Probability calculus

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szwajar1979

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Hello how to calculate the probability of hitting a set on the flop with a pair on your hands!!!
 
CRStals

CRStals

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So when you have a pair in your hand, there are 2 cards out of the 50 that will give you a set. With three cards dealt, the changes of you hitting on the first card of the flop is roughly 4% - when you multiply that over three cards, you get odds just under 12% of hitting a set.
 
tagece

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About one in eight flops, in another words.
 
amonlima

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The chance of a card hitting the board is 2%, meaning that when you have two outs, your chances of making a three-of-a-kind by the river are approximately 12%.
 
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tuitui

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Even if a player knows outs, pot odds and probabilities by heart, the situation at the table changes quickly and decisions have to be made in a split second. I find it incredible that one can calculate so quickly. I make my decisions based partly on intuition, although there is some theoretical understanding behind it. I should practice calculating the most common situations to an automatic level so that I can recall them even in a hurry, but I haven't had enough enthusiasm for it yet.
 
monkeytilter

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In game you don't calculate, you just know you will flop a set 1 time in 8 (12% chance).

You usually want better implied odds than 8:1 on someone's stack if you are calling small pairs to set mine - this allows for the times you get coolered set over set or villain just doesn't pay you off with his whole stack. i.e. don't set mine with relatively short stacks.

If you really want to calculate from scratch you can do it like this:

Calculate how often your pair will miss each card on the flop..
48 cards out of the remaining 50 (we remove the 2 cards in your hand from the 52 in the deck) miss your pair for the 1st flop card
47 cards out of the remaining 49 miss your pair for the 2nd flop card
46 cards out of the remaining 48 miss your pair for the 3rd flop card

We then multiply these probabilities together to see how often your pair misses all 3 flop cards:

48/50 x 47/49 x 46/48 = 0.88..

We want the opposite of this i.e. how often we don't miss all 3, so we take the compliment:

1-0.88 = 0.12 = 12% = 1 time 8
 
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