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Title: Satoshi Dice - need some explanations Post by: c0inbuster on February 06, 2013, 06:21:36 PM Hello,
I need some explanations about Satoshi Dice betting game. I did a little Python script (with Numpy and Pandas) in order to test differents "strategies" (I know it 's a negative expected value game so I don't expect a lot from this ;-) ). see http://pastebin.com/sMikS4xG but I don't know what I should do with "house_percent" variable. I think I did a mistake here : Code: self.df['BalanceVar'] = np.where(self.df['TossResults']>0, self.df['Size']*price_multiplier, -self.df['Size']) but I don't know how this variable (house_percent) should intervene. Kind regards Title: Re: Satoshi Dice - need some explanations Post by: wtfvanity on February 06, 2013, 06:24:45 PM Why did you post the same thing twice?
https://bitcointalk.org/index.php?topic=141588.msg1508155#msg1508155 Title: Re: Satoshi Dice - need some explanations Post by: c0inbuster on February 06, 2013, 07:34:04 PM Because I did a mistake and when I click to alert moderator the forum says that I had to wait 360 seconds ! and after waiting I get this message
An Error Has Occurred! You can't report your own post to the moderator, that doesn't make sense! Title: Re: Satoshi Dice - need some explanations Post by: wtfvanity on February 06, 2013, 07:37:42 PM Because I did a mistake and when I click to alert moderator the forum says that I had to wait 360 seconds ! You can edit your post. They look identical just different subjects. If you're just looking for the edge that the house maintains, they post that on their site http://satoshidice.com/ It is 1.9% with the exception of less than 1 which is 1.844, which no one has ever won. Title: Re: Satoshi Dice - need some explanations Post by: c0inbuster on February 06, 2013, 07:57:28 PM In fact my problem is mathematics...
Let's have a look at "less than 8000". win odds = 8000/65535 = 12.2% (and lose odds = 87.8%) According to website multiplier is 8 and house percent is 1.9% Let's imagine that I'm paying 0.1BTC for this game. Expected value is : 0.1 * 8 * 12.2 + (-0.1) * 87.8 The problem with this formula is that I get a positive expected value > 0.1*8*12.2/100-0.1*87.8/100 0.0098 I should get a negative value ! Title: Re: Satoshi Dice - need some explanations Post by: Envite on February 06, 2013, 11:50:13 PM Why negative?
Your expected income needs to be positive. Your earnings will be negative (that's what you get if you do 0.01-0.0098) Title: Re: Satoshi Dice - need some explanations Post by: c0inbuster on February 07, 2013, 05:14:58 AM Expected income IS negative
it MUST BE negative otherwise the casino always ends up close ! that's why there is a "house_percent" Title: Re: Satoshi Dice - need some explanations Post by: DannyHamilton on February 07, 2013, 06:01:14 AM Expected income IS negative it MUST BE negative otherwise the casino always ends up close ! that's why there is a "house_percent" I'm not yet sure where my mistake is, but there has to be something wrong with my math. Here's whay I came up with looking at "lessthan 8000": Play 0.01 BTC 65536 times. Assume that each possible value comes up once. Total bets = 65,536 * 0.01 BTC = 655.36 BTC in bets placed. 8,000 wins = 8,000 * 8 * 0.01 = 640 BTC in winnings 655.36 BTC - 640 BTC = 15.36 BTC in profits for "the house" 8,000 wins / 65,536 plays = 12.2070% Win Odds Satoshi Dice advertises 12.2070% Win Odds, so this looks good 15.36 BTC / 655.36 BTC = house edge of 2.34% Satoshi Dice advertises 1.9% House Percent, this is where I must be making a mistake. My calculated house edge seems higher than the actual house edge. Title: Re: Satoshi Dice - need some explanations Post by: deepceleron on February 07, 2013, 07:45:15 AM Expected income IS negative it MUST BE negative otherwise the casino always ends up close ! that's why there is a "house_percent" I'm not yet sure where my mistake is... Satoshidice pays out losers too, and you pay the transaction fee back to yourself: 1. If you lose, your bet is returned times 0.005 (0.5% for losers) 2. On a win or a lose a transaction fee of 0.0005 is subtracted from the payment amount. If this makes the payment amount zero or less the payment is set to 0.00000001. https://bitcointalk.org/index.php?topic=80312.msg1022610#msg1022610 Title: Re: Satoshi Dice - need some explanations Post by: DannyHamilton on February 07, 2013, 08:18:45 AM . . . Satoshidice pays out losers too . . . Ah ha! I hadn't realized that they ever paid more than 0.00000001 on a loser. Now the math works out.1. If you lose, your bet is returned times 0.005 (0.5% for losers) . . . Play 1 BTC 65536 times. Assume that each possible value comes up once. Total bets = 65,536 * 1 BTC = 65,536 BTC in bets placed. 8,000 wins = 8,000 * 8 * 1 = 64,000 BTC returned on winning bets 57,536 losses = 57,536 * 0.005 * 1 = 287.68 BTC returned on losing bets 65,536 BTC received - (64,000 BTC + 287.68 BTC) paid = 1,248.32 BTC in profits for "the house" 8,000 wins / 65,536 plays = 12.2070% Win Odds Satoshi Dice advertises 12.2070% Win Odds, so this looks good 1248.32 BTC / 65,536 BTC = house edge of 1.9048% Satoshi Dice advertises 1.9% House Percent, so this looks good too. Title: Re: Satoshi Dice - need some explanations Post by: c0inbuster on February 07, 2013, 12:24:27 PM Thanks a lot for your explanations.
I will try to improve my script to reflect that. I would like to try to make some martingale experiments (I know that it is a desperate and suicidal strategy that's just for fun ;-) ) I would also like to try cautious technics such as Kelly criterion. Anyway winner is always the casino ;-) Title: Re: Satoshi Dice - need some explanations Post by: c0inbuster on February 07, 2013, 01:09:54 PM I think I'm still wrong
see http://pastebin.com/pyDB3wiN I changed Code: self.df['BalanceVar'] = np.where(self.df['TossResults']>0, self.df['Size']*price_multiplier, -self.df['Size']) Code: self.df['BalanceVar'] = np.where(self.df['TossResults']>0, self.df['Size']*price_multiplier, -self.df['Size']+0.005 * self.df['Size']) I probably did a mistake... but I don't know what mistake I did !!! Any help is welcome (you will need Python 2.7, Numpy and Pandas) Title: Re: Satoshi Dice - need some explanations Post by: c0inbuster on February 07, 2013, 02:02:05 PM In fact the problem is here
Code: self.df['BalanceVar'] = np.where(self.df['TossResults']>0, self.df['Size']*price_multiplier, -self.df['Size']+0.005 * self.df['Size']) I should be : Code: self.df['BalanceVar'] = np.where(self.df['TossResults']>0, self.df['Size']*(price_multiplier-1), -self.df['Size']+0.005 * self.df['Size']) Because if you bet 1BTC and win you will earn 8 BTC (price_multiplier*size) but you ever spend 1BTC so balance variation is 7 BTC !!! That's why there is a price_multiplier-1 I tried it with very big tosses number 65536*500=32'768'000 and calculated experimental house_percent and it was very close from 1.9% so that's ok ! Code is here http://pastebin.com/LvCU1gag |