11-26-04, LearnTexasHoldem:

Odds In Relation To Number Of Players

Question: I understand the odd's on seeing a hand may be similar in different games, but are they the same for example in Draw vs. Hold 'em? We saw a royal last night, last damn hand of the game, and we had 5 players. Is there a better or worse chance to see a royal flush on the table with more or less players? Sense would say, the more players, the more chances to see a royal, because more cards are in play. Our mathematically inclined friends said it makes no difference how many players, ten or two, the odd's of seeing a royal flush are the same. I just can't see it. And, would that affect other hands like flushes and straights as well?

Can you straighten me out?

Dan

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Answer: If the question is whether the amount of players who call preflop change the collective odds of catching a royal flush, then the answer is yes it does make it more likely. On the other hand if the question is do the individual odds of each player change based on how many people call, then the answer is no. The more players who see the flop, the higher the hand strength will need to be to win. One pair won't likely win, you'll see way more two pairs, straights and flushes.

Often times when faced with a question like the one you posed, using a simpler example helps. Let's use the example of getting AA preflop. Do you think it is more likely that if I deal 10 hands I'll see someone with AA than if I only deal one hand? How about if I deal all the cards out? If we put it in those terms, it is clear that the more hands we deal out, the more likely that someone will have AA.

Notice though that the individual chance of getting AA doesn't change, just the collective chance does. This is why when you are playing with only a couple of players, having something like middle pair on the flop is a really strong hand. Compare that with playing at a 10 person table. Middle pair would be lucky to hold up and win.

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