[EnderW27]

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This is a bad and largely useless assumption. First of all, he could have the other two kings.

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I made two initial assumptions at the begining. 1) the button ONLY does this with AA or AK. 2) you're beating the caller.

I think #2 is a reasonable assumption to make. Yes, it's possible he's twice-called with the other AA or KK. But the low liklihood of that occurring shouldn't significantly skew the results. Besides, when both players have AA your chances of winning slightly increase over AA and another pocket pair.

As for #1, I only did it to simply the following equations and to show later on that if the Button's range is even wider than AA or AK it makes the ev of calling even greater.

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He has 12 possible AA combinations and 8 possible AK combinations so 60% of the time he'll have AA and 40% of the time he'll have AK.
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As noted above, this is incorrect. There are 6 combinations of AA (or any pocket pair except, in this instance, kings).


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On this point I can only plead absolute stupidity. Seriously, I know it's 4*3/2 and yet my crack addled brain at 2:30 last night made me stop at 4*3. I'll admit that screwing up this screws up everything that comes after it...but it screws it up for the better. The lower liklihood of AA occuring only makes the ev of calling greater.
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Notwithstanding the fact that you miscounted the combinations of AA (and thus your 60%-40% is totally off), you've also made yet another error. The presence of a third hand (which is required in this case for tripling up) must be factored into the equation as well. You can't just say "let's assume you've got the third hand beat." In fact, unless BOTH players have AA or one has AA and the other KK, your KK MUST be beating one of the two hands...PREFLOP. However, you're forgetting about the fact that the third-best preflop hand ALSO has a chance of winning.

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As I said above I was using simplified, reasonable, starting hands for the villians. I've already addressed the fact that, yes, they could both have AA or one could have KK. But I will tell you that my initial assumptions DID factor in the third hand. I gave third hand JJ. Yes, he could have another AK or T9 or 83. Again, the ev of calling is only going to go up in those cases. I gave him JJ to simplify the scenario. But I did factor the third hand into the % of winning calculations.

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But I would ask you to please know what you're doing before you give authoritative-sounding mathematical advice to a new player who's trying to find his way.

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Good advice. Thanks.