087598144076924810, not 0.5 as intuition would suggest. Does the formula converge towards "correctness?"

As far as I can tell, neither converge to the correct answer although they clearly converge on each other. I'll see if I can figure it out.





Edit:  I found a better estimate here: http://gato-docs.its.txstate.edu/mathworks/DistributionOfLongestRun.pdf

Expected longest run = -log(n*p)/log(q) + 0.57722.../log(1/q) -1/2

Note: 0.57722... is the Euler-Mascheroni constant, which is the limit(n -> infinity) { sum(k = 1 to k = n)[1/k] - log(n) }

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