The new-movie thread

Quote from: Drakey on December 28, 2008, 10:12:45 PM

No, the odds of getting any one hand are always the same. The odds of any hand that you get falling into a category fall drastically as the category narrows, but all hands are equally likely.

You get dealt a card. It's 100% likely to fall into one of those categories. For a royal flush, this card must be between 10 and Ace, meaning there's only a 5/13 chance of getting a card for a royal flush, whereas it can be anything for any of the other hands.

You get dealt a second card. For a royal flush, this needs to be of the same suit, between 10 and Ace, meaning there's a 4/51 chance of getting this card (One of the cards has already gone). For a full house, it can be any card at this point. For a normal flush, it's a 12/51 chance, as it must be the same suit. For a straight it must be within five cards either way of that number, and not the same number, meaning it's got a 32/51 chance (Excluding the possibility that you chose below a 5 or above a 10). For the rest, at this point, it can be any card, as you don't need four specifics in your hand.

You get dealt a third card. For a royal flush, to be in the same suit and between 10 and Ace, it's a 3/50 chance. For Four of a kind, this card must match either the first, second or both of the previous cards. this means there's about a 6/50 chance of getting a four of a kind at this point. for a full house, it can be the same as both the cards, different if 1 & 2 are the same, or, if 1 & 2 are different, match ether one, which I can't be bothered to work out. For a flush, it's now 11/50 chance. For a straight, it must be within 5 of both cards, meaning the chances vary depending on what the distance between the first two cards are (If they are 4 apart, the third card must be in between (3/50), they are one apart, then they can be three either side (6/50). The rest can be any card at this point, as they don't need three specifics.

To get a straight flush, you multiply the straight chance by the flush chance.

Do you see where this is going?

Here's another way of looking at it:

There are 4 different royal flush hands.
There are 36 different straight flush hands.
There are 624 different four of a kind hands.
There are 3744 different full house hands.
There are 5148 different flush hands.
There are 10240 different straight hands.
There are 54912 different three of a kind hands.
There are 123552 different two pair hands.
There are 1098240 different one pair hands.
There are 2598960 different high card hands.

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