Variable Buy-In tourney: what would you chose?
 

(I realize this isn't exactly right forum, but it's home and you guys like to talk about anything interesting)

Let's say you had a tourney with this buy-in structure:

$10 gets 1000 chips
$20 gets 2000 chips
etc. up to a max of $100 gets you 10,000 chips.
No rebuys. You don't get to see how many chips other people are buying before you buy yours.

How much do you buy in for and why?

Re: Variable Buy-In tourney: what would you chose?
 

Buy-in the max if you think you are better than the field. The deeper stacked you are, the less of a crapshoot it becomes. Think about it this way, say 9 people who had no idea how to play bought 1 chip each for $1. If you bought 1 chip for $1, what would their equity be? Now what if you bought $10? $100? You'll find that as your stack increases, their equity becomes proportionally less until it is nearly impossible for them to win.

Now, if you are sitting with Ivey, Greenstein, <name your pros here>, you may as well buy-in for the minimum and start gambling.

Re: Variable Buy-In tourney: what would you chose?
 

I think you'd need more info to answer definitively, since it would depend upon 1) payout schedule, 2) your relative skill level vs. field, and 3) size of the field.

An extreme example:
Total # of players = 11
Payouts = 40%/30%/20%/10% of prize pool for 1st-4th

If you buy in for the max $100, it would be possible to be a guaranteed loser even if you win (if the other 10 happen to buy in for $10 you would end up contributing 50% of the toal prize pool). So you wouldn't buy for the max in that scenario, but for some amount less.

In general though you'd obviously want to buy in for the minimum if you are a worse player than the field on average. Barring that, a larger field and/or top-heavy payout structure would nudge you toward buying in for the max.

I'll venture a guess that there would be some tipping point in terms of 1) the max % of prize pool you end up contributing and 2) the min/max % you could win that would make it game-theory correct to buy in for the max, but I'd have no idea how to compute that.