Satoshi Dice -- Statistical Analysis - page 74.

dooglus

legendary

Activity: 2940

Merit: 1333

Quote from: nibor on July 26, 2012, 07:03:54 AM

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://bitcointalksearch.org/topic/m.1053597 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.

nibor

sr. member

Activity: 438

Merit: 291

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

organofcorti

donator

Activity: 2058

Merit: 1007

Poor impulse control.

jamesg

vip

Activity: 1358

Merit: 1000

AKA: gigavps

nibor

sr. member

Activity: 438

Merit: 291

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

organofcorti

donator

Activity: 2058

Merit: 1007

Poor impulse control.

The fix is fixed.

dooglus

legendary

Activity: 2940

Merit: 1333

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.

Quote from: organofcorti on July 25, 2012, 10:38:37 PM

[...]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

donator

Activity: 2058

Merit: 1007

Poor impulse control.

Quote from: dooglus on July 25, 2012, 11:44:32 PM

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.

Quote

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

legendary

Activity: 2940

Merit: 1333

Quote from: organofcorti on July 25, 2012, 10:38:37 PM

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

donator

Activity: 2058

Merit: 1007

Poor impulse control.

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

legendary

Activity: 2940

Merit: 1333

Quote from: traderjoe on July 25, 2012, 09:59:43 PM

Quote from: dooglus on July 25, 2012, 02:59:02 PM

...
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.

traderjoe

jr. member

Activity: 34

Merit: 12

Quote from: dooglus on July 25, 2012, 02:59:02 PM

...
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.

dooglus

legendary

Activity: 2940

Merit: 1333

dooglus

legendary

Activity: 2940

Merit: 1333

Sure. I'm just saying what I see... Recently the players have been lucky. Two of the top three "Big Winners" listed on http://www.satoshidice.com/ which lists the biggest wins of all time have been in the last 24 hours. The biggest loss of all time was also in the last 24 hours, but I documented that 219 BTC loss in the post you replied to - it just happens that the biggest loss ever was part of a winning martingale chain.

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.

gmaxwell

staff

Activity: 4242

Merit: 8672

Quote from: dooglus on July 25, 2012, 02:01:34 PM

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.

elux

legendary

Activity: 1458

Merit: 1006

dooglus

legendary

Activity: 2940

Merit: 1333

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

2012-07-25 14:51:37 lessthan 16000 Bet Amount: 0.25 Outcome: LOSE Payment: 0.000750 Profit: -0.24925 Cumulative Profit: -0.24925
2012-07-25 14:52:10 lessthan 16000 Bet Amount: 0.50 Outcome: LOSE Payment: 0.002000 Profit: -0.498 Cumulative Profit: -0.74725
2012-07-25 14:52:37 lessthan 16000 Bet Amount: 1.00 Outcome: LOSE Payment: 0.004500 Profit: -0.9955 Cumulative Profit: -1.74275
2012-07-25 14:53:07 lessthan 16000 Bet Amount: 2.00 Outcome: LOSE Payment: 0.009500 Profit: -1.9905 Cumulative Profit: -3.73325
2012-07-25 14:53:38 lessthan 16000 Bet Amount: 4.00 Outcome: LOSE Payment: 0.019500 Profit: -3.9805 Cumulative Profit: -7.71375
2012-07-25 14:54:06 lessthan 16000 Bet Amount: 8.00 Outcome: LOSE Payment: 0.039500 Profit: -7.9605 Cumulative Profit: -15.67425
2012-07-25 14:54:32 lessthan 16000 Bet Amount: 16.00 Outcome: LOSE Payment: 0.079500 Profit: -15.9205 Cumulative Profit: -31.59475
2012-07-25 14:55:07 lessthan 16000 Bet Amount: 32.00 Outcome: LOSE Payment: 0.159500 Profit: -31.8405 Cumulative Profit: -63.43525
2012-07-25 14:55:41 lessthan 16000 Bet Amount: 64.00 Outcome: LOSE Payment: 0.319500 Profit: -63.6805 Cumulative Profit: -127.11575
2012-07-25 14:56:17 lessthan 16000 Bet Amount: 128.00 Outcome: LOSE Payment: 0.639500 Profit: -127.3605 Cumulative Profit: -254.47625
2012-07-25 14:58:10 lessthan 16000 Bet Amount: 219.00 Outcome: LOSE Payment: 1.094500 Profit: -217.9055 Cumulative Profit: -472.38175
2012-07-25 14:59:36 lessthan 16000 Bet Amount: 219.00 Outcome: WIN Payment: 876.589924 Profit: 657.589924 Cumulative Profit: 185.208174

dooglus

legendary

Activity: 2940

Merit: 1333

SatoshiDice profits are almost 800 BTC down since my last update:

Quote

Results: 2012-Jul-25 10:19am (up to block 190713)

Address Target Should Win | #Bets | Win | Lose | Refunds | BTC In | BTC Out | Refund | Profit | RTP
--------------------------------------------------------------------------------------------------------------------------------------------
1dice1e6p 1 0.00002 | 10981 | 0 (0.00000) | 10700 | 281 | 61.10 | 0.01 | 17.94 | 61.08 | 0.032
1dice1Qf4 2 0.00003 | 1037 | 0 (0.00000) | 967 | 70 | 11.14 | 0.00 | 5.58 | 11.14 | 0.016
1dice2pxm 4 0.00006 | 1512 | 0 (0.00000) | 1479 | 33 | 14.48 | 0.00 | 2.22 | 14.47 | 0.059
1dice2vQo 8 0.00012 | 1303 | 0 (0.00000) | 1263 | 40 | 18.66 | 0.00 | 4.15 | 18.65 | 0.042
1dice2WmR 16 0.00024 | 1523 | 0 (0.00000) | 1493 | 30 | 26.05 | 0.02 | 6.60 | 26.02 | 0.107
1dice2xkj 32 0.00049 | 3652 | 1 (0.00027) | 3640 | 11 | 130.12 | 100.42 | 1.29 | 29.69 | 77.180
1dice2zdo 64 0.00098 | 5364 | 7 (0.00131) | 5340 | 17 | 226.17 | 121.70 | 55.64 | 104.46 | 53.811
1dice37Ee 128 0.00195 | 6412 | 15 (0.00236) | 6349 | 48 | 1244.24 | 1148.24 | 40.25 | 95.99 | 92.285
1dice3jkp 256 0.00391 | 5147 | 24 (0.00468) | 5109 | 14 | 553.11 | 362.14 | 13.11 | 190.97 | 65.473
1dice4J1m 512 0.00781 | 8172 | 53 (0.00649) | 8114 | 5 | 1604.61 | 823.09 | 9.35 | 781.51 | 51.296
1dice5wwE 1000 0.01526 | 14588 | 214 (0.01467) | 14371 | 3 | 2417.52 | 2125.60 | 1.80 | 291.92 | 87.925
1dice61SN 1500 0.02289 | 8296 | 194 (0.02340) | 8096 | 6 | 3122.05 | 3552.96 | 15.00 | -430.90 | 113.802
1dice6DPt 2000 0.03052 | 10107 | 316 (0.03127) | 9788 | 3 | 3478.98 | 3206.15 | 9.24 | 272.83 | 92.158
1dice6gJg 3000 0.04578 | 8195 | 399 (0.04873) | 7789 | 7 | 5030.24 | 6550.35 | 24.99 | -1520.10 | 130.219
1dice6GV5 4000 0.06104 | 9079 | 569 (0.06269) | 8507 | 3 | 3180.27 | 2896.93 | 31.20 | 283.33 | 91.091
1dice6wBx 6000 0.09155 | 16440 | 1546 (0.09408) | 14886 | 8 | 8925.97 | 9067.97 | 7.01 | -142.00 | 101.591
1dice6YgE 8000 0.12207 | 33122 | 4110 (0.12411) | 29005 | 7 | 6585.90 | 5832.77 | 0.00 | 753.13 | 88.564
1dice7EYz 12000 0.18311 | 16604 | 3152 (0.18990) | 13446 | 6 | 6847.82 | 6997.24 | 14.50 | -149.42 | 102.182
1dice7fUk 16000 0.24414 | 44500 | 10794 (0.24261) | 33698 | 8 | 15321.65 | 15993.57 | 347.79 | -671.92 | 104.385
1dice7W2A 24000 0.36621 | 33157 | 12260 (0.37011) | 20865 | 32 | 13776.12 | 13700.65 | 212.63 | 75.46 | 99.452
1dice8EMZ 32000 0.48828 | 317884 | 154881 (0.48743) | 162872 | 131 | 99455.79 | 99929.98 | 2173.21 | -474.19 | 100.477
1dice97EC 32768 0.50000 | 131626 | 65636 (0.49895) | 65911 | 79 | 49433.29 | 47790.93 | 789.20 | 1642.36 | 96.678
1dice9wcM 48000 0.73242 | 94745 | 69696 (0.73601) | 24998 | 51 | 78368.91 | 77135.83 | 467.98 | 1233.07 | 98.427
1dicec9k7 52000 0.79346 | 972 | 778 (0.80041) | 194 | 0 | 1393.07 | 1388.75 | 0.00 | 4.32 | 99.690
1dicegEAr 56000 0.85449 | 752 | 620 (0.82447) | 132 | 0 | 425.96 | 362.98 | 0.00 | 62.97 | 85.216
1diceDCd2 60000 0.91553 | 197 | 176 (0.90722) | 18 | 3 | 51.65 | 52.15 | 0.00 | -0.49 | 100.966
1dice9wVt 64000 0.97656 | 5969 | 5715 (0.97860) | 125 | 129 | 5036.67 | 4843.84 | 239.20 | 192.82 | 96.172
--------------------------------------------------------------------------------------------------------------------------------------------
| 791336 | 331156 | 459155 | 1025 | 306741.65 | 303984.41 | 4489.97 | 2757.23 | 99.101
--------------------------------------------------------------------------------------------------------------------------------------------

SD Profit before fees: 2757.23594710 BTC (0.899%)
Cumulative Fees Paid: 398.36787500 BTC
SD Profit after fees: 2358.86807210 BTC (0.769%)
----
Since Satoshi Dice started, there have been:
Blockchain Tx: 2409837 : SatoshiDice Tx: 1458898 (60.5%)
Blockchain MB: 1017.2 : SatoshiDice Tx: 599.6 (58.9%)

Quote

dooglus

legendary

Activity: 2940

Merit: 1333

See how the blue line goes vertical at the end? It actually goes up 400 BTC then back down 400 BTC. I looked at the big bets that caused this and it appears to be a single player:

2012-07-24 05:50:58 lessthan 32000 Bet Amount: 21.50 Outcome: LOSE Payment: 0.10700000 Profit: -21.393 Cumulative Profit: -21.393
2012-07-24 05:51:51 lessthan 32000 Bet Amount: 43.00 Outcome: LOSE Payment: 0.21450000 Profit: -42.7855 Cumulative Profit: -64.1785
2012-07-24 05:52:27 lessthan 32000 Bet Amount: 86.00 Outcome: LOSE Payment: 0.42950000 Profit: -85.5705 Cumulative Profit: -149.749
2012-07-24 05:56:39 lessthan 16000 Bet Amount: 86.00 Outcome: LOSE Payment: 0.42950000 Profit: -85.5705 Cumulative Profit: -235.3195
2012-07-24 05:54:07 lessthan 32000 Bet Amount: 172.00 Outcome: LOSE Payment: 0.85950000 Profit: -171.1405 Cumulative Profit: -406.46
2012-07-24 05:58:02 lessthan 16000 Bet Amount: 107.50 Outcome: WIN Payment: 430.28932000 Profit: 322.78932 Cumulative Profit: -83.67068
2012-07-24 06:04:53 lessthan 48000 Bet Amount: 250.00 Outcome: WIN Payment: 334.39083333 Profit: 84.39083333 Cumulative Profit: 0.72015333

He bets thousands of dollars and ends up less than $10 up. Notice how after losing the 86 BTC bet he bets the same amount at double the odds rather than doubling the bet. Martingale gets scary quick!

unclemantis

member

Activity: 98

Merit: 10

(:firstbits => "1mantis")

I got lucky on a game. I ment to enter 0.10 but entered in 1 instead and i was like NO!!!!! and then I get back like over 2 and change LOL

Topic: Satoshi Dice -- Statistical Analysis - page 74. (Read 192889 times)