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My buddy and I are arguing over something that cropped up in this past weekend's Texas Hold'em tournament.

A player got "knocked out" (lost all their chips) early on in the game. The person hosting the tournament told them they could buy back in, and my buddy got upset. He argued that it gave the player buying back-in an unfair advantage, and that it changed the odds for the other players.

I argued that as long as everyone has the ability to buy back in, then whatever the mathematical ripple effects are of buying back in, they get spread over all players equally.

But I have no way to prove this mathematically and was hoping a few math gurus could lend me some help. I'm a Java developer with a math minor, so don't hold back (I can't prove it myself but I can at least follow someone else's math)!

Thanks in advance for any help here.

Edit - An example:

  • Poker tournament contains 5 players
  • Each player puts in $20 and gets 80 chips (25 cents/chip)
  • Player 3 gets knocked out (0 chips) while Players 1, 2, 4 and 5 have 20, 50, 75 and 15 chips left respectively
  • Player 3 buys back in ($20; 80 chips)
  • Every other player may buy back in once if knocked out
  • Does this give players unfair advantages/disadvantages? If so, who, why and how?
  • 0
    This is completely without any proof, but my thoughts are that (making certain simplifying assumptions about the probability distribution that are likely false) if you buy back into a tournament for the same chip amount that you began with, your chances of winning the second time around are considerably less than the first time around, since on average your opponents will have a greater chip counts than you to begin with, putting you at a material disadvantage.2012-03-12
  • 1
    If the host said the rules before the tournament started, then your friend should have not been bothered by it. However, if your friend was playing the tournament and the rule was added, then he has the right of being upset because of the following: You only play buy back tourneys if you are willing to buy back, otherwise you do not play them. I will try to look for the article written by (I think if my memory is correct) Daniel Negreanu. So if your friend was not willing to pitch in an extra twenty if he was knocked out, then yeah it is unfair.2012-03-12

3 Answers 3