sholden
Monday, July 16th, 2007, 7:52 PM
QUOTE (psujohn @ Monday, July 16th, 2007, 4:11 PM)

If he won't call more than 1/4 pot (getting 5:1) you can't profitably bet.
That part is not true. Any bet that he calls is profitable, and any bet that he folds to is also profitable.
If he has a 20% chance of winning then every dollar that you get him to call is worth 60c which is certainly profitable. If he folds then you get the 20% of the pot that was his "share".
If he won't call without the correct odds than he will only call if you bet a small enough amount that the 60c per dollar profit is less than the 20% of the pot share you can get by making him fold - but that's OK, it just means you want to bet him out since that's how you maximize your profit.
Simple example:
Pot is $100, your opponent has a 20% chance or winning, you have an 80% chance. One card to come, assume the loser will fold on the river (or that the cards are face up - ie. no implied odds to consider). Obviously if your opponent will bluff a missed draw this is all wrong...
If you bet $10 he'll call which means you win a $120 pot 80% of the time which is $96. Minus the $10 you bet leaves $86, so by betting $10 even though your opponent is correct to call you win an extra $6 over checking it down (in the long run).
However if you can bet enough to make your opponent fold you win the whole $100 and since $100 > $86 that's a much better option..
Once your bet gets to $34 you prefer the call since 80% of 168 = $134.40. Minus the $34 and $100.40 > $100 (obviously the extra rake will kill that

My long winded point, is that the bet that makes your opponent fold is the most profitable option if the opponent will only call with correct odds. But if your stack isn't big enough to bet that much, then betting as much as you can (even though it's correct to call for your opponent) is more profitable than checking it down. So in fact all bets are profitable - of course you want to make the most profitable bet not just a profitable bet.