SatoshiDICE.com - The World's Most Popular Bitcoin Game

[ErebusBat]

OMG I just saw the Blockchain.info auto plugin for SatoshiDice!!! I didn't even request that he add it, but now I will have to send him money and hookers, cause that is the coolest thing ever. Way more fun that just playing from a desktop client. 

Hrm umm.... I suggested it... ya that is right it was my idea....

[dooglus]

Sum typoes:

All transactions in that block and befor are included in the jackpot.

before

So a players own winning bet gets included in their jackpot.

player's

Winners are not payed until their bet transaction has at least 2 confirmations

'paid' is more commonly accepted as correct

It is to the winners advantage to wait for confirmation

winner's

So for the progress games we involve a trustable third party

progressive?

allowing interested parties to eaves drop on that message stream

eavesdrop is a single word

[sgravina]

Since we are correcting stuff the following text from http://www.satoshidice.com/bits.php is not correct:

If you lose, the return is one half the house edge.

In actuality you are returning .005 * the bet.

The amount of your winning payout is the bet times:

((1-h)-0.01*(1-p)/2)/p

where h = house edge, p = probability of winning.

According to your rules it should be:

((1-h)-h*(1-p)/2)/p

Since your house edge started out at 1% your winning payout was initially correct.  But now it isn't.

I figured this out by creating a SatoshiDice simulation in Excel and then in Matlab.  It made a very nice demonstration of why I lost so much money playing SatoshiDice.  As I already knew and everyone else should know also, SatoshiDice will make you poorer.  Interestingly there is a significant probability that SatoshiDice itself will loose a lot of money, despite it's house edge.  I think that is why they have had to decrease bet limits and increase the house edge.

[dooglus]

Interestingly there is a significant probability that SatoshiDice itself will loose a lot of money, despite it's house edge.  I think that is why they have had to decrease bet limits and increase the house edge.

Look how they lost over 3000 BTC ($15,000) in a 7 day period (June 2nd to June 9th):



It looks to me like a large amount of those losses stemmed from a single bet:

  http://blockchain.info/tree/7470279

Follow that bet, its winnings, and the various change outputs, and you find a sequence of large bets with unusually high win rates.  I found 45 "lessthan 32000" bets with 26/45 winning (58%) when it should be 48%, and 19 "lessthan 48000" bets with 15/19 winning (79%) when it should be 73%.  The bets are mostly 50 or 100 BTC each.

My knowledge of statistics isn't good enough to work out whether this is reasonable variance, or whether it's suspicious but I suspect that I don't have enough data points to draw any safe conclusions.

[nimda]

Interestingly there is a significant probability that SatoshiDice itself will loose a lot of money, despite it's house edge.  I think that is why they have had to decrease bet limits and increase the house edge.

Look how they lost over 3000 BTC ($15,000) in a 7 day period (June 2nd to June 9th):

https://i.imgur.com/ru1Gz.png

It looks to me like a large amount of those losses stemmed from a single bet:

  http://blockchain.info/tree/7470279

Follow that bet, its winnings, and the various change outputs, and you find a sequence of large bets with unusually high win rates.  I found 45 "lessthan 32000" bets with 26/45 winning (58%) when it should be 48%, and 19 "lessthan 48000" bets with 15/19 winning (79%) when it should be 73%.  The bets are mostly 50 or 100 BTC each.

My knowledge of statistics isn't good enough to work out whether this is reasonable variance, or whether it's suspicious but I suspect that I don't have enough data points to draw any safe conclusions.

For situations like these it's hard to set a threshold of probability. For example, according to our current understanding of quantum mechanics, it is possible but highly unlikely that Ella Fitzgerald will appear next to you right now. There's an overwhelmingly larger yet still incredibly small possibility that most of the particles in my nose will "teleport" somewhere else. I ignore this possibility in my everyday life and assume that my nose will continue to exist in its current form because the probability of mass localized long-distance quantum teleportation is so small.

To find the probability of "beating the odds," we can use a binomial probability distribution function. It's basically Bernoulli's experiment.


The probability of winning exactly 26/45 bets on 48% odds is binompdf(45, .48, 26) = 5.05%, which is fairly reasonable.
The probability of winning at least 26/45 bets on 48% odds is binompdf(45, .48, 26)+binompdf(45, .48, 27)+...+binompdf(45, .48, 45) = 12.23%, which is between 1/8 and 1/9 odds.
This makes sense when you consider that 48% is close to 1/2, and 26/45 is close to 1/2 as well.

For the second data set:
18.35% for exactly 15/19 wins on 73% odds
38.71% for at least 15/19 wins on 73% odds

I am happy to post more technical details, such as the source code of the program I used to sum up the density functions or the output answers to more decimal places, but I suspect it's not really wanted.

TL;DR no, it's not suspicious, just unlucky that it happened on such large bets.

[dooglus]

it is possible but highly unlikely that Ella Fitzgerald will appear next to you right now

She didn't.  It was quite a relief because she's been dead since 1996.

To find the probability of "beating the odds," we can use a binomial probability distributionfunction.

Oh, I was close then.  I found myself at http://en.wikipedia.org/wiki/Binomial_distribution yesterday when I was trying to work out how to do this, but didn't have enough confidence that I had the right distribution to proceed.

Thanks a lot for doing the maths.

The probability of winning at least 26/45 bets on 48% odds is 12.23%

38.71% for at least 15/19 wins on 73% odds

So a combined probability of 38.71 * 12.23 / 100 = 4.73%, or about 1 in 21.

it's not suspicious, just unlucky that it happened on such large bets.

If you look at blockexplorer you see that at 2012-06-01 08:34:55 he received 100 BTC which he lost (lose 50, win 60, lose 50, lose 71) and then at 2012-06-01 21:27:22 he received the 100 BTC which went on to win lots.

It strikes me as unlikely that he would lose the whole of his first bankroll if there was anything suspicious going on.  Perhaps this was just poor bankroll management on SatoshiDice's part.  The only refunded bet I saw was 3 days after this guy started on his winning streak.

[nimda]

Warning: heading more off-topic into probability theories.

Oh, I was close then.  I found myself at http://en.wikipedia.org/wiki/Binomial_distribution yesterday when I was trying to work out how to do this, but didn't have enough confidence that I had the right distribution to proceed.

Thanks a lot for doing the maths.

You were more than close. That formula is exactly what you need. In general, an understanding of binomial probability or "Bernoulli trials" will get you a long way. If
 n = number of trials
 r = number of specific events you wish to
       obtain
 p = probability that the event will occur
then all you need is

Where

is the binomial coefficient, also denoted C(n, k),  _nC_k, or ⁿC_k

(yes, I did steal the part beginning with "Where" from Wikipedia; it's nice, easy, and compact)

[ThePok]

i dont understand the pogressiv pots:

it says:
Llama Dance   1DiCeLLhySbEQxWMGo84NbGbZsYwMjpBYs    1.0000   1   One in 16   1.500%   3.1916

so i pay 1 btc and one in 16 times i win 3.19 BTC....whos ever gone play that???
Its only profitable if Pot is at 16 BTC but it will never get there?? (Only if silly people play?!?)

Whats the Math behind this

[nimda]

The math is that SatoshiDice carries a house edge, so it's a negative-sum game for the gambler.

[fireduck]

Sum typoes:

Thanks.

[Otoh]

Heh ... don't look now but SatoshiDICE just got even easier to use:



 - http://blockchain.info/wallet

From your Blockchain.info wallet, click Send Money, then on the left is "Games - Satoshi Dice".

The balance will update with your win or loss, or you can click Transactions.  It will update in real-time.

I've refreshed & re-logged in to my wallet but can't see any games link on the Send Money page, just this as before...

[Fredyy]

My transaction has not been processed!

https://blockchain.info/tx-index/10370227/09c0eb6102a8190b8261e0f03ec557ce81a2e37e87231199b4195cd2f0264279
http://www.satoshidice.com/lookup.php?tx=09c0eb6102a8190b8261e0f03ec557ce81a2e37e87231199b4195cd2f0264279
http://www.satoshidice.com/full.php?tx=09c0eb6102a8190b8261e0f03ec557ce81a2e37e87231199b4195cd2f0264279

still not processed

[ErebusBat]

I've refreshed & re-logged in to my wallet but can't see any games link on the Send Money page, just this as before...

Otoh,

Blockchain.info is not affiliated with SatoshiDICE, you should post in their thread: https://bitcointalk.org/index.php?topic=40264.0

[Otoh]

I've refreshed & re-logged in to my wallet but can't see any games link on the Send Money page, just this as before...

Otoh,

Blockchain.info is not affiliated with SatoshiDICE, you should post in their thread: https://bitcointalk.org/index.php?topic=40264.0

Thanks, have done

[dooglus]

I think I just saw a bug in the Progressive bet detail page.  It says the bet won, but that the payout was zero.  Also the bet tx and the payment tx are the same:



Then, a few seconds later, it fixed itself:

[dooglus]

so i pay 1 btc and one in 16 times i win 3.19 BTC....whos ever gone play that???
Its only profitable if Pot is at 16 BTC but it will never get there?? (Only if silly people play?!?)

Whats the Math behind this

Talking of silly people, look at this!

Someone bet 100 BTC to win that 3.19 BTC.  70% of the 100 BTC gets added to the available pot, so they win a total of 73.19.  Actually, they won it 4 times, and split the 73.19 with themselves 4 times.  Still a loss of 27 BTC though...

[mem]

so i pay 1 btc and one in 16 times i win 3.19 BTC....whos ever gone play that???
Its only profitable if Pot is at 16 BTC but it will never get there?? (Only if silly people play?!?)

Whats the Math behind this

Talking of silly people, look at this!

Someone bet 100 BTC to win that 3.19 BTC.  70% of the 100 BTC gets added to the available pot, so they win a total of 73.19.  Actually, they won it 4 times, and split the 73.19 with themselves 4 times.  Still a loss of 27 BTC though...

satoshidice due to the 0 confirmations makes for an awesome bitcoin laundering system

[dooglus]

satoshidice due to the 0 confirmations makes for an awesome bitcoin laundering system

But charges 27%...  there must be cheaper ways to clean 100 BTC.  Bet 5 BTC on "lessthan 48000" 20 times and you'll probably do better than losing 27%.

[ErebusBat]

so i pay 1 btc and one in 16 times i win 3.19 BTC....whos ever gone play that???
Its only profitable if Pot is at 16 BTC but it will never get there?? (Only if silly people play?!?)

Whats the Math behind this

Talking of silly people, look at this!

Someone bet 100 BTC to win that 3.19 BTC.  70% of the 100 BTC gets added to the available pot, so they win a total of 73.19.  Actually, they won it 4 times, and split the 73.19 with themselves 4 times.  Still a loss of 27 BTC though...

satoshidice due to the 0 confirmations makes for an awesome bitcoin laundering system

Progressive bets are not zero conf.

[kano]

satoshidice due to the 0 confirmations makes for an awesome bitcoin laundering system

But charges 27%...  there must be cheaper ways to clean 100 BTC.  Bet 5 BTC on "lessthan 48000" 20 times and you'll probably do better than losing 27%.

I think you missed the word 'laundering' since the satoshi bet you make points directly back to you ...