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You are not logged in. #1 20100304 15:59:09
Four card poker analysis...Hello all! Straight Flush Three of a kind Flush Straight Two pair One pair Nothing/High card These total to 21,224,216, but they should total to _{52}C_6 = 20,358,520. So I have nearly 1 million extra card combinations. My mistake(s) is (are) probably in the high card/one pair/two pair totals since these are most complicated and difficult. Last edited by Fruityloop (20100304 16:08:40) The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong. #3 20100420 15:06:42
Re: Four card poker analysis...I've finally completed my analysis of Four Card Poker. The difficult part was figuring out the probabilities for the dealer to wind up with various hands. Four of a kind Straight Flush Three of a kind Flush Straight Now subtract out the straights which are also flushes Phew! Two pair One pair Subtract out the straights Subtract out the flushes Add in the straights which are also flushes High card The number of ways for the player to wind up with the hands are as follows: Four of a kind Straight Flush Three of a kind Flush Straight Two pair One pair High card The best strategy for the player is to fold if he only has high card, bet 1x the ante for a pair of 2's through 9's, bet 3x the ante for a pair of 10's or higher. We are now in a position to estimate the player's mathematical expectation. In order to simplify the calculation, I ignored the situations where both the player and the dealer have the same hand. High card pair of 2's through pair of 9's pair of 10's through Aces Two pair Straight Flush Three of a kind Straight Flush Four of a kind Now we need to add the bonus which is as follows: So, So the casino has an advantage of on Four Card Poker. According to James Grojean, the casino has an advantage of 3.396%. So my analysis is very close. Last edited by Fruityloop (20100420 15:58:42) The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong. #4 20100420 15:18:52
Re: Four card poker analysis...Hi Fruityloop; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20100420 15:40:45
Re: Four card poker analysis...Thank You BobbyM! The eclipses from Algol (an eclipsing binary star) come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong. #6 20100420 15:44:51
Re: Four card poker analysis...Yea, tedious to do all the casework. And you know what, your problem isn't any easier with a computer. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 