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High or low?
Posted 11 January 2012 - 10:14 PM
the rules are this. he'll roll 3 dice. then he'll bet that you either get a total higher than him, or lower than him after also rolling 3 dice. if you bet the same way, and are right it's +50% of your money. if wrong, then you lose 50%. if you bet the opposite way, then its a double or nothing bet. if the result is a draw, then nothing is won or lost by either player.
as an example. he rolls 1,2,4 and bets that you get higher than him. you stake 2 dollars that you also get higher.
if right, you would now have 3 dollars. how fair is this game?
(what's your expected earnings/losses ?)
Posted 11 January 2012 - 10:47 PM
Merchant rolls, chooses a direction (high or low).
If you bet in that direction, and roll a number further in that direction, you get +50%; if you roll same total, it's a draw, you roll total in opposite direction, you get -50%.
If you bet in opposite direction, and roll a number in your direction, you get +100%, if you roll same total, it's a draw, you roll total in same direction, you get 0%.
Is this true?
Posted 11 January 2012 - 10:55 PM
Posted 12 January 2012 - 08:33 PM
Actually it's always a double or nothing bet, just the amount of stake is halved if you bet the same way.
Ex.- you stake a 2$ bet. Win the game you get 3$, loose and you get back 1$.
It's equivalent to staking 1$ for a double or nothing bet.
Since you are able to know the sum of dices of the merchant, your probability of winning are always > more than .5
So your expected earnings are aways +ve
Calculating the expected earnings is probably a lot of calculation.
Edited by ak4su, 12 January 2012 - 08:38 PM.
Posted 12 January 2012 - 09:45 PM
Draw - (2(1*1 + 2*2 + 3*3 + 4*4 + 5*5) + 6*6)/36^2 = .113
Edited by ak4su, 12 January 2012 - 09:55 PM.
Posted 12 January 2012 - 10:11 PM
Placin a bet of 2$ would mean that on winning he would get 1$ on winning and 1$ on loosing
expected earning =
1*.685 - 1*.113
It has been assumed that if the sum on the first roll is above 7 you choose low and vice versa.
Edited by ak4su, 12 January 2012 - 10:17 PM.
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