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# Odds and Number of Seated Players

• Bronze
Joined: 21.09.2012
Hello,

I'm relatively new to poker and I've began learning the mathematics behind it all. However I have a question, which may be a stupid question but I'm sure I will find out here.

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

I pose this question because say I hold 2 suited cards and I flop a four flush, there are 9 cards which can help me make my flush. If it was heads up, the probability of my opponent being dealt two of the same suited cards as I is 23% (Source). So I'll assume he doesn't have them pre-flop.

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
• 4 replies
• Bronze
Joined: 23.06.2008
Hiu Jezzabeanz,

I've moved this to Beginners Questions, it seems more appropriate there.

Regards,

Mal.
• Bronze
Joined: 21.09.2012
Thank you, Mal.
• Super Moderator
Super Moderator
Joined: 02.09.2010
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
• Bronze
Joined: 21.09.2012
Thank you for your response, VS. That definitely cleared it up for me.

Every time I learn something new in poker, I realise how much I don't know. It's exciting and I can't wait to put all this new knowledge into practice.