Satoshi Dice -- Statistical Analysis

[dooglus]

...
In case it's not clear, there is no way of winning long term on satoshi dice without cheating.  There's no way you can turn a positive house edge into a negative house edge simply by adjusting your bet sizes.  I probably assume that everyone knows this when they don't.  That's not to say you can't play and walk away with a profit.  Just that if you keep playing long enough, eventually the house edge will guarantee that you lose.

True, but don't you think that if too many of the players bet this way, the house is more likely to bust?  The table bet limits are the house's friend.

I think the house limits are dangerously high on some bets and unneccesarily low on others.  I've been talking to SD about the issue, but things have gone quiet on that front lately.  I don't really know what they're thinking now.

[organofcorti]

Biggest wins will likely be part of a martingale chain. As dooglus says, this doesn't mean a martingale method can beat the house odds - it will always tend toward:

Code:

what you bet * (1 - house percentage)

All it means is that a naive martingale method will end up requiring a large bet at some point. How many times does someone use a naive martingale method and run out of btc because they can't afford another bet? They might be ahead this set of plays, but next? Even if a player has unlimited btc, or uses a martingale strategy that prevents large losses losing too large a sum in one set of plays due to an extended series of losses, they can't make up the difference between what they bet and the house odds.

Edited for clarity

[dooglus]

All it means is that a naive martingale method will end up requiring a large bet at some point. How many times does someone use a naive martingale method and run out of btc because they can't afford another bet? They might be ahead this set of plays, but next? Even if a player has unlimited btc, or uses a martingale strategy that prevents large losses, they can't make up the difference between what they bet and the house odds.

Is there a non-naive martingale method?  I'm not arguing with you; it's an honest question.

And what martingale strategy prevents large losses?  Are you referring to the strategy you posted where you reduce your initial bet sufficiently that you're unlikely to suffer a string of losing bets long enough to cause you to have to bet bigger than you can afford?

[organofcorti]

Is there a non-naive martingale method?  I'm not arguing with you; it's an honest question.

Naive martingale uses the same strategy regardless of the game or funds to hand. Any strategy which changes with a change in game probability and your funds to hand would be non-naive.

And what martingale strategy prevents large losses? 

Edit the post - I think it means something more like I meant it to now. I really don't want anyone misunderstanding and thinking that any betting method can prevent large losses  - play any game that has a house advantage for long enough and you'll get large losses.

But a martingale method is infamous for causing an exponential growth in outlay in order to keep up with the cycle. At least if the strategy is modified somewhat you're less likely to lose all your available cash in one losing streak, and can play for more bets.

[dooglus]

Thanks.  I think you didn't mean to strikethrough 'prevents', or if you did maybe you intended to replace it with something suggesting that the expensive sequence of losses is very unlikely, rather than 'prevented'.  As it is, it's ungrammatical I think.

[...]or uses a martingale strategy that prevents large losses losing too large a sum in one set of plays due to an extended series of losses, [...]

[organofcorti]

The fix is fixed.

[nibor]

Below are the odds/winnings from players point of view.

I have assumed that after 12 losing games you would give up as even if you win after that you do not get back your stake!

As you can see you have a 96.5% chance of winning, and a 3.5% chance of losing 693 BTC!

Expected mean loss is 1.21BTC per "game".

So one in 28 games the player loses 693BTC. The other 27 games they make between 0.75 and 401BTC with different odds (401 profit is very rare 1 in 66 games).

Game	Bet	Total Cost	Win		p(lose)	p(win)		Odds	Winnings (neg is lose)
1	0.25	0.2505	1.00075		0.755859	0.244141		0.244141	0.75025
2	0.5	0.751	2.0015		0.571322827881	0.184536172119		0.184536172119	1.2505
3	1	1.7515	4.003		0.431839501359305	0.139483326521695		0.139483326521695	2.2515
4	2	3.752	8.006		0.326409773657943	0.105429727701362		0.105429727701362	4.254
5	4	7.7525	16.012		0.246719765107319	0.0796900085506238		0.0796900085506238	8.2595
6	8	15.753	32.024		0.186485354934253	0.0602344101730659		0.0602344101730659	16.271
7	16	31.7535	64.048		0.140956633895249	0.0455287210390034		0.0455287210390034	32.2945
8	32	63.754	128.096		0.106543340339429	0.0344132935558201		0.0344132935558201	64.342
9	64	127.7545	256.192		0.0805317426856207	0.0260115976538086		0.0260115976538086	128.4375
10	128	255.755	512.384		0.0608706424946106	0.0196611001910101		0.0196611001910101	256.629
11	219	474.7555	876.657		0.0460096229653339	0.0148610195292767		0.0148610195292767	401.9015
12	219	693.756	876.657		0.0347767876049543	0.0112328353603796		0.0112328353603796	182.901
Or lose						0.0347767876049543		0.0347767876049543	-693.756

[jamesg]

Below are the odds/winnings from players point of view.

I have assumed that after 12 losing games you would give up as even if you win after that you do not get back your stake!

As you can see you have a 96.5% chance of winning, and a 3.5% chance of losing 693 BTC!

Expected mean loss is 1.21BTC per "game".

So one in 28 games the player loses 693BTC. The other 27 games they make between 0.75 and 401BTC with different odds (401 profit is very rare 1 in 66 games).

Game	Bet	Total Cost	Win		p(lose)	p(win)		Odds	Winnings (neg is lose)
1	0.25	0.2505	1.00075		0.755859	0.244141		0.244141	0.75025
2	0.5	0.751	2.0015		0.571322827881	0.184536172119		0.184536172119	1.2505
3	1	1.7515	4.003		0.431839501359305	0.139483326521695		0.139483326521695	2.2515
4	2	3.752	8.006		0.326409773657943	0.105429727701362		0.105429727701362	4.254
5	4	7.7525	16.012		0.246719765107319	0.0796900085506238		0.0796900085506238	8.2595
6	8	15.753	32.024		0.186485354934253	0.0602344101730659		0.0602344101730659	16.271
7	16	31.7535	64.048		0.140956633895249	0.0455287210390034		0.0455287210390034	32.2945
8	32	63.754	128.096		0.106543340339429	0.0344132935558201		0.0344132935558201	64.342
9	64	127.7545	256.192		0.0805317426856207	0.0260115976538086		0.0260115976538086	128.4375
10	128	255.755	512.384		0.0608706424946106	0.0196611001910101		0.0196611001910101	256.629
11	219	474.7555	876.657		0.0460096229653339	0.0148610195292767		0.0148610195292767	401.9015
12	219	693.756	876.657		0.0347767876049543	0.0112328353603796		0.0112328353603796	182.901
Or lose						0.0347767876049543		0.0347767876049543	-693.756

From a betters perspective, if you have risked 693 BTC so far and not won, you are pot committed and it would be worth another 219 to regain "most" of your losses rather than giving up. I would be interested to see the odds for this 13th bet.

Also, what are the odds if you add an extra half sized bet at the top of the chain for .0625 BTC?

[organofcorti]

Below are the odds/winnings from players point of view.

I have assumed that after 12 losing games you would give up as even if you win after that you do not get back your stake!

As you can see you have a 96.5% chance of winning, and a 3.5% chance of losing 693 BTC!

Expected mean loss is 1.21BTC per "game".

So one in 28 games the player loses 693BTC. The other 27 games they make between 0.75 and 401BTC with different odds (401 profit is very rare 1 in 66 games).

Game	Bet	Total Cost	Win		p(lose)	p(win)		Odds	Winnings (neg is lose)
1	0.25	0.2505	1.00075		0.755859	0.244141		0.244141	0.75025
2	0.5	0.751	2.0015		0.571322827881	0.184536172119		0.184536172119	1.2505
3	1	1.7515	4.003		0.431839501359305	0.139483326521695		0.139483326521695	2.2515
4	2	3.752	8.006		0.326409773657943	0.105429727701362		0.105429727701362	4.254
5	4	7.7525	16.012		0.246719765107319	0.0796900085506238		0.0796900085506238	8.2595
6	8	15.753	32.024		0.186485354934253	0.0602344101730659		0.0602344101730659	16.271
7	16	31.7535	64.048		0.140956633895249	0.0455287210390034		0.0455287210390034	32.2945
8	32	63.754	128.096		0.106543340339429	0.0344132935558201		0.0344132935558201	64.342
9	64	127.7545	256.192		0.0805317426856207	0.0260115976538086		0.0260115976538086	128.4375
10	128	255.755	512.384		0.0608706424946106	0.0196611001910101		0.0196611001910101	256.629
11	219	474.7555	876.657		0.0460096229653339	0.0148610195292767		0.0148610195292767	401.9015
12	219	693.756	876.657		0.0347767876049543	0.0112328353603796		0.0112328353603796	182.901
Or lose						0.0347767876049543		0.0347767876049543	-693.756

This is why a naive Martingale is a scary thing. If you don't want to lose your shirt, modify the betting chain's starting point and multiplier appropriately. With the right parameters, you can make a bad run less devestating.

[nibor]

Only gets worse!

Now have 0.8% chance of losing 36, 0.6% of losing 255, 0.5% of losing 474, 0.4% of losing 696 and a really nasty 1.1% chance of losing 1569!

Game	Bet	Total Cost	Win		p(lose)	p(win)		Odds	Winnings (neg is lose)
1	0.25	0.251	1.001		0.756	0.244		0.244	0.75
2	0.5	0.751	2.002		0.571	0.185		0.185	1.251
3	1	1.752	4.003		0.432	0.139		0.139	2.252
4	2	3.752	8.006		0.326	0.105		0.105	4.254
5	4	7.753	16.012		0.247	0.08		0.08	8.26
6	8	15.753	32.024		0.186	0.06		0.06	16.271
7	16	31.754	64.048		0.141	0.046		0.046	32.295
8	32	63.754	128.096		0.107	0.034		0.034	64.342
9	64	127.755	256.192		0.081	0.026		0.026	128.438
10	128	255.755	512.384		0.061	0.02		0.02	256.629
11	219	474.756	876.657		0.046	0.015		0.015	401.902
12	219	693.756	876.657		0.035	0.011		0.011	182.901
13	219	912.757	876.657		0.026	0.008		0.008	-36.099
14	219	1131.757	876.657		0.02	0.006		0.006	-255.1
15	219	1350.758	876.657		0.015	0.005		0.005	-474.101
16	219	1569.758	876.657		0.011	0.004		0.004	-693.101
Give up!		0	0		0	0		0.011	-1569.758

[dooglus]

Game	Bet	Total Cost	Win		p(lose)	p(win)		Odds	Winnings (neg is lose)
12	219	693.756	876.657		0.0347767876049543	0.0112328353603796		0.0112328353603796	182.901

In https://bitcointalk.org/index.php?topic=80312.msg1053597#msg1053597 I calculated that he won 185 BTC overall.  Why do you get 183 for that case?  Are you ignoring the amounts you get back when you lose a bet?  You get 1/2% of your stake back when you lose.

I ignored transaction fees on the bet transactions, since they're optional, but they're also pretty much insignificant when we're talking about a profit of 183 BTC.

[dooglus]

Results: 2012-Jul-26 11:31am (up to block 190903)

   Address  Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
--------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    11111 |      0 (0.00000) |  10829 |     282 |      63.66 |       0.01 |    18.19 |     63.64 |   0.030
 1dice1Qf4       2      0.00003 |     1064 |      0 (0.00000) |    994 |      70 |      13.64 |       0.00 |     5.58 |     13.64 |   0.013
 1dice2pxm       4      0.00006 |     1537 |      0 (0.00000) |   1503 |      34 |      19.28 |       0.02 |     2.22 |     19.26 |   0.107
 1dice2vQo       8      0.00012 |     1337 |      0 (0.00000) |   1297 |      40 |      31.46 |       0.05 |     4.15 |     31.41 |   0.177
 1dice2WmR      16      0.00024 |     1587 |      0 (0.00000) |   1554 |      33 |      63.15 |       0.18 |     7.40 |     62.97 |   0.294
 1dice2xkj      32      0.00049 |     3789 |      1 (0.00026) |   3777 |      11 |     252.62 |     100.97 |     1.29 |    151.64 |  39.971
 1dice2zdo      64      0.00098 |     5456 |      7 (0.00129) |   5432 |      17 |     285.26 |     121.97 |    55.64 |    163.29 |  42.757
 1dice37Ee     128      0.00195 |     6502 |     16 (0.00248) |   6438 |      48 |    1273.15 |    1173.35 |    40.25 |     99.80 |  92.161
 1dice3jkp     256      0.00391 |     5314 |     25 (0.00472) |   5275 |      14 |     597.73 |     374.80 |    13.11 |    222.93 |  62.703
 1dice4J1m     512      0.00781 |     8438 |     60 (0.00711) |   8373 |       5 |    1701.75 |    1085.95 |     9.35 |    615.79 |  63.814
 1dice5wwE    1000      0.01526 |    14993 |    224 (0.01494) |  14766 |       3 |    2666.79 |    2367.19 |     1.80 |    299.59 |  88.766
 1dice61SN    1500      0.02289 |     8532 |    203 (0.02381) |   8323 |       6 |    3213.79 |    3630.07 |    15.00 |   -416.27 | 112.953
 1dice6DPt    2000      0.03052 |    10573 |    334 (0.03160) |  10236 |       3 |    3573.15 |    3307.88 |     9.24 |    265.27 |  92.576
 1dice6gJg    3000      0.04578 |     8496 |    413 (0.04865) |   8076 |       7 |    5150.38 |    6625.44 |    24.99 |  -1475.05 | 128.640
 1dice6GV5    4000      0.06104 |     9495 |    596 (0.06279) |   8896 |       3 |    3331.97 |    3117.39 |    31.20 |    214.57 |  93.560
 1dice6wBx    6000      0.09155 |    16903 |   1596 (0.09447) |  15299 |       8 |    9033.67 |    9192.76 |     7.01 |   -159.08 | 101.761
 1dice6YgE    8000      0.12207 |    35346 |   4387 (0.12414) |  30951 |       8 |    6790.71 |    6070.73 |     0.00 |    719.98 |  89.398
 1dice7EYz   12000      0.18311 |    16636 |   3159 (0.18996) |  13471 |       6 |    6877.81 |    7022.16 |    14.50 |   -144.35 | 102.099
 1dice7fUk   16000      0.24414 |    44733 |  10854 (0.24268) |  33871 |       8 |   15397.85 |   16059.35 |   347.79 |   -661.50 | 104.296
 1dice7W2A   24000      0.36621 |    33367 |  12337 (0.37009) |  20998 |      32 |   13804.34 |   13736.85 |   212.63 |     67.48 |  99.511
 1dice8EMZ   32000      0.48828 |   319411 | 155631 (0.48745) | 163648 |     132 |  100375.61 |  100875.94 |  2173.21 |   -500.33 | 100.498
 1dice97EC   32768      0.50000 |   132700 |  66185 (0.49905) |  66436 |      79 |   50814.73 |   49076.84 |   789.20 |   1737.88 |  96.580
 1dice9wcM   48000      0.73242 |    96210 |  70759 (0.73586) |  25399 |      52 |   85283.29 |   83808.25 |   467.98 |   1475.04 |  98.270
 1dicec9k7   52000      0.79346 |     1057 |    848 (0.80227) |    209 |       0 |    1646.63 |    1646.15 |     0.00 |      0.48 |  99.971
 1dicegEAr   56000      0.85449 |      805 |    665 (0.82609) |    140 |       0 |     620.80 |     579.86 |     0.00 |     40.94 |  93.405
 1diceDCd2   60000      0.91553 |      249 |    223 (0.90650) |     23 |       3 |      61.92 |      62.38 |     0.00 |     -0.45 | 100.737
 1dice9wVt   64000      0.97656 |     5998 |   5743 (0.97870) |    125 |     130 |    5052.96 |    4860.19 |   239.20 |    192.76 |  96.185
--------------------------------------------------------------------------------------------------------------------------------------------
                                |   801639 | 334266           | 466339 |    1034 |  317998.22 |  314896.82 |  4491.02 |   3101.39 |  99.025
--------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:       3101.39999807 BTC (0.975%)
Cumulative Fees Paid:         403.58410000 BTC
SD Profit after fees:        2697.81589807 BTC (0.848%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  2441888  :  SatoshiDice Tx: 1476769  (60.5%)
Blockchain MB:  1030.5  :  SatoshiDice Tx: 607.3  (58.9%)

[nibor]

Game	Bet	Total Cost	Win		p(lose)	p(win)		Odds	Winnings (neg is lose)
12	219	693.756	876.657		0.0347767876049543	0.0112328353603796		0.0112328353603796	182.901

In https://bitcointalk.org/index.php?topic=80312.msg1053597#msg1053597 I calculated that he won 185 BTC overall.  Why do you get 183 for that case?  Are you ignoring the amounts you get back when you lose a bet?  You get 1/2% of your stake back when you lose.

I ignored transaction fees on the bet transactions, since they're optional, but they're also pretty much insignificant when we're talking about a profit of 183 BTC.

I just used the 24.4141% winning odds and the 4.003x multiplier off the web site. Could be a bit of rounding in those numbers. Also did include sending transaction fees.

[dooglus]

I just used the 24.4141% winning odds and the 4.003x multiplier off the web site. Could be a bit of rounding in those numbers. Also did include sending transaction fees.

When you lose a 219 BTC bet, you get over 1 BTC back (0.5% of your stake).  I guess that's where your error is - you're forgetting about those payments.

[dooglus]

Results: 2012-Jul-27 11:14am (up to block 191066)

   Address  Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
--------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    11180 |      0 (0.00000) |  10898 |     282 |      65.22 |       0.01 |    18.19 |     65.20 |   0.030
 1dice1Qf4       2      0.00003 |     1066 |      0 (0.00000) |    996 |      70 |      13.75 |       0.00 |     5.58 |     13.75 |   0.013
 1dice2pxm       4      0.00006 |     1546 |      0 (0.00000) |   1512 |      34 |      19.35 |       0.02 |     2.22 |     19.33 |   0.106
 1dice2vQo       8      0.00012 |     1343 |      0 (0.00000) |   1303 |      40 |      31.48 |       0.05 |     4.15 |     31.43 |   0.177
 1dice2WmR      16      0.00024 |     1601 |      0 (0.00000) |   1568 |      33 |      64.81 |       0.19 |     7.40 |     64.61 |   0.298
 1dice2xkj      32      0.00049 |     3815 |      1 (0.00026) |   3803 |      11 |     256.94 |     100.98 |     1.29 |    155.96 |  39.302
 1dice2zdo      64      0.00098 |     5519 |      7 (0.00127) |   5495 |      17 |     285.58 |     121.97 |    55.64 |    163.61 |  42.709
 1dice37Ee     128      0.00195 |     6514 |     16 (0.00247) |   6450 |      48 |    1274.06 |    1173.35 |    40.25 |    100.71 |  92.095
 1dice3jkp     256      0.00391 |     5379 |     26 (0.00485) |   5339 |      14 |     607.59 |     379.58 |    13.11 |    228.01 |  62.473
 1dice4J1m     512      0.00781 |     8559 |     61 (0.00713) |   8493 |       5 |    1729.56 |    1087.30 |     9.35 |    642.25 |  62.866
 1dice5wwE    1000      0.01526 |    15157 |    226 (0.01491) |  14928 |       3 |    2707.58 |    2387.17 |     1.80 |    320.41 |  88.166
 1dice61SN    1500      0.02289 |     8589 |    204 (0.02377) |   8379 |       6 |    3233.39 |    3651.47 |    15.00 |   -418.07 | 112.930
 1dice6DPt    2000      0.03052 |    10824 |    341 (0.03151) |  10480 |       3 |    3611.14 |    3343.93 |     9.24 |    267.20 |  92.601
 1dice6gJg    3000      0.04578 |     8595 |    417 (0.04856) |   8171 |       7 |    5183.89 |    6651.15 |    24.99 |  -1467.25 | 128.304
 1dice6GV5    4000      0.06104 |     9626 |    601 (0.06245) |   9022 |       3 |    3372.52 |    3137.21 |    31.20 |    235.30 |  93.023
 1dice6wBx    6000      0.09155 |    16923 |   1597 (0.09441) |  15318 |       8 |    9037.51 |    9197.04 |     7.01 |   -159.52 | 101.765
 1dice6YgE    8000      0.12207 |    35667 |   4418 (0.12391) |  31236 |      13 |    6871.23 |    6116.17 |     0.00 |    755.05 |  89.011
 1dice7EYz   12000      0.18311 |    16657 |   3165 (0.19008) |  13486 |       6 |    6878.43 |    7023.19 |    14.50 |   -144.75 | 102.105
 1dice7fUk   16000      0.24414 |    45085 |  10938 (0.24265) |  34139 |       8 |   15553.51 |   16245.60 |   347.79 |   -692.08 | 104.450
 1dice7W2A   24000      0.36621 |    33590 |  12412 (0.36987) |  21146 |      32 |   13825.33 |   13762.52 |   212.63 |     62.81 |  99.546
 1dice8EMZ   32000      0.48828 |   320174 | 156004 (0.48745) | 164036 |     134 |  100874.43 |  101381.77 |  2173.21 |   -507.34 | 100.503
 1dice97EC   32768      0.50000 |   133947 |  66842 (0.49932) |  67025 |      80 |   52658.10 |   51088.57 |   789.20 |   1569.52 |  97.019
 1dice9wcM   48000      0.73242 |    98791 |  72641 (0.73569) |  26098 |      52 |   88368.22 |   86876.33 |   467.98 |   1491.88 |  98.312
 1dicec9k7   52000      0.79346 |     1325 |   1060 (0.80000) |    265 |       0 |    2993.36 |    3075.08 |     0.00 |    -81.72 | 102.730
 1dicegEAr   56000      0.85449 |      850 |    703 (0.82706) |    147 |       0 |     866.91 |     832.12 |     0.00 |     34.79 |  95.987
 1diceDCd2   60000      0.91553 |      279 |    252 (0.91304) |     24 |       3 |      78.51 |      75.87 |     0.00 |      2.64 |  96.633
 1dice9wVt   64000      0.97656 |     6020 |   5765 (0.97878) |    125 |     130 |    5128.39 |    4935.94 |   239.20 |    192.44 |  96.247
--------------------------------------------------------------------------------------------------------------------------------------------
                                |   808621 | 337697           | 469882 |    1042 |  325590.91 |  322644.68 |  4491.03 |   2946.22 |  99.095
--------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:       2946.22962098 BTC (0.905%)
Cumulative Fees Paid:         407.10480000 BTC
SD Profit after fees:        2539.12482098 BTC (0.780%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  2467594  :  SatoshiDice Tx: 1489900  (60.4%)
Blockchain MB:  1040.8  :  SatoshiDice Tx: 612.7  (58.9%)

[dooglus]

Here's another lucky martingale escape which accounts for the last spike up and back down on the blue line:

Make sure to chronically the flipside too. The failures, though sad, are also entertaining... and can serve as a cautionary tale for others.

Here's a cautionary tale if ever I saw one:

2012-07-28 00:37:45 <24000  Bet:   4.20000000  Outcome: LOSE  Payment:  0.02050000   Profit:   -4.1795      Cumulative:   -4.1795     
2012-07-28 00:37:54 <24000  Bet:   6.80000000  Outcome: LOSE  Payment:  0.03350000   Profit:   -6.7665      Cumulative:  -10.946     
2012-07-28 00:38:06 <24000  Bet:  10.80000000  Outcome: LOSE  Payment:  0.05350000   Profit:  -10.7465      Cumulative:  -21.6925     
2012-07-28 00:38:27 <24000  Bet:  17.20000000  Outcome: LOSE  Payment:  0.08550000   Profit:  -17.1145      Cumulative:  -38.807     
2012-07-28 00:39:01 <24000  Bet:  27.40000000  Outcome: LOSE  Payment:  0.13650000   Profit:  -27.2635      Cumulative:  -66.0705     
2012-07-28 00:39:18 <24000  Bet:  43.80000000  Outcome: LOSE  Payment:  0.21850000   Profit:  -43.5815      Cumulative: -109.652     
2012-07-28 00:39:40 <24000  Bet:  70.00000000  Outcome: LOSE  Payment:  0.34950000   Profit:  -69.6505      Cumulative: -179.3025   
2012-07-28 00:40:02 <24000  Bet: 112.00000000  Outcome: LOSE  Payment:  0.55950000   Profit: -111.4405      Cumulative: -290.743     

2012-07-28 00:40:49 <24000  Bet:   4.20000000  Outcome: LOSE  Payment:  0.02050000   Profit:   -4.1795      Cumulative: -294.9225   
2012-07-28 00:41:04 <24000  Bet:   6.80000000  Outcome: WIN   Payment: 18.15638853   Profit:   11.35638853  Cumulative: -283.56611147

2012-07-28 00:41:25 <24000  Bet:   4.20000000  Outcome: WIN   Payment: 11.21404880   Profit:    7.0140488   Cumulative: -276.55206267

2012-07-28 00:42:29 <24000  Bet:   4.20000000  Outcome: LOSE  Payment:  0.02050000   Profit:   -4.1795      Cumulative: -280.73156267
2012-07-28 00:43:10 <24000  Bet:   6.80000000  Outcome: LOSE  Payment:  0.03350000   Profit:   -6.7665      Cumulative: -287.49806267
2012-07-28 00:43:39 <24000  Bet:  10.80000000  Outcome: LOSE  Payment:  0.05350000   Profit:  -10.7465      Cumulative: -298.24456267
2012-07-28 00:44:19 <24000  Bet:  17.20000000  Outcome: LOSE  Payment:  0.08550000   Profit:  -17.1145      Cumulative: -315.35906267
2012-07-28 00:48:23 <24000  Bet:  27.40000000  Outcome: LOSE  Payment:  0.13650000   Profit:  -27.2635      Cumulative: -342.62256267
2012-07-28 00:50:52 <24000  Bet:  43.80000000  Outcome: LOSE  Payment:  0.21850000   Profit:  -43.5815      Cumulative: -386.20406267
2012-07-28 00:51:23 <24000  Bet:  70.00000000  Outcome: LOSE  Payment:  0.34950000   Profit:  -69.6505      Cumulative: -455.85456267

[dooglus]

I wonder what this guy is playing at:

  http://www.satoshidice.com/lookup.php?tx=b1ea542f3db289d3d4aebbd1948ea53590dd38f37930c8613fba6dc1787fbcf0

He bets the same bet over and over in a single transaction.  It has the same result as if you bet just a single larger bet - only one 'lucky number' is picked per transaction.

[dooglus]

Results: 2012-Jul-28 05:03pm (up to block 191263)

   Address  Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
--------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    11300 |      0 (0.00000) |  11016 |     284 |      68.67 |       0.01 |    18.39 |     68.65 |   0.028
 1dice1Qf4       2      0.00003 |     1080 |      0 (0.00000) |   1010 |      70 |      15.10 |       0.00 |     5.58 |     15.10 |   0.012
 1dice2pxm       4      0.00006 |     1643 |      0 (0.00000) |   1609 |      34 |      19.87 |       0.02 |     2.22 |     19.84 |   0.104
 1dice2vQo       8      0.00012 |     1350 |      1 (0.00076) |   1309 |      40 |      31.55 |       8.05 |     4.15 |     23.50 |  25.516
 1dice2WmR      16      0.00024 |     1657 |      1 (0.00062) |   1623 |      33 |      65.51 |       4.19 |     7.40 |     61.32 |   6.399
 1dice2xkj      32      0.00049 |     4048 |      2 (0.00050) |   4035 |      11 |     258.88 |     102.98 |     1.29 |    155.90 |  39.780
 1dice2zdo      64      0.00098 |     5822 |      8 (0.00138) |   5797 |      17 |     288.45 |     122.97 |    55.64 |    165.48 |  42.631
 1dice37Ee     128      0.00195 |     6819 |     17 (0.00251) |   6754 |      48 |    1276.46 |    1173.85 |    40.25 |    102.61 |  91.961
 1dice3jkp     256      0.00391 |     5763 |     27 (0.00470) |   5722 |      14 |     616.02 |     382.08 |    13.11 |    233.93 |  62.025
 1dice4J1m     512      0.00781 |     8829 |     63 (0.00714) |   8761 |       5 |    1738.30 |    1089.80 |     9.35 |    648.50 |  62.693
 1dice5wwE    1000      0.01526 |    15637 |    233 (0.01490) |  15401 |       3 |    2754.44 |    2449.38 |     1.80 |    305.05 |  88.925
 1dice61SN    1500      0.02289 |     8961 |    210 (0.02345) |   8745 |       6 |    3255.89 |    3665.55 |    15.00 |   -409.66 | 112.582
 1dice6DPt    2000      0.03052 |    11275 |    353 (0.03132) |  10919 |       3 |    3646.23 |    3354.52 |     9.24 |    291.71 |  92.000
 1dice6gJg    3000      0.04578 |     8908 |    427 (0.04797) |   8474 |       7 |    5216.56 |    6683.19 |    24.99 |  -1466.62 | 128.115
 1dice6GV5    4000      0.06104 |    10004 |    621 (0.06209) |   9380 |       3 |    3419.84 |    3170.09 |    31.20 |    249.75 |  92.697
 1dice6wBx    6000      0.09155 |    16999 |   1607 (0.09459) |  15383 |       9 |    9072.46 |    9216.16 |     7.01 |   -143.69 | 101.584
 1dice6YgE    8000      0.12207 |    36575 |   4516 (0.12352) |  32046 |      13 |    6988.81 |    6224.50 |     0.00 |    764.30 |  89.064
 1dice7EYz   12000      0.18311 |    16685 |   3171 (0.19012) |  13508 |       6 |    6886.12 |    7051.57 |    14.50 |   -165.44 | 102.403
 1dice7fUk   16000      0.24414 |    45701 |  11086 (0.24262) |  34607 |       8 |   15975.11 |   16674.57 |   347.79 |   -699.45 | 104.378
 1dice7W2A   24000      0.36621 |    34264 |  12671 (0.37015) |  21561 |      32 |   15694.96 |   15690.03 |   212.63 |      4.92 |  99.969
 1dice8EMZ   32000      0.48828 |   321674 | 156724 (0.48742) | 164816 |     134 |  102229.80 |  102692.64 |  2173.21 |   -462.84 | 100.453
 1dice97EC   32768      0.50000 |   135347 |  67518 (0.49918) |  67741 |      88 |   54948.38 |   53182.77 |   789.20 |   1765.61 |  96.787
 1dice9wcM   48000      0.73242 |   102305 |  75226 (0.73572) |  27022 |      57 |   90118.49 |   88509.89 |   467.98 |   1608.59 |  98.215
 1dicec9k7   52000      0.79346 |     1818 |   1465 (0.80583) |    353 |       0 |    4312.15 |    4492.53 |     0.00 |   -180.38 | 104.183
 1dicegEAr   56000      0.85449 |     1116 |    939 (0.84215) |    176 |       1 |    1307.62 |    1318.74 |     0.00 |    -11.12 | 100.850
 1diceDCd2   60000      0.91553 |      506 |    466 (0.92644) |     37 |       3 |     318.73 |     316.55 |     0.00 |      2.18 |  99.316
 1dice9wVt   64000      0.97656 |     6047 |   5791 (0.97871) |    126 |     130 |    5148.47 |    4951.10 |   239.20 |    197.36 |  96.166
--------------------------------------------------------------------------------------------------------------------------------------------
                                |   822133 | 343143           | 477931 |    1059 |  335673.00 |  332527.85 |  4491.23 |   3145.14 |  99.063
--------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:       3145.14824664 BTC (0.937%)
Cumulative Fees Paid:         413.90882500 BTC
SD Profit after fees:        2731.23942164 BTC (0.814%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  2509244  :  SatoshiDice Tx: 1513290  (60.3%)
Blockchain MB:  1057.0  :  SatoshiDice Tx: 622.2  (58.9%)

[dooglus]

Results: 2012-Jul-29 05:03pm (up to block 191430)

   Address  Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
--------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    11554 |      0 (0.00000) |  11270 |     284 |      69.64 |       0.01 |    18.39 |     69.62 |   0.028
 1dice1Qf4       2      0.00003 |     1087 |      0 (0.00000) |   1017 |      70 |      15.50 |       0.00 |     5.58 |     15.50 |   0.011
 1dice2pxm       4      0.00006 |     1644 |      0 (0.00000) |   1610 |      34 |      19.87 |       0.02 |     2.22 |     19.85 |   0.104
 1dice2vQo       8      0.00012 |     1353 |      1 (0.00076) |   1312 |      40 |      31.87 |       8.05 |     4.15 |     23.82 |  25.257
 1dice2WmR      16      0.00024 |     1663 |      1 (0.00061) |   1629 |      33 |      65.67 |       4.19 |     7.40 |     61.48 |   6.383
 1dice2xkj      32      0.00049 |     4054 |      2 (0.00049) |   4041 |      11 |     258.94 |     102.98 |     1.29 |    155.96 |  39.770
 1dice2zdo      64      0.00098 |     5829 |      8 (0.00138) |   5804 |      17 |     288.83 |     122.97 |    55.64 |    165.86 |  42.576
 1dice37Ee     128      0.00195 |     6826 |     17 (0.00251) |   6761 |      48 |    1276.62 |    1173.85 |    40.25 |    102.77 |  91.950
 1dice3jkp     256      0.00391 |     5827 |     27 (0.00464) |   5786 |      14 |     616.51 |     382.08 |    13.11 |    234.42 |  61.975
 1dice4J1m     512      0.00781 |     8892 |     63 (0.00709) |   8824 |       5 |    1739.31 |    1089.80 |     9.35 |    649.50 |  62.657
 1dice5wwE    1000      0.01526 |    15925 |    236 (0.01482) |  15685 |       4 |    2756.39 |    2450.40 |     1.80 |    305.98 |  88.899
 1dice61SN    1500      0.02289 |     8967 |    210 (0.02343) |   8751 |       6 |    3256.01 |    3665.55 |    15.00 |   -409.53 | 112.578
 1dice6DPt    2000      0.03052 |    11337 |    354 (0.03123) |  10980 |       3 |    3646.61 |    3354.68 |     9.24 |    291.92 |  91.995
 1dice6gJg    3000      0.04578 |     8927 |    427 (0.04787) |   8493 |       7 |    5216.73 |    6683.19 |    24.99 |  -1466.45 | 128.111
 1dice6GV5    4000      0.06104 |    10143 |    626 (0.06174) |   9514 |       3 |    3567.93 |    3171.19 |    31.20 |    396.73 |  88.880
 1dice6wBx    6000      0.09155 |    17029 |   1611 (0.09465) |  15409 |       9 |    9079.47 |    9226.85 |     7.01 |   -147.37 | 101.623
 1dice6YgE    8000      0.12207 |    37526 |   4629 (0.12340) |  32884 |      13 |    7005.33 |    6237.39 |     0.00 |    767.93 |  89.038
 1dice7EYz   12000      0.18311 |    16709 |   3175 (0.19009) |  13528 |       6 |    6889.23 |    7054.31 |    14.50 |   -165.07 | 102.396
 1dice7fUk   16000      0.24414 |    46103 |  11191 (0.24278) |  34904 |       8 |   16027.59 |   16745.35 |   347.79 |   -717.75 | 104.478
 1dice7W2A   24000      0.36621 |    34421 |  12722 (0.36994) |  21667 |      32 |   15737.97 |   15719.00 |   212.63 |     18.96 |  99.880
 1dice8EMZ   32000      0.48828 |   327695 | 159682 (0.48749) | 167878 |     135 |  107120.63 |  107556.79 |  2173.21 |   -436.15 | 100.407
 1dice97EC   32768      0.50000 |   136499 |  68098 (0.49921) |  68313 |      88 |   55731.87 |   53925.25 |   789.20 |   1806.61 |  96.758
 1dice9wcM   48000      0.73242 |   103661 |  76242 (0.73591) |  27360 |      59 |   90711.92 |   89152.46 |   467.98 |   1559.45 |  98.281
 1dicec9k7   52000      0.79346 |     1985 |   1607 (0.80957) |    378 |       0 |    4459.43 |    4658.13 |     0.00 |   -198.70 | 104.456
 1dicegEAr   56000      0.85449 |     1449 |   1233 (0.85152) |    215 |       1 |    1374.72 |    1391.61 |     0.00 |    -16.88 | 101.228
 1diceDCd2   60000      0.91553 |      588 |    540 (0.92308) |     45 |       3 |     364.32 |     357.23 |     0.00 |      7.09 |  98.053
 1dice9wVt   64000      0.97656 |     6061 |   5805 (0.97876) |    126 |     130 |    5171.27 |    4973.99 |   239.20 |    197.27 |  96.185
--------------------------------------------------------------------------------------------------------------------------------------------
                                |   833754 | 348507           | 484184 |    1063 |  342500.33 |  339207.45 |  4491.23 |   3292.87 |  99.039
--------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:       3292.87867058 BTC (0.961%)
Cumulative Fees Paid:         419.73287500 BTC
SD Profit after fees:        2873.14579558 BTC (0.839%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  2543951  :  SatoshiDice Tx: 1534859  (60.3%)
Blockchain MB:  1071.1  :  SatoshiDice Tx: 630.9  (58.9%)

[dooglus]

A bad night for SatoshiDice - down around 1000 BTC.  It seems there have been a lot of double-spend attempts too.  I wonder if there's a connection between the two things.

Results: 2012-Jul-30 07:18am (up to block 191543)

   Address  Target   Should Win |    #Bets |       Win        |  Lose  | Refunds |   BTC In   |  BTC Out   |  Refund  |   Profit  |   RTP 
--------------------------------------------------------------------------------------------------------------------------------------------
 1dice1e6p       1      0.00002 |    11615 |      0 (0.00000) |  11331 |     284 |      69.96 |       0.01 |    18.39 |     69.94 |   0.028
 1dice1Qf4       2      0.00003 |     1090 |      0 (0.00000) |   1020 |      70 |      15.71 |       0.00 |     5.58 |     15.71 |   0.011
 1dice2pxm       4      0.00006 |     1648 |      0 (0.00000) |   1614 |      34 |      20.08 |       0.02 |     2.22 |     20.06 |   0.105
 1dice2vQo       8      0.00012 |     1357 |      1 (0.00076) |   1315 |      41 |      32.29 |       8.05 |     4.15 |     24.23 |  24.940
 1dice2WmR      16      0.00024 |     1666 |      1 (0.00061) |   1632 |      33 |      66.58 |       4.19 |     7.40 |     62.39 |   6.301
 1dice2xkj      32      0.00049 |     4081 |      2 (0.00049) |   4068 |      11 |     279.31 |     103.07 |     1.29 |    176.23 |  36.904
 1dice2zdo      64      0.00098 |     5848 |      8 (0.00137) |   5823 |      17 |     297.90 |     123.01 |    55.64 |    174.89 |  41.292
 1dice37Ee     128      0.00195 |     6845 |     17 (0.00250) |   6780 |      48 |    1286.70 |    1173.89 |    40.25 |    112.81 |  91.232
 1dice3jkp     256      0.00391 |     5902 |     29 (0.00493) |   5859 |      14 |     628.51 |     572.02 |    13.11 |     56.49 |  91.011
 1dice4J1m     512      0.00781 |     8955 |     65 (0.00726) |   8885 |       5 |    1750.23 |    1184.79 |     9.35 |    565.44 |  67.693
 1dice5wwE    1000      0.01526 |    16382 |    248 (0.01514) |  16130 |       4 |    3562.43 |    3767.40 |     1.80 |   -204.97 | 105.754
 1dice61SN    1500      0.02289 |     8968 |    210 (0.02343) |   8752 |       6 |    3256.21 |    3665.55 |    15.00 |   -409.33 | 112.571
 1dice6DPt    2000      0.03052 |    11551 |    361 (0.03126) |  11187 |       3 |    3648.06 |    3356.74 |     9.24 |    291.31 |  92.014
 1dice6gJg    3000      0.04578 |     8928 |    427 (0.04786) |   8494 |       7 |    5216.73 |    6683.19 |    24.99 |  -1466.45 | 128.111
 1dice6GV5    4000      0.06104 |    10208 |    632 (0.06193) |   9573 |       3 |    3573.37 |    3172.16 |    31.20 |    401.20 |  88.772
 1dice6wBx    6000      0.09155 |    17052 |   1614 (0.09470) |  15429 |       9 |    9084.06 |    9232.62 |     7.01 |   -148.55 | 101.635
 1dice6YgE    8000      0.12207 |    37679 |   4646 (0.12335) |  33019 |      14 |    7017.50 |    6243.20 |     0.00 |    774.30 |  88.966
 1dice7EYz   12000      0.18311 |    16748 |   3182 (0.19006) |  13560 |       6 |    6921.33 |    7113.30 |    14.50 |   -191.96 | 102.774
 1dice7fUk   16000      0.24414 |    46268 |  11233 (0.24282) |  35027 |       8 |   16154.92 |   16916.37 |   347.79 |   -761.45 | 104.713
 1dice7W2A   24000      0.36621 |    34466 |  12740 (0.36998) |  21694 |      32 |   15741.96 |   15723.30 |   212.63 |     18.65 |  99.881
 1dice8EMZ   32000      0.48828 |   331769 | 161677 (0.48752) | 169957 |     135 |  116410.91 |  117177.20 |  2173.21 |   -766.29 | 100.658
 1dice97EC   32768      0.50000 |   137585 |  68666 (0.49940) |  68831 |      88 |   56301.01 |   54423.28 |   789.20 |   1877.72 |  96.665
 1dice9wcM   48000      0.73242 |   104513 |  76881 (0.73603) |  27573 |      59 |   92526.80 |   91112.63 |   467.98 |   1414.17 |  98.472
 1dicec9k7   52000      0.79346 |     2059 |   1667 (0.80962) |    392 |       0 |    4661.48 |    4903.43 |     0.00 |   -241.94 | 105.190
 1dicegEAr   56000      0.85449 |     1499 |   1273 (0.84980) |    225 |       1 |    1563.72 |    1604.60 |     0.00 |    -40.87 | 102.614
 1diceDCd2   60000      0.91553 |      609 |    557 (0.91914) |     49 |       3 |     378.25 |     368.39 |     0.00 |      9.86 |  97.393
 1dice9wVt   64000      0.97656 |     6062 |   5806 (0.97876) |    126 |     130 |    5171.28 |    4974.01 |   239.20 |    197.27 |  96.185
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                                |   841353 | 351943           | 488345 |    1065 |  355637.43 |  353606.54 |  4491.23 |   2030.88 |  99.429
--------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees:       2030.88983388 BTC (0.571%)
Cumulative Fees Paid:         423.63052500 BTC
SD Profit after fees:        1607.25930888 BTC (0.452%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx:  2566538  :  SatoshiDice Tx: 1548823  (60.3%)
Blockchain MB:  1080.6  :  SatoshiDice Tx: 637.0  (58.9%)