Strategy Question for 2+2 Authors

[Ed Miller]

In terms of bets collected, putting two cold to them isn't different than one bet to them after you've 3bet preflop. Both situations add up to 4 small bets. The only difference is you've given them a chance to fold correctly. Why would you actively plan to give them this chance?

This is not the correct way to view the situation. Your pot equity changes DRASTICALLY between the first two cards and the flop (depending on what the flop is). Three bets preflop and one on the flop is not at all the same as two bets before the flop and two on the flop.

Think about it this way:

You are in a four way pot. It is before the flop, and your hand will win exactly 26% of the time (you just happen to know this). Should you raise?

Well, a raise certainly makes money. You win more than 25% of the time, so you make money on every additional bet that enters the pot. But you make only a TINY BIT on every additional bet. In fact, you make about 0.04 bets by raising.

But just because a raise makes money doesn't mean you should do it. That's because not raising could make EVEN MORE money ON A LATER STREET.

Now assume that raising preflop changes the action after the flop. If you raise, your opponents will check and call your bet. If you don't, an opponent will bet into you, and you can raise if you choose to do so.

Say there are two possible flops.

Flop 1 is good for you. It gives you a 40% chance to win, and each of your opponents a 20% chance.

Flop 2 is bad. It gives you a 10% chance to win, and each of your opponents a 30% chance.

So say you didn't raise, and flop 1 comes. Your opponent bets, and you raise. All your opponents call. You now get 40% of all the extra bets... or 0.6 bets of added EV!

Getting to raise after a favorable flop netted you much more money than raising before the flop. Unfortunately, flop 1 doesn't always come... maybe it comes only 30% of the time. But that means that you get 0.6 extra bets 30% of the time.. giving you an extra 0.18 bets of EV by getting to raise the flop. You gave up 0.04 bets of EV preflop for the chance to make 0.18 bets on the flop. If you had taken your 0.04 bets preflop, you would have missed out on the flop raise.

Does this make sense? Sometimes your opponents will fold instead of call... but when they have a 20% chance to win the hand, YOU ARE BETTER OFF HAVING THEM FOLD FOR TWO BETS THAN HAVING THEM CALL FOR ONE BET. So it is STILL to your advantage to get a flop raise in.

Finally, the fact that the FTOP breaks down (i.e. that sometimes you want them to fold even though they should fold) is NOT RELEVANT. It is still WAY BETTER that it be two bets to them rather than one, no matter what you want them to do. This is why 2+2 hasn't discussed it before... knowledge of Morton's Theorem ALMOST NEVER changes the correct way to play your hand.

[karlson]

Ed, I think you forgot to take into account the bets that you'd win when you raise preflop and they call your flop bet. Now, you have to divide the final (0.18) number by two, and all of a sudden it's much closer. Make it 30% preflop, and I'd rather raise preflop.

[Ed Miller]

Now, you have to divide the final (0.18) number by two, and all of a sudden it's much closer.

No. That 0.18 is just for the EXTRA bet. I got the number this way:

40% of 4 bets (you get one EXTRA bet from each player when you raise the flop) = 1.6 bets. 1.6 - 1 (the bet you used to raise) = 0.6 bets.

[Ed Miller]

As your preflop edge gets bigger (26% to 30% to 40%), the more important it is to raise IMMEDIATELY rather than to wait for the flop. This is why I advocate raising preflop a lot more for value in loose low-limit games... your edge is larger against poor hands.

[karlson]

Sorry about that, you're right.