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Topic: Satoshi Dice -- Statistical Analysis - page 33. (Read 192896 times)

legendary
Activity: 2940
Merit: 1333
March 11, 2013, 03:19:40 PM
New highs!

Quote
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%)



legendary
Activity: 2940
Merit: 1333
March 11, 2013, 03:01:25 PM
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

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

for ourselves.  Smiley
donator
Activity: 2058
Merit: 1007
Poor impulse control.
March 11, 2013, 10:40:52 AM
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.
hero member
Activity: 518
Merit: 500
March 11, 2013, 10:34:05 AM
So based on the plots, would it be a fair assessment to say that SDICE should consider lowering the minimum bid to increase revenue?
sr. member
Activity: 272
Merit: 250
March 11, 2013, 09:05:42 AM
Thank you.
The violin plot is pretty cool.
donator
Activity: 2058
Merit: 1007
Poor impulse control.
March 11, 2013, 08:41:24 AM
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.
legendary
Activity: 2940
Merit: 1333
March 11, 2013, 05:46:11 AM
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 Wink

Thank you very much.  Smiley
sr. member
Activity: 446
Merit: 250
March 11, 2013, 01:32:12 AM
Thanks for keeping it up Dooglus, the charts and the level-headed responses. I sent a little bit your way again Wink
sr. member
Activity: 686
Merit: 250
March 11, 2013, 01:12:50 AM
Good to see that SD is break-even for the month. Hopefully, the rest of the month produces dividends.
legendary
Activity: 1078
Merit: 1006
100 satoshis -> ISO code
March 11, 2013, 12:50:52 AM
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...
legendary
Activity: 2940
Merit: 1333
March 10, 2013, 11:53:28 PM
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):

Quote
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.
legendary
Activity: 2940
Merit: 1333
March 10, 2013, 04:02:49 PM
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.  I'm a little busy at the moment getting ready to give back $82k that I've become kind of attached to tomorrow.  But I'll prepare the bet list when I get a chance.

Quote
Total of 24 bets unaccounted for.

Results: 2013-Mar-10 01:58pm (up to block 225242)

   Address  Target   Should Win |    #Bets |        Win        |   Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP  
----------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    97797 |       1 (0.00001) |   96258 |    1538 |    1128.50 |    1280.12 |   122.46 |   -151.61 | 113.435
 1dice1Qf4       2      0.00003 |     5152 |       0 (0.00000) |    4632 |     520 |      87.00 |       0.02 |    19.91 |     86.98 |   0.028
 1dice2pxm       4      0.00006 |     7607 |       1 (0.00014) |    7153 |     453 |     114.74 |     159.99 |    12.83 |    -45.24 | 139.433
 1dice2vQo       8      0.00012 |    11922 |       5 (0.00044) |   11460 |     457 |     223.84 |     431.97 |    10.07 |   -208.13 | 192.980
 1dice2WmR      16      0.00024 |    13552 |       1 (0.00008) |   13113 |     438 |     454.34 |       4.85 |    22.06 |    449.49 |   1.068
 1dice2xkj      32      0.00049 |    17221 |       6 (0.00036) |   16815 |     400 |     940.35 |     813.90 |     1.38 |    126.44 |  86.553
 1dice2zdo      64      0.00098 |    18504 |      19 (0.00105) |   18022 |     463 |    1351.72 |     451.96 |    55.81 |    899.76 |  33.436
 1dice37Ee     128      0.00195 |    19441 |      36 (0.00190) |   18949 |     456 |    2329.67 |    1547.65 |    48.38 |    782.02 |  66.432
 1dice3jkp     256      0.00391 |    24171 |     105 (0.00441) |   23682 |     384 |    4574.58 |    7357.25 |    13.20 |  -2782.67 | 160.829
 1dice4J1m     512      0.00781 |    33135 |     266 (0.00820) |   32172 |     697 |    5681.90 |    5648.44 |    10.01 |     33.46 |  99.411
 1dice5wwE    1000      0.01526 |   116106 |    1765 (0.01527) |  113829 |     512 |   35674.60 |   30946.84 |     2.05 |   4727.76 |  86.748
 1dice61SN    1500      0.02289 |    24440 |     564 (0.02342) |   23520 |     356 |    7642.67 |    8116.88 |    15.09 |   -474.20 | 106.205
 1dice6DPt    2000      0.03052 |    73050 |    2269 (0.03123) |   70385 |     396 |   36599.03 |   33294.69 |     9.36 |   3304.34 |  90.972
 1dice6gJg    3000      0.04578 |    28583 |    1295 (0.04601) |   26853 |     435 |    9185.74 |    9992.64 |    25.17 |   -806.90 | 108.784
 1dice6GV5    4000      0.06104 |    34384 |    2095 (0.06163) |   31898 |     391 |    7601.72 |    7417.69 |    31.35 |    184.03 |  97.579
 1dice6wBx    6000      0.09155 |    46102 |    4217 (0.09235) |   41447 |     438 |   15893.24 |   17665.29 |     7.26 |  -1772.04 | 111.150
 1dice6YgE    8000      0.12207 |   179501 |   21980 (0.12280) |  157017 |     504 |   90316.60 |   88902.10 |   100.45 |   1414.49 |  98.434
 1dice7EYz   12000      0.18311 |    91901 |   16749 (0.18331) |   74622 |     530 |  169299.83 |  171039.94 |  3314.87 |  -1740.10 | 101.028
 1dice7fUk   16000      0.24414 |   238889 |   58142 (0.24395) |  180193 |     554 |  364448.62 |  350823.74 |  2322.40 |  13624.88 |  96.262
 1dice7W2A   24000      0.36621 |   240217 |   88169 (0.36793) |  151469 |     579 |  582144.14 |  573880.85 |  1013.21 |   8263.28 |  98.581
 1dice8EMZ   32000      0.48828 |  1104941 |  538454 (0.48803) |  564867 |    1620 |  865098.75 |  847579.77 |  2924.87 |  17518.97 |  97.975
 1dice97EC   32768      0.50000 |   590929 |  294737 (0.49970) |  295093 |    1099 |  656935.31 |  641231.25 |  6521.11 |  15704.05 |  97.609
 1dice9wcM   48000      0.73242 |   332680 |  244096 (0.73511) |   87959 |     625 |  297266.69 |  289904.63 |  5455.25 |   7362.06 |  97.523
 1dicec9k7   52000      0.79346 |    73546 |   57965 (0.79370) |   15066 |     515 |   60823.13 |   59474.12 |  1187.54 |   1349.00 |  97.782
 1dicegEAr   56000      0.85449 |    61170 |   51901 (0.85640) |    8703 |     566 |   76787.21 |   76164.40 |   400.52 |    622.81 |  99.189
 1diceDCd2   60000      0.91553 |    94091 |   85718 (0.91627) |    7833 |     540 |   70164.87 |   69369.23 |     0.48 |    795.64 |  98.866
 1dice9wVt   64000      0.97656 |    16365 |   14974 (0.97972) |     310 |    1081 |   23964.48 |   23553.02 |   240.17 |    411.45 |  98.283
----------------------------------------------------------------------------------------------------------------------------------------------
           small (bets < 4 BTC) |  3481872 | 1433439           | 2032178 |   16255 |  760085.53 |  745835.80 |   258.71 |  14249.73 |  98.125
            big (bets >= 4 BTC) |   113525 |   52091           |   61142 |     292 | 2626647.87 | 2571217.53 | 23628.70 |  55430.33 |  97.890
----------------------------------------------------------------------------------------------------------------------------------------------
                                |  3595397 | 1485530           | 2093320 |   16547 | 3386733.40 | 3317053.33 | 23887.41 |  69680.07 |  97.943
----------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:      69680.07288378 BTC (2.057%)
Cumulative Fees Paid:        2796.14317500 BTC
SD Profit after fees:       66883.92970878 BTC (1.975%)
Pending Liabilities:           -5.93485875 BTC
Final SD Profit:            66889.86456753 BTC (1.975%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 11312047  :  SatoshiDice Tx:  6621333  (58.5%)
Blockchain MB:   4853.5  :  SatoshiDice MB:   2720.6  (56.1%)



donator
Activity: 2058
Merit: 1007
Poor impulse control.
March 10, 2013, 03:43:23 AM
This is where boxplots or violin plots might be more useful. If you're not sure what I mean (and tbh I haven't exactly explained myself well) if you post the data (or pm me) I'll post some examples.

http://dooglus.com/sd-data.txt.gz has 2 numbers per line.  Time (seconds since 1970) and average bet size in the block with that timestamp:

Quote
1362850998 0.0800365152562
1362851859 0.44658473297
1362852003 5.26315630659e-05

Is it possible paste a list of all bets, rather than the average size per time period (I'm guessing it's per block)?
legendary
Activity: 2940
Merit: 1333
March 10, 2013, 03:32:05 AM
It also might be interesting to see what fraction of users are selecting to have winnings routed to another address. 
If the money goes back to the same address, it's hardly a very useful launderer.

Well, if I send my money to satoshidice with a public note saying "send my winnings back to 1MyOtherSecretAddress so they don't know it's me" then that's not a very useful laundry either.

I've seen this "SDICE launders money" argument before, but I think it's bogus.  Everything they do is public, so is absolutely not laundering money.
legendary
Activity: 1264
Merit: 1008
March 10, 2013, 03:24:14 AM
All bets * (1-.981).  That is roughly how much the house is expected to rake.

Think of SatoshiDice as a laundrer, it returns you 98% (roughly) of your money over time.  Now some people play wierdly trying to "beat the numbers" and they might actually lose 100% of their money.  That sweetens Satoshi's profits.  But as Dooglus has shown, pretty much it's just laundering and taking a 1.9% fee.

Thanks for the stats folks Smiley
It also might be interesting to see what fraction of users are selecting to have winnings routed to another address. 
If the money goes back to the same address, it's hardly a very useful launderer.

legendary
Activity: 2940
Merit: 1333
March 10, 2013, 03:20:25 AM
This is where boxplots or violin plots might be more useful. If you're not sure what I mean (and tbh I haven't exactly explained myself well) if you post the data (or pm me) I'll post some examples.

http://dooglus.com/sd-data.txt.gz has 2 numbers per line.  Time (seconds since 1970) and average bet size in the block with that timestamp:

Quote
1362850998 0.0800365152562
1362851859 0.44658473297
1362852003 5.26315630659e-05
donator
Activity: 2058
Merit: 1007
Poor impulse control.
March 10, 2013, 12:32:56 AM
I don't have data readily available about the average bet size

... but I do now.

This is where boxplots or violin plots might be more useful. If you're not sure what I mean (and tbh I haven't exactly explained myself well) if you post the data (or pm me) I'll post some examples.
legendary
Activity: 2940
Merit: 1333
March 09, 2013, 11:16:32 PM
I don't have data readily available about the average bet size

... but I do now.

This graph shows the moving average bet size (in BTC) over the previous 7 days:



I also tried using a 1-day window, but it's very spiky:



and here's the average over the previous 28 days:

legendary
Activity: 2940
Merit: 1333
March 09, 2013, 09:35:00 PM
If a million people bet 1 BTC each, or 100k people bet 10 BTC each, the total bet volume is 1 million BTC either way, and the house will keep 19k BTC on average in both cases.

But this assumes that the average bet will remain in the same range.

My contention is that the average bet will keep on reducing as the BTC / USD rate keeps on increasing. The amount of total BTC bet on the first 100,000 bets will be higher than the amount of BTC made on the next 100,000. (I have not looked at the numbers and I don't know if I'm right or wrong, it just feels that way to me intuitively.)

I don't think anything I said assumes anything about the average bet size.

I don't have data readily available about the average bet size, but I do have the total amount bet over time.  Here's a graph showing the total bet volume over time since September last year when the price was down around $10/BTC.  Notice how the slope of the line (indicating bet volume per unit time) is about the same now as it was then.  There are a few very steep parts from when the whale was playing, but the overall volume doesn't seem to be affected by the dollar value of Bitcoins, odd as that seems.  Maybe the price goes up because more people are using it, so more people are betting, which offsets the small size per bet, but that's just a guess.

sr. member
Activity: 272
Merit: 250
March 09, 2013, 05:22:49 PM
I thought the house edge was based on the number of bets. And not on the amount of betting.

The house keeps 1.9% of all bets, on average.

If a million people bet 1 BTC each, or 100k people bet 10 BTC each, the total bet volume is 1 million BTC either way, and the house will keep 19k BTC on average in both cases.

Does that make sense?

Thanks.

But this assumes that the average bet will remain in the same range.

My contention is that the average bet will keep on reducing as the BTC / USD rate keeps on increasing. The amount of total BTC bet on the first 100,000 bets will be higher than the amount of BTC made on the next 100,000. (I have not looked at the numbers and I don't know if I'm right or wrong, it just feels that way to me intuitively.)

If I'm right, then the gap between the black line and the red line won't go away as more time goes by.
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