Mind Blowing

This is my second post of the day, again dealing with poker theory in general rather than my own results. I was taking the quiz over at www.donkeytest.com for probably the 3rd time (scored 122 this time), when I had one of those mind blowing *eureka* moments.

One of the questions is the following:

5/10 NL. $1,000 stacks. You raise to $40 from late position. A loose-aggressive player in the big blind (who has been re-raising from the blinds a lot) re-raises to $130 and you call.

Your image is loose aggressive. You and the BB have been in a few big re-raised pots so far, both of you have been bluffing and semi-bluffing relentlessly.

Flop is: 2c 6d 10s

He makes a $200 continuation bet. Which hand is best if you plan to raise all-in on this flop?

A) 88
B) AK
C) A9
D) QJ

Obviously A9 and QJ don't really make sense since, so lets discount those.

I'm pretty sure the first couple times I took the quiz I thought this was a no brainer, 88 was the obvious answer. I imagine most lower stakes players would think this way, because our opponents 3-bet range contains a lot of combinations of AK and AQ that missed, and we are way ahead of these hands with 88!

The reason why we bluff in the first place however, is to have better hands fold. If we bluff raise with 88, the only better hand we are likely to fold out is 99, with which our villain may even find a hero call. We very likely fold out all hands worse than ours which include smaller pairs and and AQ/AK (which still has some overcard equity, so AQ/AK folding isn't terrible from an EV perspective). However, should we get called by better hands, which in this case would be JJ+ or sets, in all cases we are drawing to 2 outs or worse. Sets are certainly significantly less likely than the overpairs.

Now consider what happens when we bluff shove with AK. Do better hands fold? Certainly. We fold out most small pairs, as well as AK most of the time (which we'd chop with) and of course AQ. We will still get called by better hands, but against JJ and QQ we have now improved to 6 outs, with 3 outs versus KK. As with 88, we are nearly dead against sets and AA.

Thus, the right answer is very probably B) AK.

What's the lesson we should take from this? With medium strength hands (like 88 on this flop versus villain's range) we should be trying to get to a cheap showdown rather than turning them into bluffs. They don't make great bluffs because we only fold out worse hands which we could potentially extract value from on later streets, though that might be difficult in this particular example as it is a 3-bet pot to start with and any action on the turn or river likely means getting it all-in.

On the other hand, with AK we do often fold out better hands, and still have some equity against much of villain's calling range.

(Of course, we probably should have taken a 4b/call line preflop with AK versus this villain.)