4/8k blinds, you have 220k, you raise to 24k, some guy pushes all-in. Pot contains 220+24+12 = 256k, it costs you 196k to call. You have 256 to 196 odds or 196/(196+256) = 43.4% equity. If you're 43.4% against his range, you're even money to call. This is how you calculate. If, in fact, you are 100% sure your opponent has AKo or AKs, then this is a substantially +EV (Expected Value) call, since you're close to 54% equity against a range of AKo and AKs. HOWEVER, this is assuming you've identified his range correctly as AKo and AKs ONLY. Unless you have a super, super read, or your opponent flips his AK face up and shows it to you, then your estimate of your opponent's range is probably too narrow. Villain won't play 88-JJ the same way? You said your gut. A problem many players have is assigning your opponent to a specific hand w/ insufficient information. It's folded to the button, who raises to 3x bb. You think, he probably holds some junk like KJ, you have AT in the bb and call. Then the flop comes T85, you say to yourself, oh well, KJ missed that flop, so i'll bet. You bet, your opponent raises, you're SURE he's bluffing since you read your opponent for KJ, you reraise all-in, he calls and shows 88. Many times you won't be able to assign your opponent to a specific hand until the turn or even river. You'll have an idea, a RANGE, of the hands your opponent may have. Now, this is barring super reads, betting patterns, etc. Against tight opponents, it's easier to assign a range since they play fewer hands. Vice versa for loose opponents.

Here's a good article that touches on some common No Limit Hold'em Errors: http://www.cardplayer.com/poker_maga...amp;m_id=65568

If you had a 100% reliable read that your opponent has AK in the 77 situation above, then call. If you expand that range to AK-AT, JJ-66 (since you reason that your opponent won't push w/ AA-QQ but would just raise a small amount to induce a call), then you'll get a different number for equity.

Here's a quick example for calculating equity.

You identified his range as AK-AT, 66-JJ. After you take out 77 from the deck...

AK-AT = 16 combos each; 5*16 = 80 combos
88-JJ = 6 combos each; 4*6 = 24 combos
77 = 1 combo
66 = 6 combos

Total combos = 80+24+1+6 = 111 combos
Your equity = 80/111*(.54) + 24/111*(.2) + 1/111*(.5) + 6/111*(.8) = .48

You're a slight dog against the above range. You only need to have .434 equity, as dictated by pot odds. With the above range, it's still a call w/ 77. If you trim his range to AK-AQ, 88-JJ, then your equity becomes .396, and it's a fold. Try doing some of these calculations. It looks like a pain in the ass, but you'll get the hang of it.

Your gut told you your opponent held AK. This is fine, your gut probably thought this because a good % of the time, villain will show up w/ AK or AQ. But next time, ask your gut, does villain make this same play w/ 99 too? Be flexible when assigning a starting range. Don't forget pocket pairs. If you want to become a better player, read more, do math like this, and be a flexible thinker. Please read the Anthology.