Do Your Hand Odds Change Depending On The Number Of Players?

Written by Raj on May 17th, 2006


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As a math + computer geek, I have this undeniable need to calculate averages and odds, even if the result is meaningless. Okay, well, maybe not that extreme. One of the first things that I asked myself when I took up writing for this blog was whether it’s easier to predict your chances of winning a hand, pre-flop and post-flop, if there are, say 10 players or just 3. Well, that’s not a simple question to answer, but I’ll make an attempt.

The odds of being dealt any particular hand from a single deck of 52 cards is not affected by the number of players. Texas Hold’em has very defined but simple rules of dealing:

  • (1) Two cards per player, pre-flop
  • (2) Burn one, turn three. After both blind bets and pre-flop betting, the dealer burns (discards) one card and turns three cards face up - all off the top of the deck.
  • (3) Burn one, turn one. For each of the two remaining cards (turn/ 4th street, river/ 5th street)

That’s all. TV poker commentators seem to imply that your odds of seeing a particular two cards in your hand, plus the 5 cards faceup on the table does not change, regardless of how many players are at the table. I’m not entirely sure I agree with that, but need some probability formulas to disprove them.

As well, I strongly believe that you have an advantage on your weaker pre-flop hand if there are more players. That’s because having more players at the table reduces the chances of any one player holding a strong pre-flop hand. So for example, I’m more likely to play, say, 9-9 if there are, say, seven players than only three players. That is, I’m more likely play to tighter if there are fewer players and I haven’t been able to read them well.

Now I just have to come up with a formula to prove what I’m saying is actually true. Otherwise, I’m just going on geek intuition here. More on this fabled formula in the future, if I can deduce it.

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