I Know 2+2 Wants To Kill Me For This......

[StellarWind]

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Here is an example that I made up a long time ago in a preflop EV thread.

You are playing heads up hold'em but the deal is rigged. One of you will flop TPTK. The other player will receive a standard gutshot. It is completely random as to who will receive what.

Scenario 1: Both players are perceptive and skillful and will play FTOP-correctly postflop. Whoever gets TPTK will bet and his opponent will compute pot odds and act accordingly. There are no implied odds because no one ever chases a made straight. There are no redraws to full houses.

Analyze the preflop play.

Scenario 2: Exactly like scenario 1 except that Villain has a bit of gamble. He will always peel one card to try and make his straight. Other than this he plays properly.

Analyze the preflop play.

I'll post again later after you've had some time to absorb this. This example has great significance when a good player is considering raising the field for value with some mediocre hand like QJs that has a small PokerStove edge over the marching nitwits. Specifically I am thinking of opponents who only play their cards and don't consider pot size or what hand the PFR is representing.

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First let me emphasize that this constructed problem is face-up poker postflop because I specified FTOP (Sklansky) correct postflop play. Whoever is losing will check and whoever is winning will bet.

If both players play correctly postflop then neither can possibly have an advantage in this symmetrical situation. Any extra bets preflop are even money on a 50% chance and thus zero EV.

When playing versus the gambler you have a substantial advantage thanks to his incorrect flop calls.

The first thing to realize is that if you each player made a very large ante the gambler would be playing correctly by drawing to his gutshot and your advantage would completely disappear.

So obviously it is to your advantage to keep the preflop pot small. But how can we reconcile this with the facts that the preflop betting is zero-EV while the postflop betting is unchanged by the preflop action?

The postflop part of the explanation is quite correct. The money lost in the postflop betting is independent of pot size.

However the preflop bets are not zero EV. The preflop odds of winning the pot are not something that comes out of PokerStove. Your chance of winning the pot is based on a combination of cards and players. You will be winning the pot less than 50% of the time because you fold gutshots and he doesn't. You are getting 1-1 odds on your preflop bet but that money will be coming back to you only about 46% of the time.

Your preflop bets and raises are errors that are costing you money. That is why your profit margin is disappearing as the pot size increases. Once the pot gets so large that chasing is correct, your winning chances increase to 50% and any additional raises become zero EV. You've managed to lose your entire edge through incorrect preflop raises.

Now think about all the times you have been preflop with QTs or something versus four calling-stations. You just called the blind (wimp!) and some bright poster points out that you have 21% equity in a 5-way pot and you are a moron for not pushing that equity edge with a PFR [img]/images/graemlins/grin.gif[/img].

The problem is you are a good player and they are calling stations. I'm really happy for you getting to play a pot against these guys. No doubt you will make lots of money postflop. But it doesn't change the fact that you are not going to see that 21% share of the pots because you use your fold button and they don't. So unless some other factor is operating to make you PFR profitable, your 21% is going to shrink to 18% or whatever and your PFR will be a money-losing turkey.

A related concept is position. Undeserved pots flow from the blinds toward the button. Any value raise from the blinds should plan on winning less than a fair share of pots.

[Guruman]

this thread makes makes me smile. [img]/images/graemlins/smile.gif[/img]

[Jake (The Snake)]

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But it doesn't change the fact that you are not going to see that 21% share of the pots because you use your fold button and they don't. So unless some other factor is operating to make you PFR profitable, your 21% is going to shrink to 18% or whatever and your PFR will be a money-losing turkey.

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Wow, I don't think I ever quite thought of that.

I think, though, that against most opponents raising increases folding equity and thus our opponents will be the ones not seeing a showdown quite as often. This is especially true when we have position.

Against calling stations out of position though, I certainly see your point.

[Dave G.]

Very interesting concepts, I'm glad I found this thread.

Here is my take on it. Let me know if I'm not understanding something here please...

If you are in an EV neutral situation, you, as a good postflop player, are best served by not raising and bloating the pot. This allows your postflop edge to work more for you when your situation changes from an EV neutral situation to a +EV situation. The other players will be making bigger mistakes because the size of the pot does not cover their losses, and you will therefore be making bigger gains. Also, if your situation becomes a -EV situation, you can dump your hand, preventing you from making those mistakes too.

This seems analogous to the concept of protecting your hand, or of waiting until the turn to protect your hand a la SSH.

[Wynton]

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The problem is you are a good player and they are calling stations. I'm really happy for you getting to play a pot against these guys. No doubt you will make lots of money postflop. But it doesn't change the fact that you are not going to see that 21% share of the pots because you use your fold button and they don't. So unless some other factor is operating to make you PFR profitable, your 21% is going to shrink to 18% or whatever and your PFR will be a money-losing turkey.

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I knew there was a sound reason I'm so wimpy preflop.

Look, obviously this concept can be taken too far. At some point our equity has to be high enough to compensate for the "problem" that we fold more than our opponents. Now all we have to do is figure out one catch-all formula for knowing where to draw the line.

Go to work math geeks. And make sure the formula takes into account that not all calling stations chase to an equal degree.