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I came to know about a gambling game with following conditions:

a> Betting option for 3/4 winning chance.

1> You will have to bet 1 of 4 numbers.

2> If the out come of game doesn't match with your bet, You WON 100 coins.

3> If the out come of game matched with your bet, You LOSS 300 coins.

b> Betting option for 1/4 winning chance.

1> you will have to bet 1 of 4 numbers.

2> If your bet matched out come of game, you got 3 times. i.e., if you bet 100 coins, you get 300 coins if you won.

3> In case it you loss, you pay to dealer 100 coins.

c> Betting option for 2/4 winning chance.

1> For same game, You will have to bet any two 2 out of 4 numbers.

2> If you won you get double.

In case a , your probability of winning is 3/4 and loss 1/4. Ratio of of money you get when win to money you pay when loss is 1:3.

Here is my questions:

1> I think in big picture, the player have more chance to win because odd of player winning is higher. How do dealer make money at all?

2> If player triple his stake when player loss the bet, next time player win the bet, he should got his money back. The probability of loosing 3 game consecutively is very low (0.25*0.25*0.25 = 0.015). So there is more chance for dealer to went bankrupt. Again How do dealer make money at all?

3> Do you think there is another way to win this game or increase probability of winning the game?

P.S. : This question is truly for academic purpose. I am not trying promoting gambling here.

Thanks in advance

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1 Answer

Try this simple simulation and see who wins at the end.

play = function(asset){
outcome = sample(c(1,2,3,4),1)
yourpick = sample(c(1,2,3,4),1)

if(outcome != yourpick)
asset = asset + 100

asset = asset - 300

return (asset)

asset = 5000
times = 1

while (times < 100 & asset > 0){
asset = play(asset)
times = times + 1

It is generally true that the dealer won't make any money if the winning chance is greater than 50% (the dealer, however, can charge a fee for playing the game and make money that way).

You can play around with my code and test your strategy in part 2).

For 3), read a bit more about Gambler's Ruin.

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Thanks Linda. I tried writ a code (in c++) to simulate the situation. but its look like there is some pattern in random number i generated. in the simulation, this game will cause player bankrupt and on the other hand, the player playing roulette (33.33% winning chance) is winner. So i was looking for mathematical proof that this game give player advantage. –  someone_ smiley May 27 '13 at 3:11
appreciate your answer, thanks :) –  someone_ smiley May 27 '13 at 3:12
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