specific theory question

[Guruman]

Here's the Q:

Hero is at a 1/2 party game with plenty of semi-loose passive opponents. He open raises from MP1 with AKo and gets one caller from the button. the blinds both fold (a rarity)

The pot is 5.5 sb. the flop comes 222. Hero bets, villain calls.

assumptions:

villain would have called the preflop raise with any two broadways, any ace and any suited king.
villain does not have a pocket pair.
villain will call down with any ace
villain will raise if he pairs a card on the turn or river to make a boat.

Q1:how often must the villain miss his boat in order to make leading into him on every street profitable?

Q2:what are the odds of him missing entirely occurring?

thanks!

[R_Ellender]

If he calls with any ace or king, and you hold both an ace and a king, he only has three outs to win(his kicker). The chances of improving with three outs by the river is about 12.5%, so you could bet all day if he'll call in hopes of making a full house. If he holds QJ, he has six outs and a 24.1% chance of improving, so again, you could bet all day.

Even if the pot had 100sb's in it, it would still be profitable to bet all the way. However, you would hope for a fold from the villain since he gains when he calls with proper odds to chase.

[AaronBrown]

You have listed 325 of the 1,225 possible hands your opponent can hold. Four of the 325, A2 and K2s, mean you've already lost. Nine of the 325, AK, mean you're guaranteed to tie. For the remaining 312, you somewhere between 660 and 743 chances to win out of 990 possible turn and river cards. Counting ties as half a win, your chance of winning in these cases ranges from 74% to 84%. Your worst situation is if he holds Ax, suited and matching one of the three 2's. Then you have 660 ways to win and 147 to tie. Your best situation is if he holds two of Q/J/T either unsuited or suited with the missing 2. Then you have 732 ways to win and 207 to tie (if he holds Kx without flush possibilities you have more ways to win, 743, but fewer to tie, 111).

You have to bet this all the way and take your lumps if he's got a 2, or pairs up. Unless this guy is completely transparent, so a raise guarantees a full house, I think you have to try to make as much as you can. He could feel pretty confident with an Ax.

[Guruman]

Thanks Aaron. I took this line yesterday against a passive and predictable player but felt kind of uncomfortable doing it. He paid off the river with Ace high, but my kicker played and I took the pot.

Thanks again for the analysis.

[Guruman]

As a follow up question -

How low would an offsuit kicker have to go to make this line EV neutral. AQ? A8?

It seems like with every step down you run a bigger risk of the kicker not playing and you either losing or splitting against another random ace.

thanks.