Satoshi Dice -- Statistical Analysis

[dooglus]

Is it possible paste a list of all bets, rather than the average size per time period (I'm guessing it's per block)?

I don't have a list of all bets but can generate it.

OK, here it is.

  http://dooglus.com/allbets.txt.bz2

It's 4.8MB compressed,  69.5 MB uncompressed, one bet per line.  Time (seconds since 1970) and bet size (in satoshis):

1362966232 40000000
1335029321 2000000
1335029321 500000000
[...]
1362966232 40000000
1362966232 12300000
1362966232 150000000

The timestamp is the timestamp of the block which paid the bet out.

[solex]

dooglus, quick q if you would oblige...

Two days ago Erik implemented a change which returns 0.5% on a losing bet. The significant benefit of this to Bitcoin is that unspendable bitdust utxo is nearly eliminated. Only bets of <=0.06 BTC create such outputs.

For information can you advise what percentage of SD bets are 0.06 or less?
(the last two days is probably fine enough for a sampling).

Edit. Don't bother. I saw your file above and sampled that and about 54% of recent bets are 0.06 or less. Wow. Most of these are really small!
In any case, an fx rate of $200 will mean that all utxo since the change will be spendable. This is not a permanent problem then...

[BTCdude007]

Good to see that SD is break-even for the month. Hopefully, the rest of the month produces dividends.

[smickles]

Thanks for keeping it up Dooglus, the charts and the level-headed responses. I sent a little bit your way again

[dooglus]

Two days ago Erik implemented a change which returns 0.5% on a losing bet. The significant benefit of this to Bitcoin is that unspendable bitdust utxo is nearly eliminated. Only bets of <=0.06 BTC create such outputs.

Do you have a reference for that?  I must have missed it.  I thought losing bets have always paid out half a percent.  Here's what I think it probably my biggest ever losing SD bet: http://blockchain.info/tx-index/12114983

I bet 6 BTC and got 0.03 back - that's 0.5%.

Edit: my bad - I once lost 31 BTC and got 0.155 BTC back, but still it was 0.5%.

So I guess I don't know what has changed...

Thanks for keeping it up Dooglus, the charts and the level-headed responses. I sent a little bit your way again

Thank you very much.  

[organofcorti]

Is it possible paste a list of all bets, rather than the average size per time period (I'm guessing it's per block)?

I don't have a list of all bets but can generate it.

OK, here it is.

  http://dooglus.com/allbets.txt.bz2

Thanks!

Weekly mean and + 1 sigma
You already posted some of these and I'm including this one as a comparison to the next plots.

Here are a couple of other ways to visualise the data. Boxplots weren't very useful since a large portion of the large bets were considered "outliers".

Violin plots.
If you haven't come across a violin plot before, think of it as a vertical density plot, width being proportional to number of bets for a particular amount of btc. The advantge of this type of plot is that it also allows easy comparison of limits (compared to a density plot) and provides a more intuitive understanding of the results than traditional boxplots. The plot shows clearly that bettors prefer even amounts to bet - for example 0.01 btc, 0.02 btc, 0.05 btc, 0.1 btc, 0.2 btc etc, and that most are probably not martingaling much lately.

Percentile plots.
These are similar to the mean and sd plot, instead showing percentiles. For those not familiar, if you place the bests in order of size, the nth percentile bet is the value of the bet below which n percent of bet values fall. The 50th percentile bet is the median bet.

Are any of these good visualisation tools for most readers? If so, let me know.

Thanks for the data, dooglus. That was interesting.

Edit: These plots can be done on a much shorter timescale, such as the ones you posted earlier.

[wisard]

Thank you.
The violin plot is pretty cool.

[ThickAsThieves]

So based on the plots, would it be a fair assessment to say that SDICE should consider lowering the minimum bid to increase revenue?

[organofcorti]

So based on the plots, would it be a fair assessment to say that SDICE should consider lowering the minimum bid to increase revenue?

No, I don't think so. In this case large number of tiny bets doesn't equal a small number of extremely large bets. The large bets might only make up a small percentage of bets, but they are the largest proportion of overall bet value.

[dooglus]

Violin plots.
If you haven't come across a violin plot before, think of it as a vertical density plot, width being proportional to number of bets for a particular amount of btc. The advantge of this type of plot is that it also allows easy comparison of limits (compared to a density plot) and provides a more intuitive understanding of the results than traditional boxplots. The plot shows clearly that bettors prefer even amounts to bet - for example 0.01 btc, 0.02 btc, 0.05 btc, 0.1 btc, 0.2 btc etc, and that most are probably not martingaling much lately.

That's cool.

I should probably mention for completeness than my data doesn't include any bets that were refunded for being too big or too small.  That's why you see nothing at all less than 0.01 BTC in 2013.

I'm wondering if it would be interesting to plot a violin plot where the thickness indicates the volume (in BTC) bet at each price rather than the number of bets at that price.  Then we'd be able to see that

large bets might only make up a small percentage of bets, but they are the largest proportion of overall bet value

for ourselves. 

[dooglus]

New highs!

Total of 48 bets unaccounted for.

Results: 2013-Mar-11 01:15pm (up to block 225420)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    98490 |       1 (0.00001) |   96941 |    1548 |    1137.79 |    1280.17 |   123.19 |   -142.37 | 112.513
 1dice1Qf4       2      0.00003 |     5168 |       0 (0.00000) |    4645 |     523 |      87.68 |       0.02 |    20.45 |     87.65 |   0.032
 1dice2pxm       4      0.00006 |     7621 |       1 (0.00014) |    7167 |     453 |     115.21 |     160.00 |    12.83 |    -44.78 | 138.866
 1dice2vQo       8      0.00012 |    11927 |       5 (0.00044) |   11463 |     459 |     224.05 |     431.97 |    10.07 |   -207.92 | 192.800
 1dice2WmR      16      0.00024 |    13566 |       1 (0.00008) |   13127 |     438 |     455.75 |       4.85 |    22.06 |    450.89 |   1.066
 1dice2xkj      32      0.00049 |    17254 |       6 (0.00036) |   16848 |     400 |     941.60 |     813.91 |     1.38 |    127.68 |  86.439
 1dice2zdo      64      0.00098 |    18540 |      19 (0.00105) |   18058 |     463 |    1353.85 |     451.97 |    55.81 |    901.88 |  33.384
 1dice37Ee     128      0.00195 |    19480 |      37 (0.00195) |   18986 |     457 |    2332.33 |    1557.65 |    48.39 |    774.67 |  66.785
 1dice3jkp     256      0.00391 |    24201 |     105 (0.00441) |   23712 |     384 |    4578.00 |    7357.27 |    13.20 |  -2779.26 | 160.709
 1dice4J1m     512      0.00781 |    33219 |     266 (0.00818) |   32254 |     699 |    5694.27 |    5648.50 |    10.02 |     45.77 |  99.196
 1dice5wwE    1000      0.01526 |   116838 |    1775 (0.01526) |  114546 |     517 |   36342.08 |   31626.90 |     2.06 |   4715.17 |  87.026
 1dice61SN    1500      0.02289 |    24479 |     567 (0.02350) |   23556 |     356 |    7651.70 |    8160.42 |    15.09 |   -508.71 | 106.648
 1dice6DPt    2000      0.03052 |    73453 |    2279 (0.03120) |   70776 |     398 |   37295.68 |   33638.60 |     9.37 |   3657.07 |  90.194
 1dice6gJg    3000      0.04578 |    28615 |    1297 (0.04603) |   26881 |     437 |    9194.02 |   10002.07 |    25.18 |   -808.04 | 108.789
 1dice6GV5    4000      0.06104 |    34425 |    2098 (0.06164) |   31936 |     391 |    7610.48 |    7419.65 |    31.35 |    190.83 |  97.493
 1dice6wBx    6000      0.09155 |    46530 |    4253 (0.09228) |   41837 |     440 |   15975.14 |   17711.64 |     7.27 |  -1736.49 | 110.870
 1dice6YgE    8000      0.12207 |   180548 |   22108 (0.12279) |  157935 |     505 |   90960.97 |   89585.15 |   100.46 |   1375.81 |  98.487
 1dice7EYz   12000      0.18311 |    92714 |   16905 (0.18339) |   75276 |     533 |  169888.80 |  171507.93 |  3314.88 |  -1619.13 | 100.953
 1dice7fUk   16000      0.24414 |   240584 |   58572 (0.24402) |  181456 |     556 |  365294.35 |  351490.89 |  2322.41 |  13803.46 |  96.221
 1dice7W2A   24000      0.36621 |   241822 |   88780 (0.36802) |  152457 |     585 |  582461.96 |  574219.91 |  1013.23 |   8242.04 |  98.585
 1dice8EMZ   32000      0.48828 |  1109711 |  540813 (0.48806) |  567264 |    1634 |  869074.47 |  851440.31 |  2924.92 |  17634.16 |  97.971
 1dice97EC   32768      0.50000 |   596916 |  297754 (0.49975) |  298049 |    1113 |  658368.77 |  642306.17 |  6521.16 |  16062.60 |  97.560
 1dice9wcM   48000      0.73242 |   336630 |  246989 (0.73508) |   89013 |     628 |  297651.44 |  290236.94 |  5455.26 |   7414.49 |  97.509
 1dicec9k7   52000      0.79346 |    74000 |   58318 (0.79360) |   15167 |     515 |   61028.28 |   59670.36 |  1187.54 |   1357.91 |  97.775
 1dicegEAr   56000      0.85449 |    61794 |   52443 (0.85656) |    8782 |     569 |   77033.81 |   76413.99 |   400.53 |    619.82 |  99.195
 1diceDCd2   60000      0.91553 |    95203 |   86724 (0.91615) |    7937 |     542 |   70370.78 |   69576.47 |     0.49 |    794.31 |  98.871
 1dice9wVt   64000      0.97656 |    16496 |   15095 (0.97962) |     314 |    1087 |   23987.67 |   23575.20 |   240.18 |    412.46 |  98.280
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  3506070 | 1444956           | 2044776 |   16338 |  764128.50 |  749718.49 |   260.20 |  14410.00 |  98.114
            big (bets >= 4 BTC) |   114154 |   52255           |   61607 |     292 | 2632982.57 | 2576570.54 | 23628.70 |  56412.02 |  97.857
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  3620224 | 1497211           | 2106383 |   16630 | 3397111.07 | 3326289.03 | 23888.90 |  70822.03 |  97.915
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      70822.03769213 BTC (2.085%)
Cumulative Fees Paid:        2821.04347500 BTC
SD Profit after fees:       68000.99421713 BTC (2.002%)
Pending Liabilities:          113.38859173 BTC
Final SD Profit:            67887.60562540 BTC (1.998%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 11375123  :  SatoshiDice Tx:  6667948  (58.6%)
Blockchain MB:   4882.1  :  SatoshiDice MB:   2740.3  (56.1%)

[solex]

Two days ago Erik implemented a change which returns 0.5% on a losing bet. The significant benefit of this to Bitcoin is that unspendable bitdust utxo is nearly eliminated. Only bets of <=0.06 BTC create such outputs.

Do you have a reference for that?  I must have missed it.  I thought losing bets have always paid out half a percent.  Here's what I think it probably my biggest ever losing SD bet: http://blockchain.info/tx-index/12114983

I bet 6 BTC and got 0.03 back - that's 0.5%.

Edit: my bad - I once lost 31 BTC and got 0.155 BTC back, but still it was 0.5%.

So I guess I don't know what has changed...

Thanks for keeping it up Dooglus, the charts and the level-headed responses. I sent a little bit your way again

Thank you very much.  

Interesting! My mistake then.

I took this at face value:
https://bitcointalk.org/index.php?topic=150493.msg1603935#msg1603935

because I kept seeing comments like this beforehand:
https://bitcointalk.org/index.php?topic=150405.msg1601927#msg1601927

There has been some SD change because those excellent violin plots show clearly that the min bet size increased 10x at the end of 2012.

[dooglus]

Interesting! My mistake then.

I took this at face value:
https://bitcointalk.org/index.php?topic=150493.msg1603935#msg1603935

OK, I get it now.  They always paid 0.5% for a losing bet, but they used to subtract the transaction fee of 0.0005 (50k satoshis) from that, often leaving less than 0, so they'd send you a token 1 satoshi.  Now they don't subtract the transaction fee, so the min bet (0.01) pays out the full 0.5% when you lose, which is 0.00005000 BTC, or 5k satoshis.

That will result in less dust spam, or at least more easily spendable dust spam.

[solex]

Interesting! My mistake then.

I took this at face value:
https://bitcointalk.org/index.php?topic=150493.msg1603935#msg1603935

OK, I get it now.  They always paid 0.5% for a losing bet, but they used to subtract the transaction fee of 0.0005 (50k satoshis) from that, often leaving less than 0, so they'd send you a token 1 satoshi.  Now they don't subtract the transaction fee, so the min bet (0.01) pays out the full 0.5% when you lose, which is 0.00005000 BTC, or 5k satoshis.

That will result in less dust spam, or at least more easily spendable dust spam.

Aha. The mist clears in this jungle.

[Dabs]

I don't know if its in this thread anywhere, but is there data available that shows number of consecutive wins or losses, basically streaks? For example, in the 50% bet, what is the longest winning and losing streak? It's like heads or tails, but with the number of bets already made, has there been anything similar to the Monte Carlo gambler's fallacy of 26 consecutive losses?

Of course, you can't see this for each person unless one person uses the same address all the time (like from Bitcoin Spinner.)

I'm interested in all the other categories as well, not just the 50%. I'm curious what is the longest losing streak in the higher win odds (better than 50%) as it won't make much sense in the lower odds since the less than 1 (0.0015%) is obviously going to have 50,000+ consecutive losses.

[zebedee]

In any case, an fx rate of $200 will mean that all utxo since the change will be spendable. This is not a permanent problem then...

They were always spendable, apart from to those who wished to make a mountain out of a molehill.

[solex]

In any case, an fx rate of $200 will mean that all utxo since the change will be spendable. This is not a permanent problem then...

They were always spendable, apart from to those who wished to make a mountain out of a molehill.

I believe you! I need to learn more about bitcoin tx minutiae before I can begin to argue this 

[organofcorti]

I don't know if its in this thread anywhere, but is there data available that shows number of consecutive wins or losses, basically streaks? For example, in the 50% bet, what is the longest winning and losing streak? It's like heads or tails, but with the number of bets already made, has there been anything similar to the Monte Carlo gambler's fallacy of 26 consecutive losses?

Of course, you can't see this for each person unless one person uses the same address all the time (like from Bitcoin Spinner.)

I'm interested in all the other categories as well, not just the 50%. I'm curious what is the longest losing streak in the higher win odds (better than 50%) as it won't make much sense in the lower odds since the less than 1 (0.0015%) is obviously going to have 50,000+ consecutive losses.

We discussed this earlier in the thread, but theoretically:

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)

[organofcorti]

I'm wondering if it would be interesting to plot a violin plot where the thickness indicates the volume (in BTC) bet at each price rather than the number of bets at that price.  Then we'd be able to see that

large bets might only make up a small percentage of bets, but they are the largest proportion of overall bet value

for ourselves. 

I was thinking the same thing last night but it was getting late, so I left it until now.

The first plot below shows to volume, and the monthly volumes can be directly compared to each other (March is low because it's only one third the way through). However it doesn't really show much detail for most months which had low volumes compared to January 2013.

The second plot makes the maximum width equal for each month, meaning the volume is presented as a proportion of the total monthly volume. This means that months cannot be compared directly, but much more detail is presented for any given month.

Three things are clear:
1. The number and size of Bets on SatoshiDice are increasing;
2. People prefer to bet "round numbers" of btc - this is the reason for the "wiggliness" of the plots.
3. The maximum bet size often produces the most monthly volume; the largest portion of most monthly volumes are due to bets 1btc or greater.

Also, from these plots I'd expect the month with the greatest volume to be January 2013, followed by December 2012 and then February 2013.

I also reckon I could sell these plots to psychiatrists as Rorshach ink blots. 

[StarenseN]

I'm wondering if it would be interesting to plot a violin plot where the thickness indicates the volume (in BTC) bet at each price rather than the number of bets at that price.  Then we'd be able to see that

large bets might only make up a small percentage of bets, but they are the largest proportion of overall bet value

for ourselves.  

I was thinking the same thing last night but it was getting late, so I left it until now.

The first plot below shows to volume, and the monthly volumes can be directly compared to each other (March is low because it's only one third the way through). However it doesn't really show much detail for most months which had low volumes compared to January 2013.

The second plot makes the maximum width equal for each month, meaning the volume is presented as a proportion of the total monthly volume. This means that months cannot be compared directly, but much more detail is presented for any given month.

Three things are clear:
1. The number and size of Bets on SatoshiDice are increasing;
2. People prefer to bet "round numbers" of btc - this is the reason for the "wiggliness" of the plots.
3. The maximum bet size often produces the most monthly volume; the largest portion of most monthly volumes are due to bets 1btc or greater.

Also, from these plots I'd expect the month with the greatest volume to be January 2013, followed by December 2012 and then February 2013.

I also reckon I could sell these plots to psychiatrists as Rorshach ink blots.  

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