Realization

Most players know that aggression is a key to victory in hold 'em. It's such a fundamental concept that it's taken for granted.

But one thing I hadn't fully considered was the interaction between aggression and equity.

Here's the 2+2 post that got me thinking about this topic. Down on the page, W. Deranged makes a point about the difference between betting for value and betting to realize your equity. The concepts are closely related, but they're not exactly the same.

We bet for ostensibly the same reason: we need to find a way to protect and cash in the equity we do have in the pot, even if it's below 50%.

Betting is the best way to do this. When we bet, villain is more likely to put in money with an inferior hand than he is if we check. In other words, betting is a better value play not because we have a pure, logical 50% value bet, but because it is simply better than checking in terms of our return. It "realizes" our equity, while also gaining some extra value from weaker hands that we would not have gained had we checked.

I don't have much to add. Just something to read.

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EDIT: At least one part of the quoted text is doubtful. I do not believe that the "villain is more likely to put in money with an inferior hand than he is if we check." A check on the turn will induce a bet a high percentage of the time.

Let's look at our options:

1) Check-call the turn and river. Cost: 2 bb
2) Bet the turn and river, and be prepared to call a raise if it comes. Cost: 2-3 bb
3) Bet and fold to a turn raise: Cost: 1 bb

I'd rule out option three because I think it's plenty feasible that the villain also has AK for a split pot, or even a lesser hand.

Option one is the safest choice, and it could induce a bluff.

Option two is viable if a worse hand will call or raise, or if the villain would check behind a worse hand. Can we quantify this?

If the villain's hand range is 99 TT JJ QQ KK AA, AK, AQ, AJs and KQs, he has 45 possible hands (if my math is right).

The chance that a worse or tied hand will call or raise only really encompasses the six other AK combinations of 36 worse or tied hands, or 16.7 percent.

The chance that he would check behind with a worse hand that would also call a bet is hard to determine. Really, the only combination that makes sense for this action would be the nine AQ hands, and even that is doubtful after a flop check-raise. I'll estimate downward to six hands out of 36 worse or tied hands, or 16.7 percent.

Add in about 10 percent for a potential bluff raise, and you get a total of 43.4 percent (10 + 16.7 + 16.7). That might still be a bit too high.

You typically need to be ahead at least 50 percent of the time for a bet to be for value, so it doesn't look like we get there. Additionally, we aren't scared of many draw combinations out there except for two outers or a rare gutshot possibility.

I may be looking at this hand the wrong way, but as far as I can tell, a bet on the turn is incorrect.

That would seem to disqualify my initial babble at the top of my post. Now we're only left with the babble at the bottom of the post.