Head Up Theory Question

[FishAndChips]

Well I'll take my shot at a guess...

Assuming no bluffs, and given the pot odds, when you first bet, you are offering your opponent 3-1 odds to call. Thus, you would value bet with a hand that's a favorite when called. Assuming your opponent calls with a range from 250,000- 1,000,000, you could bet hands greater than 625,000 for value. Knowing this, your opponent would raise for value against you, if his hand was a favorite against your range of 625,000-1,000,000. Therefore he could raise with hands from 812,500- 1,000,000. Once again, you would raise with a hand that was favored over that range etc.

By halfing the range of hands each time, and assuming all raises are for value, it would seem you should call on the 20th bet.

For pot-limit, you offer your opponent 2-1 on a call when you bet and therefore you should bet for value if you are a favorite over a range of hands from 333,333- 1,000,000. Thus it seems you could value bet any hand from 666,666-1,000,000. Knowing this, your opponent could raise for value with hands 833,334-1,000,000 etc. Using this logic, you would call on the 20th bet.

I'm not sure if any of this is correct. I'm tired and it's time for bed. [img]/images/graemlins/smile.gif[/img] I look forward to David's analysis.