A Contrived Example
The way this hand will play out is not possible by any standards, but I think it answers some of my questions and perhaps brings up some more theoretical ones. Here it goes, and feel free to chime in if I'm wrong in some spots as I haven't done much math in a while.
You pick up QQ in the BB after the entire table has limped in. What to do? What to do?
You Raise:
The flop is a 23T rainbow. You bet out and only get called in one place by a guy holding 56. You put the 21st bet into the pot and he calls getting 21:1. He doesn't hit on the turn and calls your bet again getting 12:1 on his call. The odds of completing a gut-shot by the river are 5:1, so five times your QQ wins when he folds on the river after getting no help. Five times you win 14BB for a total of 70BB. One time in five he spikes and you will lose 4.5BB (he gets a raise in there along the way, and you call him down). Net total of 65.5BB per six times you play this hand out.
The guy with 56 loses 2.5BB five times for -12.5BB. One time he hits and wins 17BB for a net profit of 4.5BB per six play-outs.
You Don't Raise
The flop is the same 23T rainbow, but this time you check to the bluff-aholic button who bets, and you check-raise him. He folds, but 56 calls-cold getting 6.5:1 on his call. He'll call the turn also if he doesn't hit. Five times your QQ wins 9.5BB for 47.5 BB net, and lose 4.5BB once for a total profit of 43BB per six hands. 56 will lose five times to the tune of 2.5BB for a total of -12.5BB. But he'll also win once and get an extra bet for a single 14.5BB. He makes only 2BB per six play-outs.
The Interesting Part
I couldn't contrive an example in a family pot where you don't raise and the gut-shot is not getting at least a little profit on any call he could make, so I had to make due with giving him less pretty odds than in the first hand.
When you raise in the first situation, the profit that 56 shows over an average six hands is 0.069% of yours.
When you check-raise in the second situation, the profit that 56 shows over an average six hands is 0.047% of yours.
Now the 0.022% isn't a monster of a percentage, but what I've inferred from this is that your edge is greater when you choose to manipulate the pot odds in your favor. You don't take down as big of a pot when your hand holds up, but you are making better money on the hand when you play it out the same way in similar circumstances. You get paid off slightly better in the long-run when you manipulate the pot odds to "widen the gap" between their EV and yours.
Is this what Sklansky is talking about and did I just re-invent the wheel on this one? I think I finally understand the concept behind this one now, and I'm open to any comments or criticisms regarding this post.
Thanks for reading the novel.
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