Another Interesting Hypothetical Question

[EnderW27]

I haven't read any of the answers.
This is just my quick guess using some dirty math.

If we're starting with a large stack, we assume the odds aren't there to gamble with a catchup hand like 6-5. Thus, the only hands we want to call with are pocket pairs and AKs.

Given you know one AK is out of the deck, I'll just assume that it all evens out to you getting a playable hand 1 out of 17 times. So on average you'll lose $16 in antes before finding a hand to play.

Also, I'll just go with the assumption that you'll win, on average, 55% of the time you call.

So when .05x=16, there's your answer. I get $320.

Again, it's all just estimating math. But I don't think my numbers are too far off.

[AaronBrown]

Okay, same assumptions as before, but going against A8s. I again did five categories, but might have made an error. You can wait for AA, which you get 0.24% of the time and have an 88.03% chance of winning. It takes 1,399 or more chips for this to be the best choice.

Next, you can take any pair 8's or above, or A with anything 9 or better. You'll get one of those hands 7.84% of the time and have a 68.63% chance of winning. Do this with at least 49 but no more than 1,398 chips.

If you play any pair and Ace with 8 or better, you'll play 12% of your hands with a 62.86% chance of winning. This is right when you have between 11 and 48 chips.

If you play any hand without an 8, plus A8 and 88, you'll play 89.22% of your hands and have a 37.88% chance of winning. This is the right strategy with between 4 and 10 chips.

If you play anything, you play 100% of your hands and have a 36.60% chance of winning. You do this with between 1 and 3 chips.

The worst starting bankroll is 16 chips, you expect to lose 3.19 of them. 36 chips is the smallest profitable buy-in.

[David Sklansky]

Thanks one more time. Hopefully everyone sees that these questions relate to the subject of chips reducing in value as they inrease in a tournament. With very small stacks and many players yet to be eliminated, the opposite is true.