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?