The Way to Play AK?

[pudley4]

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Let's say that you win 100 total bets with each hand and along the way you have also lost some. With AA you lose 40 bets (1/3 of 140 bets) for a net win of 60 bets

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What does that mean? Where does the "1/3 of 140 bets" come from?


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With AK you win the same 100 hypothetical bets but you lose fewer bets because you throw AK away when you don't make anything on the flop, thus a net win of more than 60 bets and more profitable

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This analysis is so wrong it's not even funny. This doesn't mean AK is more profitable than AA. It means this strategy of playing AK has a lower variance than a strategy of aggressively playing AA.

Take a look at this example:

Hand 1 - wins 50% of the time. When it wins, it wins 10 bets. When it loses, it loses 4 bets.
Hand 2 - wins 25% of the time. When it wins, it wins 10 bets. When it loses, it loses 1 bet.

Hand 1 sounds like your AA - wins frequently but can also lose a lot of money. Hand 2 sounds like your AK - wins much less often, but loses a lot less when it loses.

Ok, so to "win" 100 bets for hand 1, we need to play 20 hands. 20 hands = 10 wins @ 10 bets each = 100 bets. 10 losses @ 4 bets each = -40 bets. Net = 100 - 40 = 60 bets.

Now, hand 2. To "win" 100 bets, we need 40 hands. 40 hands = 10 wins @ 10 bets each = 100 bets. 30 losses @ 1 bet each = -30 bets. Total = 100 - 30 = 70. Wow, it looks like hand 2 is better, just as you said.

Wrong. Here's why:

When we look at the profitability of hand vs hand, we don't look at the comparison of bets won vs bets lost. We look at the average result of each hand. This is also known as the "expected value" (or EV) of each hand.

For hand 1 - 50% of the time we win 10 bets and 50% of the time we lose 4 bets. To calculate this we take the probability of a win (.5) times the return (+10) and add the probability of a loss (.5) times the return (-4). We get:

.5*10 + .5*(-4) = 5-2 = +3 bets per hand. So in the long run we expect to win 3 bets per hand every time we get hand 1.

Let's figure out hand 2. Probability of a win (.25) times the return (10) plus probability of a loss (.75) times the return (-1) = .25*10 + .75*(-1) = 2.5 - .75 = 1.75. So in the long run we expect to win 1.75 bets per hand every time we get hand 2.

Which is more profitable, winning 3 bets each time, or winning 1.75 bets each time?

[Jim Easton]

If you check the turn you are inviting the bluff, TELLING them what you have

How often do you check raise the turn with your good hands? You must be doing this (See HFAP - when first to act they say "check . . .as much as 60% of the time with your good and bad hands alike" p. 141).

There are many "any pair to the river specialists", who put you on AK and will call to the river unless an A or K comes. The next time you get a big pair in this situation, check raise the turn. You'll get an extra big bet, and throw off their read of you in the future. When you find one that will fold to your check raise, you can try it with your AK, too.

[JohnShaft]

Yeah Jim I'm aware of that and since getting a hold of HPFAP a couple of months ago I have started doing that frequently. It's not worked for me much but the theory is sound, and eventually my application of it will be also.

I was talking moreso about a lone opponent (or maybe 2) you had position on though, so checking the turn in that case is a dead giveaway.

Everyone's thoughts have been helpful but I guess the real crux of the matter is that I have to learn to be very opponent specific.
If the opponent in the hand posted would have allowed me to check the turn AND river then I lose 2BB less when I'm beaten by the hands that should be bad enough to fold. But for those that will bet the river no matter what they have after you check the turn after them I guess betting the turn for the free showdown is the best option.

But even when you really have a handle on opponent specific betting in this situation what to do when you have NO read on the opponent?

[DeliciousDi]

Thanks for your reply, Pudley4. Well done! Obviously I would rather win the 3 bets, which leads me to the conclusions that I should not believe everything I read and I'm going to refrain from buying waterfront property any time soon. Thanks for your excellent analysis.