*Originally posted by Jezzabeanz*

My question is this: How does the number of players affect the odds?

Therefore I know that there are 9 cards that can help me (unless he holds 1 of the suit). This of course changes as the number of seated players increases, should it factor in to the odds? It seems that calculating the odds based on the number of seen cards doesn't factor in the number of total cards dealt and the remaining cards in the deck.

I'm not very good at mathematics but it seems that something is missing. I'm probably wrong but I thought I would ask to clear it up.

Thanks

It is a good question, actually, because it shows you're thinking beyond your own hand.

In short, whether there is 1, 2, 3 players or even 9 playing against you, the odds are calculated the same way:

Available cards minus known cards == Missing Cards.

Missing cards are known as "Outs"

The odds are "missing cards" divided by "available cards"

So in your example, you know of 5 -- 4 of which are

There are 9

left in the deck. 9/47 = so there is a 19% chance that the next card is a

.

Since there is a 19% chance that one IS a

, there is an 81% chance that one is NOT a

-- so 4:1 against it being a

We are NOT ignoring all of the other players, but if you try to take them into account, then you have to do that with every one of the missing cards, and you find that the probabilities cancel out.

The article

Mathematics of Poker: Odds and Outs should tell you everything you need to know.

All the best,

--VS