Satoshi Dice -- Statistical Analysis

[dooglus]

Very nice graphs.  The 2nd one reminds me of big scary needles rather than violins.

1. The number and size of Bets on SatoshiDice are increasing;

Is that true?  They increased for a few months Dec 2012 to early Feb this year, but other than that has there been an upwards trend?

A version of your first graph with the horizontal scale magnified about x10 would let us see that - just truncate the high values while the whale was playing.

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[StarenseN]

What about this graph but with every "violon" as proportion to the highest month volume?

[organofcorti]

That's 0.5 BTC tip my dear (I've sent the same to dooglus). Thanks a lot for your contribution!

Thanks! Much appreciated.

It's dooglus' data and he does much more work than I do so I've passed half onto him.

[StarenseN]

That's 0.5 BTC tip my dear (I've sent the same to dooglus). Thanks a lot for your contribution!

Thanks! Much appreciated.

It's dooglus' data and he does much more work than I do so I've passed half onto him.

That's really kind from you. Respect!

What about my request? Do you think it would be more revelant to normalize with the higest month volume? It would be easier to spot the trends month to month, I think.

[organofcorti]

Very nice graphs.  The 2nd one reminds me of big scary needles rather than violins.

1. The number and size of Bets on SatoshiDice are increasing;

Is that true?  They increased for a few months Dec 2012 to early Feb this year, but other than that has there been an upwards trend?

A version of your first graph with the horizontal scale magnified about x10 would let us see that - just truncate the high values while the whale was playing.

Got some ideas, will get something up tomorrow. I could be wrong - I might have been letting the percentile charts guide me a bit.

[organofcorti]

That's 0.5 BTC tip my dear (I've sent the same to dooglus). Thanks a lot for your contribution!

Thanks! Much appreciated.

It's dooglus' data and he does much more work than I do so I've passed half onto him.

That's really kind from you. Respect!

What about my request? Do you think it would be more revelant to normalize with the higest month volume? It would be easier to spot the trends month to month, I think.

The first of the pair of charts actually does that - sorry if I didn't make that clear.

[Dabs]

Hi, I understand the theoretical part (on consecutive wins or losses). What I'm looking for is actual historical data, and I think you guys already have it. (or the block chain has it.) It just needs to be sorted out. I mean, Mr. Dooglus is already posting statistics of wins vs lose. Like, for the under 48000 I can see that there have been 336630 bets of which 246989 have won and 89013 have lost. I am just curious as to how many of those losses were consecutive and what is the longest chain.

Then you can plot the theoretical formula beside the actual results to compare the "should be" and the "what actually happened already", similar to the comparison of the odds and how each 1dice has actually performed.

[dooglus]

Hi, I understand the theoretical part (on consecutive wins or losses). What I'm looking for is actual historical data, and I think you guys already have it. (or the block chain has it.) It just needs to be sorted out. I mean, Mr. Dooglus is already posting statistics of wins vs lose. Like, for the under 48000 I can see that there have been 336630 bets of which 246989 have won and 89013 have lost. I am just curious as to how many of those losses were consecutive and what is the longest chain.

Hi Dabs.

Sorry, I was stressed out with other business yesterday when you posted about this.

One problem with your request is that there's not really a definitive ordering on the bets.  Do we count the time the bet transaction was seen by some random host on the network?  Or the timestamp on the block it got into?  Or the depth of the block?  (Blocks aren't always in order of timestamp).  Or do we count the order that the bets were paid out?

There are lots of different ways of ordering the bets, which will change the longest sequence of losses.

Another problem, and what puts me off from looking into this, is "who cares".  Are you wanting the information to check whether the dice rolls are random?  ie. "we would expect to see a chain of 10 losses but the longest chain is 20 so SDICE is cheating"?  Because other than that I don't really see the point.  Runs of good and bad luck happen, due to the random nature of the dice rolls.  Suppose I go through the blockchain and find that once there were 21 losses on the 50% game in a row, given some arbitrary ordering of the bets.  Then what?

I guess I'll do this when I'm bored, but I don't expect it to tell us anything very useful or interesting.  Maybe I'm just being grouchy though.  That happens too. 

Thanks for the tip organofcorti - that's very kind of you. 

[StarenseN]

Dabs it's just random probabilities. You can do it by your own.

[dooglus]

I was expecting to see a dead flat spot due to yesterday's temporary hard fork.  Any idea why I don't?

Total of 75 bets unaccounted for.

Results: 2013-Mar-12 01:55pm (up to block 225543)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    98853 |       1 (0.00001) |   97293 |    1559 |    1141.96 |    1280.19 |   124.04 |   -138.22 | 112.104
 1dice1Qf4       2      0.00003 |     5182 |       0 (0.00000) |    4659 |     523 |      88.08 |       0.03 |    20.45 |     88.05 |   0.034
 1dice2pxm       4      0.00006 |     7633 |       1 (0.00014) |    7179 |     453 |     115.45 |     160.00 |    12.83 |    -44.54 | 138.582
 1dice2vQo       8      0.00012 |    11959 |       5 (0.00043) |   11494 |     460 |     224.58 |     431.97 |    10.07 |   -207.38 | 192.341
 1dice2WmR      16      0.00024 |    13599 |       1 (0.00008) |   13159 |     439 |     456.49 |       4.86 |    22.06 |    451.63 |   1.065
 1dice2xkj      32      0.00049 |    17362 |       6 (0.00035) |   16955 |     401 |     944.77 |     813.93 |     1.39 |    130.84 |  86.151
 1dice2zdo      64      0.00098 |    18623 |      19 (0.00105) |   18140 |     464 |    1358.11 |     451.99 |    55.81 |    906.12 |  33.281
 1dice37Ee     128      0.00195 |    19519 |      37 (0.00194) |   19024 |     458 |    2334.50 |    1557.67 |    48.39 |    776.83 |  66.724
 1dice3jkp     256      0.00391 |    24231 |     105 (0.00440) |   23742 |     384 |    4579.33 |    7357.28 |    13.20 |  -2777.94 | 160.663
 1dice4J1m     512      0.00781 |    33274 |     266 (0.00817) |   32309 |     699 |    5718.45 |    5648.62 |    10.02 |     69.83 |  98.779
 1dice5wwE    1000      0.01526 |   117218 |    1778 (0.01524) |  114919 |     521 |   36524.77 |   31953.25 |     2.07 |   4571.51 |  87.484
 1dice61SN    1500      0.02289 |    24535 |     569 (0.02353) |   23610 |     356 |    7654.14 |    8165.12 |    15.09 |   -510.97 | 106.676
 1dice6DPt    2000      0.03052 |    73764 |    2286 (0.03116) |   71080 |     398 |   37528.25 |   33650.28 |     9.37 |   3877.96 |  89.667
 1dice6gJg    3000      0.04578 |    28698 |    1304 (0.04614) |   26956 |     438 |    9214.32 |   10003.67 |    25.18 |   -789.34 | 108.566
 1dice6GV5    4000      0.06104 |    34508 |    2104 (0.06167) |   32012 |     392 |    7613.68 |    7420.70 |    31.35 |    192.97 |  97.465
 1dice6wBx    6000      0.09155 |    47042 |    4298 (0.09224) |   42300 |     444 |   16018.62 |   17743.72 |     7.28 |  -1725.09 | 110.769
 1dice6YgE    8000      0.12207 |   181359 |   22203 (0.12277) |  158649 |     507 |   91379.48 |   90211.21 |   100.47 |   1168.26 |  98.722
 1dice7EYz   12000      0.18311 |    93410 |   17030 (0.18336) |   75847 |     533 |  170435.35 |  172432.54 |  3314.88 |  -1997.19 | 101.172
 1dice7fUk   16000      0.24414 |   242100 |   58933 (0.24399) |  182609 |     558 |  365696.95 |  351841.35 |  2322.42 |  13855.59 |  96.211
 1dice7W2A   24000      0.36621 |   242930 |   89192 (0.36805) |  153147 |     591 |  582622.60 |  574398.05 |  1013.24 |   8224.54 |  98.588
 1dice8EMZ   32000      0.48828 |  1113677 |  542749 (0.48807) |  569287 |    1641 |  870341.77 |  852589.61 |  2924.93 |  17752.16 |  97.960
 1dice97EC   32768      0.50000 |   600136 |  299328 (0.49970) |  299684 |    1124 |  658985.50 |  642918.15 |  6521.21 |  16067.34 |  97.562
 1dice9wcM   48000      0.73242 |   338327 |  248253 (0.73514) |   89443 |     631 |  297988.60 |  290575.71 |  5455.26 |   7412.89 |  97.512
 1dicec9k7   52000      0.79346 |    74267 |   58534 (0.79367) |   15217 |     516 |   61219.85 |   59875.51 |  1187.55 |   1344.34 |  97.804
 1dicegEAr   56000      0.85449 |    62398 |   52977 (0.85686) |    8850 |     571 |   77209.45 |   76593.02 |   400.54 |    616.42 |  99.202
 1diceDCd2   60000      0.91553 |    95911 |   87374 (0.91620) |    7992 |     545 |   70581.58 |   69778.98 |     0.50 |    802.59 |  98.863
 1dice9wVt   64000      0.97656 |    16558 |   15147 (0.97956) |     316 |    1095 |   23993.71 |   23581.20 |   240.19 |    412.51 |  98.281
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  3522656 | 1452152           | 2054095 |   16409 |  766592.38 |  752057.27 |   261.23 |  14535.10 |  98.104
            big (bets >= 4 BTC) |   114417 |   52348           |   61777 |     292 | 2635378.11 | 2579381.45 | 23628.70 |  55996.66 |  97.875
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  3637073 | 1504500           | 2115872 |   16701 | 3401970.49 | 3331438.72 | 23889.93 |  70531.76 |  97.927
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      70531.76560380 BTC (2.073%)
Cumulative Fees Paid:        2837.93797500 BTC
SD Profit after fees:       67693.82762880 BTC (1.990%)
Pending Liabilities:          -74.93245984 BTC
Final SD Profit:            67768.76008864 BTC (1.992%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 11423662  :  SatoshiDice Tx:  6698542  (58.6%)
Blockchain MB:   4904.6  :  SatoshiDice MB:   2753.4  (56.1%)

[ThickAsThieves]

They didnt shut off betting, just payouts afaik.

[dooglus]

They didnt shut off betting, just payouts afaik.

I think my graph only shows payouts though.  It ignores bets until they have been paid out.

[miscreanity]

They didnt shut off betting, just payouts afaik.

I think my graph only shows payouts though.  It ignores bets until they have been paid out.

It seems to be as expected since the analysis is done by block - a chart of betting would've levelled off for ~6 hours or so, but payouts would follow the consistent climb. Transactions still had to be processed into the blockchain block by block.

[Dabs]

Sorry, I was stressed out with other business yesterday when you posted about this.

One problem with your request is that there's not really a definitive ordering on the bets.  Do we count the time the bet transaction was seen by some random host on the network?  Or the timestamp on the block it got into?  Or the depth of the block?  (Blocks aren't always in order of timestamp).  Or do we count the order that the bets were paid out?

There are lots of different ways of ordering the bets, which will change the longest sequence of losses.

Another problem, and what puts me off from looking into this, is "who cares".  Are you wanting the information to check whether the dice rolls are random?  ie. "we would expect to see a chain of 10 losses but the longest chain is 20 so SDICE is cheating"?  Because other than that I don't really see the point.  Runs of good and bad luck happen, due to the random nature of the dice rolls.  Suppose I go through the blockchain and find that once there were 21 losses on the 50% game in a row, given some arbitrary ordering of the bets.  Then what?

I guess I'll do this when I'm bored, but I don't expect it to tell us anything very useful or interesting.  Maybe I'm just being grouchy though.  That happens too. 

Thanks for the tip organofcorti - that's very kind of you. 

Hi, Sorry for adding to the stress. I guess you just pick one way of ordering it, and use that for consistency. Actually, a real world example of a 50% game had 26 losses in a row, in a casino.

If you're bored ... you can do this. When you got more bored, you can also do the different ways of ordering.

I don't know if it will tell us anything useful, but I think it will be interesting. And the minute you post your analysis, all the gamblers who are reading this thread will suddenly start betting a little bit more, thinking that they can attempt 21 consecutive attempts to martinegale from 0.01 to 500. (I just might do it, hehe.)

If you're being grouchy, let me know what I need to download and I will try to do this. (Or at least someone else will, so you have less stress.)

Unfortunately, I'm on a crappy OS machine (windows), so I don't know if it's even possible.

[organofcorti]

Very nice graphs.  The 2nd one reminds me of big scary needles rather than violins.

1. The number and size of Bets on SatoshiDice are increasing;

Is that true?  They increased for a few months Dec 2012 to early Feb this year, but other than that has there been an upwards trend?

A version of your first graph with the horizontal scale magnified about x10 would let us see that - just truncate the high values while the whale was playing.

I plotted your request below - normalising to the volume of bets under 50btc (as an arbitrary cut off). I also plotted all bets before December, to make those trends a bit more obvious, too. Tbh, I should have written "the size and volume of bets in December 2012, January 2013 and February 2013 have increased compared to the previous months". Even so, it's not obvious from the plots.

I'm working on something similar to the "percentile" plots I did that will hopefully show this sort of information in a more intuitive and cntinuous way than either the violin - er scary hypodermic needle - plots or the percentile plots. Hopefully I'll be able to post it tonight.

[organofcorti]

I played around and got some quite beautiful tile plots and contour plots, but they didn't really help show bet size of volume trends. Then I realised that all I had to do was use the proportional violin plots and use colour as a guide to the volume. I hope this works for you. Please don't tell me you're colour blind - I didn't use the colour blind palette.

The two below just use different colour schema.

[bb113]

Amazing charts OoC, does GGplot let you do multiple axes? It would be good to overlay a line showing total number of bets per month, or perhaps median number per day as well as max/day and min/day for each month.

[miscreanity]

I played around and got some quite beautiful tile plots and contour plots, but they didn't really help show bet size of volume trends. Then I realised that all I had to do was use the proportional violin plots and use colour as a guide to the volume. I hope this works for you. Please don't tell me you're colour blind - I didn't use the colour blind palette.

If the 2-3 month cycles are valid and hold, May-June ought to be the start of a very active period.

[organofcorti]

Amazing charts OoC, does GGplot let you do multiple axes? It would be good to overlay a line showing total number of bets per month, or perhaps median number per day as well as max/day and min/day for each month.

ggplot doesn't do multiple axes. I read (I think) that the devs planned on support for multiple axes when the axes scale linearly to each other, but they don't plan on the sort of multiple axes you're thinking of. I ccould annotate the chart with the actual numbers, but that's not very pretty.

So, number of bets as well as volume of betting? I have a think about it. I hadn't considered that, although it's might be interesting data to have.

[dooglus]

Those colourful violin plots are very nice.   

Meanwhile, back to the regular ugly graphs...

Total of 81 bets unaccounted for.

Results: 2013-Mar-13 02:23pm (up to block 225709)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    99299 |       1 (0.00001) |   97728 |    1570 |    1148.91 |    1280.22 |   125.02 |   -131.31 | 111.429
 1dice1Qf4       2      0.00003 |     5203 |       0 (0.00000) |    4680 |     523 |      88.80 |       0.03 |    20.45 |     88.77 |   0.038
 1dice2pxm       4      0.00006 |     7650 |       1 (0.00014) |    7196 |     453 |     116.02 |     160.00 |    12.83 |    -43.98 | 137.909
 1dice2vQo       8      0.00012 |    11977 |       5 (0.00043) |   11510 |     462 |     224.75 |     431.97 |    10.07 |   -207.22 | 192.203
 1dice2WmR      16      0.00024 |    13667 |       1 (0.00008) |   13225 |     441 |     459.72 |       4.87 |    22.07 |    454.84 |   1.061
 1dice2xkj      32      0.00049 |    17583 |       6 (0.00035) |   17176 |     401 |     960.20 |     814.00 |     1.39 |    146.19 |  84.775
 1dice2zdo      64      0.00098 |    18802 |      20 (0.00109) |   18318 |     464 |    1373.62 |     573.00 |    55.81 |    800.62 |  41.715
 1dice37Ee     128      0.00195 |    19574 |      37 (0.00194) |   19079 |     458 |    2339.11 |    1557.69 |    48.39 |    781.42 |  66.593
 1dice3jkp     256      0.00391 |    24252 |     105 (0.00440) |   23763 |     384 |    4580.14 |    7357.28 |    13.20 |  -2777.14 | 160.634
 1dice4J1m     512      0.00781 |    33412 |     268 (0.00819) |   32444 |     700 |    5728.28 |    5673.66 |    10.03 |     54.62 |  99.046
 1dice5wwE    1000      0.01526 |   117777 |    1787 (0.01524) |  115468 |     522 |   36563.46 |   32007.45 |     2.07 |   4556.00 |  87.539
 1dice61SN    1500      0.02289 |    24571 |     570 (0.02354) |   23645 |     356 |    7656.00 |    8165.57 |    15.09 |   -509.57 | 106.656
 1dice6DPt    2000      0.03052 |    74115 |    2295 (0.03113) |   71422 |     398 |   37546.55 |   33664.34 |     9.37 |   3882.21 |  89.660
 1dice6gJg    3000      0.04578 |    28754 |    1309 (0.04623) |   27007 |     438 |    9216.93 |   10005.02 |    25.18 |   -788.09 | 108.550
 1dice6GV5    4000      0.06104 |    34595 |    2111 (0.06172) |   32092 |     392 |    7615.02 |    7422.49 |    31.35 |    192.53 |  97.472
 1dice6wBx    6000      0.09155 |    47213 |    4314 (0.09224) |   42453 |     446 |   16023.99 |   17754.90 |     7.29 |  -1730.91 | 110.802
 1dice6YgE    8000      0.12207 |   182495 |   22345 (0.12278) |  159640 |     510 |   91427.22 |   90252.05 |   100.47 |   1175.16 |  98.715
 1dice7EYz   12000      0.18311 |    94075 |   17150 (0.18335) |   76389 |     536 |  170500.40 |  172503.68 |  3314.89 |  -2003.28 | 101.175
 1dice7fUk   16000      0.24414 |   243386 |   59221 (0.24388) |  183604 |     561 |  366002.29 |  352136.29 |  2322.43 |  13866.00 |  96.211
 1dice7W2A   24000      0.36621 |   244037 |   89577 (0.36796) |  153867 |     593 |  583031.35 |  574788.43 |  1013.25 |   8242.92 |  98.586
 1dice8EMZ   32000      0.48828 |  1118230 |  544976 (0.48807) |  571607 |    1647 |  872360.39 |  854669.94 |  2924.95 |  17690.45 |  97.972
 1dice97EC   32768      0.50000 |   604294 |  301452 (0.49979) |  301711 |    1131 |  660037.16 |  643964.23 |  6521.23 |  16072.92 |  97.565
 1dice9wcM   48000      0.73242 |   340319 |  249684 (0.73504) |   90002 |     633 |  298705.42 |  291222.38 |  5455.27 |   7483.03 |  97.495
 1dicec9k7   52000      0.79346 |    74537 |   58760 (0.79383) |   15261 |     516 |   61463.64 |   60155.50 |  1187.55 |   1308.14 |  97.872
 1dicegEAr   56000      0.85449 |    63042 |   53532 (0.85696) |    8935 |     575 |   77608.81 |   76990.19 |   400.55 |    618.62 |  99.203
 1diceDCd2   60000      0.91553 |    96782 |   88168 (0.91620) |    8064 |     550 |   70754.87 |   69949.74 |     0.52 |    805.13 |  98.862
 1dice9wVt   64000      0.97656 |    16654 |   15234 (0.97962) |     317 |    1103 |   24018.55 |   23606.13 |   240.21 |    412.42 |  98.283
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           small (bets < 4 BTC) |  3541669 | 1460455           | 2064743 |   16471 |  769737.69 |  755242.21 |   262.34 |  14495.48 |  98.117
            big (bets >= 4 BTC) |   114626 |   52474           |   61860 |     292 | 2637814.03 | 2581868.96 | 23628.70 |  55945.06 |  97.879
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                                |  3656295 | 1512929           | 2126603 |   16763 | 3407551.72 | 3337111.17 | 23891.04 |  70440.55 |  97.933
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SD Profit before fees:      70440.55165630 BTC (2.067%)
Cumulative Fees Paid:        2857.17677500 BTC
SD Profit after fees:       67583.37488130 BTC (1.983%)
Pending Liabilities:          -57.51910827 BTC
Final SD Profit:            67640.89398957 BTC (1.985%)
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Since Satoshi Dice started, there have been:
Blockchain Tx: 11481028  :  SatoshiDice Tx:  6734316  (58.7%)
Blockchain MB:   4930.3  :  SatoshiDice MB:   2768.0  (56.1%)