odd s calculations

[Banmemods]

hope this is easy to understand, it's a bit of a muddled post.

A q for all the maths buffs out there. When calculating your outs in a % move in a game, let's say you have an up and down straight draw and you are considering a semi bluff post flop agianst a player that has AA.

In these calculations do you purely base your possible outs on the 45 cards in the deck OR do you had some probability calculation into the fact that when 10 handed for example 20 of the 45 cards are out so in all likelyhood some of your outs are dead in the water. I've seen calculations that work out your odds based on the whole deck but I've not seen anyone add in the probably factor of dead cards versus players at the table.



Rgds
William C

[strategery]

Your opponents' cards are unknown just like the remaining cards in the deck. Therefore, they are treated the same when you're counting outs.

However, based on the board cards, the action in the hand, and your opponents' ranges, you can sometimes make a more accurate calculation of the odds of hitting certain outs.

There is an article in this month's internet magazine which discusses this issue in detail card removal effects.

[Banmemods]

thanks I'll read it later ....cool.

I realise your opponents cards are unknown but there must be a probability factor based on players folding etc that you can assign to what these cards may be thus effecting your % of outs....no? I'll read the article anyway thanks for it.

[jay_shark]

Here is my own explanation .

Lets say that you have AhKh and the flop is 2h 6h Qs . You're up against two random hands .

Solution 1: The probability that you hit another heart on the turn is 9/47 . Pretty easy .

Solution 2 : This one is a bit more involving but the answer is the same . The deck contains 43 cards of which may or may not contain 9 hearts .

The probability that there are no hearts amongst the 4 cards and 9 hearts in the stock pile of 43 cards is 38c4/47c4*9/43

The probability there is only one heart amongst the 4 cards and 8 hearts amongst the 43 cards is 9*38c3/47c4 .

The probability there are two hearts amongst the 4 cards and 7 hearts amongst the 43 cards . 9c2*38c2/47c4

Likewise we have 9c3*38c1/47c4 and 9c4/47c4 for three hearts and 4 hearts respectively .

Now we use conditional probability to compute the probability that the turn is a heart given the additional information of your opponents cards .

1)38c4/47c4*9/43

2)9*38c3/47c4*8/43

3)9c2*38c2/47c4*7/43

4)9c3*38c1/47c4*6/43

5)9c4/47c4*5/43

Now if we add all these mutually exclusive events , we get the probability is equivalent to 9/47 !!
This is no coincidence .

Which method do you like better ?