Interesting FP and thanks for that.
However, I can understand that when your opponent is only 15% to win the pot, but what about when the other person is say 25%?
Say u put another 10% into a pot (for example only) I can`t get my thick head around it, but does that not mean u r making a mistake, even though you are ahead?
I appreciate you answering FP - I know u r ahighly skilled limit player.
No, the example extends.
Even if you're only 51% to win, you're still winning 51% of the money going in.
I think you're having trouble wrapping your head around this because you're stuck on the idea of a "mistake" and you define making a mistake as "the other guy not making a mistake." It's perfectly normal (especially in limit) that you have several players not make a single mistake postflop. One of them will still win more money over the long haul, but because there's dead money in the pot there can often be situations where neither you nor your opponent make any mistakes.
Mistakes aren't "digital". It's a smooth line. Look:
You're playing no-limit, and you can bet any amount you want to. It's on the turn, let's say that the pot is $1,000 and you and your opponent have infinitely deep stacks. You know, because he showed you, that your opponent has a flush draw. You also know, because you've studied odds, that your opponent is 20% to win this pot. Here's the thing:
If you bet your whole stack -
infinity - your opponent will make an infinitely large mistake to call you.
If you bet
$1,000, he will make a mistake to the tune of
$400 (losing $1k 80% of the time, winning $2k 20% of the time).
If you bet
$500, he will make a
$200 mistake.
If you bet
$250, he will make a
$0 mistake. This is the breakeven point.
If you bet
$100, he will gain
$140.
If you bet
$50, he will gain
$170
If you bet
$0, he will gain
$200
So while it's true that he's not making a mistake when you bet less than $250, he's winning
more and more the less you bet. And who is he winning this extra money from?
You.
As an extreme example: The huge pot. Let's say that you play $3/$6 LHE, and it's heads-up on the turn. For whatever reason, some millionaire walks by and tosses $1,000 in the pot and says "here's something for you to play for." Your opponent is now correct to call with virtually any hand, because unless he knows that he's drawing dead, it doesn't matter even if he has a one-outer. I know you already understand this, but here's the kicker:
You STILL want to bet your strong
hands. It doesn't matter that he's correct to call with any-two, because you will STILL collect the lion's share of whatever amount of money you get him to put in. The dead money in the pot is there to help the weaker hand chase, but the strong hand wants to win even MORE money.