Satoshi Dice -- Statistical Analysis - page 60.

Meni Rosenfeld

donator

Activity: 2058

Merit: 1054

Quote from: nibor on November 01, 2012, 04:41:07 AM

Quote from: Meni Rosenfeld on October 31, 2012, 07:32:45 AM

Ok. We have a total of 79,000 bets resulting in a total profit of -5121 BTC. If we assume the bets are fixed and their results are variable, then the mean profit is 1285 BTC and the variance is 3084000 BTC^2. This means the result is 3.65 sd below the mean.

The probability for a normal random variable to be this low is 0.000132. We need to correct for selection bias; there may be better ways to do it but multiplying by 1000 would be the right ballpark (the effective number of choices for the period to investigate). This means that there would be about 13% chance of getting results this bad somewhere on the graph. This means they indeed have some bad luck, but not so much so to indicate something may be wrong.

1000 seems too big to me.

there have been 1.5m bets in total so 20 seems more reasonable than 1000.

This has very little to do with the number of bets (in particular you seem to want to use the base-2 log but I see no justification for that. Probabilities are not on the same scale as information bits). It's about how many choices there are to choose the period to analyze. With a very simplistic calculation, you have 180 choices for the start date and about 10 choices for the length, which would come up as 1800. Now you have to correct for the correlations, the fact that we didn't actually go and optimize the worst period, etc. Maybe something like 500 or even less is more appropriate but again this is just a back-of-the-envelope calculation. I agree that it is unusual enough to look into it further.

nibor

sr. member

Activity: 438

Merit: 291

Quote from: Meni Rosenfeld on October 31, 2012, 07:32:45 AM

Ok. We have a total of 79,000 bets resulting in a total profit of -5121 BTC. If we assume the bets are fixed and their results are variable, then the mean profit is 1285 BTC and the variance is 3084000 BTC^2. This means the result is 3.65 sd below the mean.

The probability for a normal random variable to be this low is 0.000132. We need to correct for selection bias; there may be better ways to do it but multiplying by 1000 would be the right ballpark (the effective number of choices for the period to investigate). This means that there would be about 13% chance of getting results this bad somewhere on the graph. This means they indeed have some bad luck, but not so much so to indicate something may be wrong.

1000 seems too big to me.

there have been 1.5m bets in total so 20 seems more reasonable than 1000.

Meni Rosenfeld

donator

Activity: 2058

Merit: 1054

Quote from: dooglus on October 31, 2012, 12:22:55 PM

Quote from: Meni Rosenfeld on October 31, 2012, 07:32:45 AM

Ok. We have a total of 79,000 bets resulting in a total profit of -5121 BTC. If we assume the bets are fixed and their results are variable, then the mean profit is 1285 BTC and the variance is 3084000 BTC^2. This means the result is 3.65 sd below the mean.

The probability for a normal random variable to be this low is 0.000132. We need to correct for selection bias; there may be better ways to do it but multiplying by 1000 would be the right ballpark (the effective number of choices for the period to investigate). This means that there would be about 13% chance of getting results this bad somewhere on the graph. This means they indeed have some bad luck, but not so much so to indicate something may be wrong.

It just occurred to me that not all the bets are independent events. You can't tell from the data I provided, but it's possible to place multiple bets within a single transaction. All such bets get the same 'magic number'.

I don't know what impact that would have on your calculations. If you like, I could add a txid to each bet so you can tell which are grouped with which.

It would be a bit more work to take into account grouped bets. But the impact of the fact that those exist is that the variance will be higher, meaning the results are even more plausible.

I think it would be fine to try to carry out a more sophisticated statistical test, and/or ask the operators if they know of anything which could cause a problem. But if not that's also fine, the results are within the realm of possibility.

dooglus

legendary

Activity: 2940

Merit: 1333

Quote

Results: 2012-Oct-31 10:56am (up to block 205877)

Address Target Should Win | #Bets | Win | Lose | Refunds | BTC In | BTC Out | Refund | Profit | RTP
--------------------------------------------------------------------------------------------------------------------------------------------
1dice1e6p 1 0.00002 | 32390 | 0 (0.00000) | 31955 | 435 | 229.18 | 0.01 | 37.05 | 229.16 | 0.008
1dice1Qf4 2 0.00003 | 2101 | 0 (0.00000) | 2015 | 86 | 29.39 | 0.00 | 10.45 | 29.39 | 0.006
1dice2pxm 4 0.00006 | 3210 | 0 (0.00000) | 3168 | 42 | 41.70 | 0.03 | 5.65 | 41.67 | 0.075
1dice2vQo 8 0.00012 | 3925 | 2 (0.00052) | 3879 | 44 | 71.75 | 16.06 | 5.65 | 55.69 | 22.391
1dice2WmR 16 0.00024 | 5448 | 1 (0.00018) | 5408 | 39 | 160.06 | 4.29 | 8.40 | 155.77 | 2.680
1dice2xkj 32 0.00049 | 7068 | 3 (0.00043) | 7053 | 12 | 464.66 | 303.36 | 1.29 | 161.29 | 65.287
1dice2zdo 64 0.00098 | 8929 | 8 (0.00090) | 8897 | 24 | 737.83 | 124.60 | 55.64 | 613.22 | 16.888
1dice37Ee 128 0.00195 | 10925 | 19 (0.00175) | 10849 | 57 | 1658.28 | 1274.79 | 48.25 | 383.49 | 76.874
1dice3jkp 256 0.00391 | 12459 | 55 (0.00442) | 12387 | 17 | 1840.81 | 2621.90 | 13.12 | -781.08 | 142.432
1dice4J1m 512 0.00781 | 18926 | 143 (0.00756) | 18772 | 11 | 3548.87 | 3432.83 | 9.35 | 116.03 | 96.730
1dice5wwE 1000 0.01526 | 40265 | 615 (0.01528) | 39637 | 13 | 10024.92 | 9652.85 | 1.80 | 372.07 | 96.289
1dice61SN 1500 0.02289 | 17552 | 418 (0.02383) | 17126 | 8 | 5680.16 | 5969.40 | 15.00 | -289.23 | 105.092
1dice6DPt 2000 0.03052 | 25267 | 804 (0.03183) | 24459 | 4 | 6404.69 | 6116.42 | 9.24 | 288.26 | 95.499
1dice6gJg 3000 0.04578 | 18013 | 835 (0.04638) | 17170 | 8 | 7762.14 | 9127.40 | 24.99 | -1365.25 | 117.589
1dice6GV5 4000 0.06104 | 17885 | 1116 (0.06241) | 16765 | 4 | 5129.26 | 4751.49 | 31.20 | 377.76 | 92.635
1dice6wBx 6000 0.09155 | 24079 | 2256 (0.09377) | 21804 | 19 | 11072.34 | 11275.17 | 7.01 | -202.83 | 101.832
1dice6YgE 8000 0.12207 | 97633 | 12012 (0.12306) | 85597 | 24 | 13373.28 | 11887.83 | 0.00 | 1485.45 | 88.892
1dice7EYz 12000 0.18311 | 24292 | 4527 (0.18649) | 19748 | 17 | 9412.69 | 9708.52 | 14.50 | -295.83 | 103.143
1dice7fUk 16000 0.24414 | 110685 | 27026 (0.24423) | 83633 | 26 | 65814.07 | 64973.82 | 566.79 | 840.25 | 98.723
1dice7W2A 24000 0.36621 | 78812 | 28984 (0.36799) | 49779 | 49 | 55512.94 | 56799.35 | 212.64 | -1286.41 | 102.317
1dice8EMZ 32000 0.48828 | 643802 | 314481 (0.48882) | 328860 | 461 | 376146.46 | 373287.86 | 2923.41 | 2858.59 | 99.240
1dice97EC 32768 0.50000 | 232858 | 116146 (0.49920) | 116520 | 192 | 221882.56 | 219108.13 | 1709.77 | 2774.42 | 98.750
1dice9wcM 48000 0.73242 | 171071 | 125890 (0.73624) | 45100 | 81 | 167442.96 | 165379.64 | 704.58 | 2063.31 | 98.768
1dicec9k7 52000 0.79346 | 17441 | 13873 (0.79602) | 3555 | 13 | 28467.20 | 28490.24 | 1187.00 | -23.03 | 100.081
1dicegEAr 56000 0.85449 | 16236 | 13903 (0.85752) | 2310 | 23 | 26834.11 | 26711.24 | 400.00 | 122.86 | 99.542
1diceDCd2 60000 0.91553 | 7917 | 7244 (0.91580) | 666 | 7 | 20225.02 | 20175.20 | 0.00 | 49.81 | 99.754
1dice9wVt 64000 0.97656 | 8306 | 7995 (0.98002) | 163 | 148 | 17934.44 | 17654.39 | 239.21 | 280.04 | 98.439
--------------------------------------------------------------------------------------------------------------------------------------------
small (bets < 4 BTC) | 1604287 | 651548 | 951095 | 1644 | 397936.35 | 390164.85 | 157.60 | 7771.49 | 98.047
big (bets >= 4 BTC) | 53208 | 26808 | 26180 | 220 | 659965.53 | 658682.09 | 8084.50 | 1283.43 | 99.806
--------------------------------------------------------------------------------------------------------------------------------------------
| 1657495 | 678356 | 977275 | 1864 | 1057901.89 | 1048846.95 | 8242.11 | 9054.93 | 99.144
--------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees: 9054.93751467 BTC (0.856%)
Cumulative Fees Paid: 851.09407500 BTC
SD Profit after fees: 8203.84343967 BTC (0.775%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 5590392 : SatoshiDice Tx: 3076136 (55.0%)
Blockchain MB: 2355.1 : SatoshiDice Tx: 1257.2 (53.4%)

dooglus

legendary

Activity: 2940

Merit: 1333

Quote from: Meni Rosenfeld on October 31, 2012, 07:32:45 AM

Ok. We have a total of 79,000 bets resulting in a total profit of -5121 BTC. If we assume the bets are fixed and their results are variable, then the mean profit is 1285 BTC and the variance is 3084000 BTC^2. This means the result is 3.65 sd below the mean.

The probability for a normal random variable to be this low is 0.000132. We need to correct for selection bias; there may be better ways to do it but multiplying by 1000 would be the right ballpark (the effective number of choices for the period to investigate). This means that there would be about 13% chance of getting results this bad somewhere on the graph. This means they indeed have some bad luck, but not so much so to indicate something may be wrong.

It just occurred to me that not all the bets are independent events. You can't tell from the data I provided, but it's possible to place multiple bets within a single transaction. All such bets get the same 'magic number'.

I don't know what impact that would have on your calculations. If you like, I could add a txid to each bet so you can tell which are grouped with which.

Meni Rosenfeld

donator

Activity: 2058

Merit: 1054

Ok. We have a total of 79,000 bets resulting in a total profit of -5121 BTC. If we assume the bets are fixed and their results are variable, then the mean profit is 1285 BTC and the variance is 3084000 BTC^2. This means the result is 3.65 sd below the mean.

The probability for a normal random variable to be this low is 0.000132. We need to correct for selection bias; there may be better ways to do it but multiplying by 1000 would be the right ballpark (the effective number of choices for the period to investigate). This means that there would be about 13% chance of getting results this bad somewhere on the graph. This means they indeed have some bad luck, but not so much so to indicate something may be wrong.

dooglus

legendary

Activity: 2940

Merit: 1333

Quote from: Meni Rosenfeld on October 30, 2012, 02:19:06 PM

Quote from: dooglus on October 30, 2012, 02:17:31 PM

Quote from: Meni Rosenfeld on October 30, 2012, 02:09:59 PM

It is indeed important. If we assume the extreme that all bets are either 0 or the max bet, the variance increases 100-fold which means that the result is only about 1.2 sd below the mean. A list of bets can resolve this particular issue.

What fields do you want to see per bet?

block number, date, bet type, stake, result, return?

Anything else?

These should be enough.

OK, I made a text file of the bets from the last 1500 blocks or so (since the decline started) here (both the same, the 2nd is gzip compressed)

http://dooglus.rincevent.net/random/details.txt (4955 KB)
http://dooglus.rincevent.net/random/details.txt.gz (299 KB)

In doing so, I noticed that the SD bottom line has dropped further since this morning's stats post. Now it's:

SD Profit after fees: 8122.86383142 BTC (0.772%)

Here's the first 7 lines from the file, where things started going downhill:

Code:

204245,Sat Oct 20 20:33:17 2012,6000,WIN,1.00000000,10.66502266
204245,Sat Oct 20 20:33:17 2012,6000,WIN,1.00000000,10.66502266
204245,Sat Oct 20 20:33:17 2012,12000,WIN,0.30000000,1.60007840
204246,Sat Oct 20 20:35:27 2012,1000,WIN,2.00000000,127.93577200
204246,Sat Oct 20 20:35:27 2012,512,WIN,2.00000000,249.86550000
204246,Sat Oct 20 20:35:27 2012,1500,WIN,1.00000000,42.64659066
204246,Sat Oct 20 20:35:27 2012,32000,LOSE,0.50000000,0.00200000

That's block_number,time_and_date,target,result,stake,return

So the first line is a "lessthan 6000" bet winning, and so is the 2nd line. 2 separate bets, both winning:

http://www.satoshidice.com/lookup.php?tx=0a4d8505e11b3af56f31016c8d738927a0a62aececc0b0e8c81dd8d471ef8f83
http://www.satoshidice.com/lookup.php?tx=b6723d3c2227c288910088dff5f332fff675014b12e46dddb75278aa1efc8d03

Meni Rosenfeld

donator

Activity: 2058

Merit: 1054

Quote from: dooglus on October 30, 2012, 02:17:31 PM

Quote from: Meni Rosenfeld on October 30, 2012, 02:09:59 PM

It is indeed important. If we assume the extreme that all bets are either 0 or the max bet, the variance increases 100-fold which means that the result is only about 1.2 sd below the mean. A list of bets can resolve this particular issue.

What fields do you want to see per bet?

block number, date, bet type, stake, result, return?

Anything else?

These should be enough.

dooglus

legendary

Activity: 2940

Merit: 1333

Quote from: Meni Rosenfeld on October 30, 2012, 02:09:59 PM

It is indeed important. If we assume the extreme that all bets are either 0 or the max bet, the variance increases 100-fold which means that the result is only about 1.2 sd below the mean. A list of bets can resolve this particular issue.

What fields do you want to see per bet?

block number, date, bet type, stake, result, return?

Anything else?

Meni Rosenfeld

donator

Activity: 2058

Merit: 1054

Quote from: dooglus on October 30, 2012, 01:35:06 PM

Quote from: Meni Rosenfeld on October 30, 2012, 09:21:52 AM

For each type of bet I calculated the average amount put in, and assumed the actual bets are distributed uniformly from 0 to twice the average.

I don't know how important this is, but I doubt that's at all close to the actual distribution. I would expect tiny bets to be the vast majority of bets placed. I suspect that there are thousands of sub-1 BTC bets, and very few larger bets.

I will make a text file available detailing all the bets processed in the last couple of weeks, so that you can make a proper analysis.

But first I have to go light some fires and let a little dog out to pee.

It is indeed important. If we assume the extreme that all bets are either 0 or the max bet, the variance increases 100-fold which means that the result is only about 1.2 sd below the mean. A list of bets can resolve this particular issue.

Quote from: nimda on October 30, 2012, 01:50:52 PM

Honestly it looks like its in the realm of possibility to me. Compare it to the 11/08 jump.

That's what I think too. I did those calculations in an attempt to demonstrate that this is indeed nothing to worry about (not the best way to do science, but my methodology was simple enough not to be influenced by my prejudice). Which is why I was a bit surprised by my result, but variance in the bet amounts may explain them away.

nimda

hero member

Activity: 784

Merit: 1000

0xFB0D8D1534241423

Wheee!

Honestly it looks like its in the realm of possibility to me. Compare it to the 11/08 jump.

dooglus

legendary

Activity: 2940

Merit: 1333

Quote

Results: 2012-Oct-30 10:58am (up to block 205738)

Address Target Should Win | #Bets | Win | Lose | Refunds | BTC In | BTC Out | Refund | Profit | RTP
--------------------------------------------------------------------------------------------------------------------------------------------
1dice1e6p 1 0.00002 | 31845 | 0 (0.00000) | 31414 | 431 | 226.76 | 0.01 | 36.82 | 226.74 | 0.009
1dice1Qf4 2 0.00003 | 2093 | 0 (0.00000) | 2009 | 84 | 29.37 | 0.00 | 10.29 | 29.37 | 0.006
1dice2pxm 4 0.00006 | 3192 | 0 (0.00000) | 3151 | 41 | 40.70 | 0.03 | 5.45 | 40.67 | 0.077
1dice2vQo 8 0.00012 | 3918 | 2 (0.00052) | 3872 | 44 | 71.75 | 16.06 | 5.65 | 55.68 | 22.393
1dice2WmR 16 0.00024 | 5441 | 1 (0.00019) | 5401 | 39 | 159.98 | 4.29 | 8.40 | 155.69 | 2.682
1dice2xkj 32 0.00049 | 7057 | 3 (0.00043) | 7042 | 12 | 464.45 | 303.36 | 1.29 | 161.08 | 65.317
1dice2zdo 64 0.00098 | 8888 | 8 (0.00090) | 8857 | 23 | 736.57 | 124.60 | 55.64 | 611.97 | 16.916
1dice37Ee 128 0.00195 | 10911 | 19 (0.00175) | 10835 | 57 | 1653.16 | 1274.76 | 48.25 | 378.39 | 77.111
1dice3jkp 256 0.00391 | 12125 | 55 (0.00454) | 12056 | 14 | 1837.42 | 2621.90 | 13.11 | -784.47 | 142.694
1dice4J1m 512 0.00781 | 18847 | 143 (0.00759) | 18693 | 11 | 3545.36 | 3432.83 | 9.35 | 112.53 | 96.826
1dice5wwE 1000 0.01526 | 39924 | 610 (0.01528) | 39301 | 13 | 9978.69 | 9650.07 | 1.80 | 328.62 | 96.707
1dice61SN 1500 0.02289 | 17535 | 418 (0.02385) | 17109 | 8 | 5654.31 | 5969.28 | 15.00 | -314.96 | 105.570
1dice6DPt 2000 0.03052 | 25239 | 803 (0.03182) | 24432 | 4 | 6402.66 | 6116.10 | 9.24 | 286.55 | 95.524
1dice6gJg 3000 0.04578 | 17976 | 835 (0.04647) | 17133 | 8 | 7757.95 | 9127.38 | 24.99 | -1369.43 | 117.652
1dice6GV5 4000 0.06104 | 17851 | 1116 (0.06253) | 16731 | 4 | 5125.32 | 4751.48 | 31.20 | 373.83 | 92.706
1dice6wBx 6000 0.09155 | 23965 | 2243 (0.09367) | 21703 | 19 | 11016.96 | 11152.09 | 7.01 | -135.12 | 101.227
1dice6YgE 8000 0.12207 | 97261 | 11968 (0.12308) | 85269 | 24 | 13225.64 | 11725.18 | 0.00 | 1500.45 | 88.655
1dice7EYz 12000 0.18311 | 24236 | 4514 (0.18637) | 19706 | 16 | 9383.85 | 9664.49 | 14.50 | -280.63 | 102.991
1dice7fUk 16000 0.24414 | 109717 | 26794 (0.24427) | 82897 | 26 | 65214.41 | 64342.94 | 566.79 | 871.47 | 98.664
1dice7W2A 24000 0.36621 | 77988 | 28677 (0.36794) | 49262 | 49 | 54512.85 | 55785.23 | 212.64 | -1272.37 | 102.334
1dice8EMZ 32000 0.48828 | 643035 | 314131 (0.48886) | 328444 | 460 | 374595.21 | 371536.31 | 2673.41 | 3058.90 | 99.183
1dice97EC 32768 0.50000 | 229582 | 114547 (0.49935) | 114843 | 192 | 219125.35 | 216348.79 | 1709.77 | 2776.55 | 98.733
1dice9wcM 48000 0.73242 | 170660 | 125592 (0.73627) | 44987 | 81 | 167267.34 | 165222.79 | 704.58 | 2044.55 | 98.778
1dicec9k7 52000 0.79346 | 17385 | 13829 (0.79605) | 3543 | 13 | 28362.54 | 28372.86 | 1187.00 | -10.32 | 100.036
1dicegEAr 56000 0.85449 | 16139 | 13821 (0.85759) | 2295 | 23 | 26514.22 | 26345.44 | 400.00 | 168.77 | 99.363
1diceDCd2 60000 0.91553 | 7798 | 7143 (0.91683) | 648 | 7 | 19631.18 | 19592.08 | 0.00 | 39.10 | 99.801
1dice9wVt 64000 0.97656 | 8289 | 7978 (0.97998) | 163 | 148 | 17910.32 | 17630.18 | 239.21 | 280.14 | 98.436
--------------------------------------------------------------------------------------------------------------------------------------------
small (bets < 4 BTC) | 1596110 | 648642 | 945836 | 1632 | 396027.19 | 388408.86 | 157.02 | 7618.33 | 98.076
big (bets >= 4 BTC) | 52787 | 26608 | 25960 | 219 | 654417.26 | 652701.78 | 7834.50 | 1715.48 | 99.738
--------------------------------------------------------------------------------------------------------------------------------------------
| 1648897 | 675250 | 971796 | 1851 | 1050444.46 | 1041110.64 | 7991.53 | 9333.81 | 99.111
--------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees: 9333.81729799 BTC (0.889%)
Cumulative Fees Paid: 842.47867500 BTC
SD Profit after fees: 8491.33862299 BTC (0.808%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 5561537 : SatoshiDice Tx: 3060185 (55.0%)
Blockchain MB: 2342.5 : SatoshiDice Tx: 1250.5 (53.4%)

dooglus

legendary

Activity: 2940

Merit: 1333

Quote from: Meni Rosenfeld on October 30, 2012, 09:21:52 AM

For each type of bet I calculated the average amount put in, and assumed the actual bets are distributed uniformly from 0 to twice the average.

I don't know how important this is, but I doubt that's at all close to the actual distribution. I would expect tiny bets to be the vast majority of bets placed. I suspect that there are thousands of sub-1 BTC bets, and very few larger bets.

I will make a text file available detailing all the bets processed in the last couple of weeks, so that you can make a proper analysis.

But first I have to go light some fires and let a little dog out to pee.

Herbert

hero member

Activity: 488

Merit: 500

Secret leaked?

Come-from-Beyond

legendary

Activity: 2142

Merit: 1010

Newbie

Quote from: Meni Rosenfeld on October 30, 2012, 09:21:52 AM

Now, of course picking the most suspicious-looking 9-day period among half a year of statistics would skew the results. But still it would only be reasonable to get maybe 4 or 5 sd difference. 12.5 is just too much, and warrants further investigation.

Max bets where changed recently. This could change the pattern of bets and winnings.

Meni Rosenfeld

donator

Activity: 2058

Merit: 1054

I did a few hasty calculations, with lots of assumptions and room for errors along the way, but:

I took your table for Oct 29 stats and subtracted from it the Oct 20 stats, to get the stats for the period in question.

For each type of bet I calculated the average amount put in, and assumed the actual bets are distributed uniformly from 0 to twice the average.

From this I calculated the mean and variance of the profit from each type, summed over all types and compared it to the actual total profit.

I got a result which is 12.5 standard deviations below the mean (and we're talking about an approximately normal distribution).

Now, of course picking the most suspicious-looking 9-day period among half a year of statistics would skew the results. But still it would only be reasonable to get maybe 4 or 5 sd difference. 12.5 is just too much, and warrants further investigation.

Again, I could be wrong about the whole thing but at least it indicates someone needs to do a more careful analysis. A better analysis can be obtained with a table of the individual bets.

organofcorti

donator

Activity: 2058

Merit: 1007

Poor impulse control.

Quote from: dooglus on October 29, 2012, 11:23:41 AM

This is starting to look weird. The slide just isn't stopping. What's going on here?

I looks like a random walk with drift to me. You could use the Augmented Dickey Fuller test to test if the change is likely give a null hypothesis that nothing abnormal has occurred. Or I can do it if I have time.

Herbert

hero member

Activity: 488

Merit: 500

Quote from: dooglus on October 29, 2012, 11:23:41 AM

This is starting to look weird. The slide just isn't stopping. What's going on here?

Indeed this looks fishy. Given the amount of bets I am tempted to not accept this as pure coincidence/bad luck.

kidgorgeous

member

Activity: 75

Merit: 10

If you look at the difference between small bets and big bets, the small bets aren't winning or losing particularly well but it just seems that theres a few bigger bets that are just killing the house. If you think about it, it doesn't take alot of big winning bets to hurt the house.

Come-from-Beyond

legendary

Activity: 2142

Merit: 1010

Newbie

Quote from: dooglus on October 29, 2012, 11:23:41 AM

This is starting to look weird. The slide just isn't stopping. What's going on here?

Maybe PR. Maybe bad karma. Maybe just fluctuation.
Or maybe u was right regarding dividends.

Topic: Satoshi Dice -- Statistical Analysis - page 60. (Read 192896 times)