How much should i bet?

[pzhon]

If the players both know exactly what the situation is, not betting anything is worth $70 to the player with the 70% advantage. Betting n is worth 70 + 0.4n, up to n=75. For n greater than 75, betting n is worth $100, since the underdog will fold.

In reality, the players don't know exactly what the other has. Someone with a draw to the nuts expects a bit more money to go in after the draw hits. They might also expect to be able to bluff profitably when the draw misses, but another draw appears to hit. They might already be ahead, or a weaker draw might hit that puts them ahead. How much is bet on the turn affects the actions on the river.

[DougOzzzz]

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I'm fairly new to poker and I have found this particular set of posts to be very interesting. I have a question about the whole scenario where the guy considering a bet is a 70% favorite to win the hand with $100 already in the pot. It seems to me that any bet made by the guy with a 70% chance ("favorite") will be profitable for favorite. If favorite bets small enough, the call will still be a good one to make for the underdog. If favorite and underdog are both good players, wouldn't favorite want to make a bet such that underdog would just barely be making a profitable call? Doesn't favorite want to get called with his 70% edge?

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Trying to entice your opponent to call by giving him favorable pot odds is a stupid, stupid play. Let's look at the following possibilities here:

Player A bets $40 into $100 pot. Player B will call this bet 100% of the time, 3.5-1 odds as a 7-3 underdog.

Player A bets $120 into a $100 pot. Player B now has 11-6 odds - not good enough to call, but maybe he'll call 20% of the time and fold the rest.

The first case, player A will win $140 70% of the time and lose $40 30 percent of the time. His EV on this bet therefore is .7*140 - .3*40 = 86 dollars.

The 2nd case, player A will win $100 80% of the time, $220 14% of the time (70% of 20) and lose $120 6 percent of the time.

The EV on this play is 100*.8+220*.14-120*.06 = 103.6.

The point is, you MUST bet such that your opponent is not getting the pot odds to make the call. A humongous overbet is always better than any underbet, no matter how small. Your EV on the play will never be greater than $100 if you give your opponent correct odds to call - it will always be somewhere between 70 and 100 depending on the size of your bet. Once you start giving him incorrect odds to call then your EV goes above $100 - where it maxes out depends on how likely your opponent is to call each size bet.

It turns out a bet of $75 gives your opponent exactly the odds to call. A bet of $80 that is called 100% of the time has an EV of $102. A bet of $100 needs to be called just 20% of the time to have the same EV.

By the way, I am looking at this as a 1 card scenario and things change somewhat when there are 2 to come. By "luring" him in with a undersized bet you might be able to get more out of him next round if he misses - but with 1 card to go you absolutely must not let your opponent call profitably.

[Msogard]

Consider this:

Every call your opponent makes is either correct or incorrect, given his pot odds and win percentage. When you bet too much for your opponent to call correctly, yet he calls anyway, you profit. Conversely, if you don't bet enough, and he folds, you also profit.

Let's assume that your opponent has a 1% chance of winning a particular pot. The pot has $10,000 in it, and I bet $10. If my opponent calls with his extreme longshot, (being 1/100 to win) in the long run, he will profit. It seems like a ridiculous call, being only a 1/100 shot, but if this action was repeated a thousand times, the pot odds make this call very profitable.

Remember, every action you take is always dependant on the amount of money you can win.