Paying off a true maniac when you miss

[melange]

Assume a 4-handed table where you are often heads-up with a true maniac (caps every street every single hand). Should you be paying off with your J-hi's and T-hi's? Since my selection of hands will be above-average vs his exactly average hands, wouldn't paying off with T-hi every time be very slightly +ev? Or am I missing some vital piece of logic?

If I'm wrong, how low is it +ev to be paying off with when you miss, K-hi?

[A_C_Slater]

It takes two to cap. Why would you be capping every street with ten high? Why would you have to gamble with this sort of player? Just fold, fold, fold, and wait til you have a strong hand (at least top pair strong kicker) and you'll make all the money back and then some from the folded blinds and flop folds. Even random bluff hands have lots of potential to beat ten high.

[melange]

Not capping, I should have mentioned that I'm assuming you just check-call to him every street if you miss. so it's costing you a preflop raise, and 2.5 big bets.

[Jeff W]

A true theoretical maniac raises on every street with any two cards:

Assume he has a random hand and cap every street where you have >50% equity. Call down whenever your equity is <50% against a random hand, but the pot is laying you odds to call.

[bxpeter]

In terms of EV, it may be profitable to call down with J-high, I'm not sure about T-high. I think when you have T-high, it becomes too likely that he either has a higher card or hit some pair.

However, considering how incredibly easy its going to be to take all of this guy's money, I would probably just fold the J-highs, and maybe call down with Q-high or better, and go to town with any pair or a strong ace.

I guess this is sort of a question of how much variance you are willing to take. In the end, you know you're taking this guy's money. However, you would hope that the others don't finish him off before you get a piece.

[sqvirrel]

If I'm wrong, how low is it +ev to be paying off with when you miss, K-hi?

Think about it this way. Regardless of what you hold 6% of the time your opponent will have a pocket pair and 49% of the remaining time your opponent will pair the board. A high card will beat a random hand with a lower high card 47% of the time or less.

Additionally if you are considering calling down a J high bear in mind that there is a 43% chance that your opponent holds a Q or better. (There is ~ 30% that he holds K or better and 16% that he holds an A) I would try to avoid getting to the river with J-high only, but once there you should often call.

J high will beat a random unpaired hand 45% and chop 12% so combined with the possibility that your opponent is paired up - or has flush or straight (roughly 2%) - your J high will win about 20% of showdowns and tie (kicker battle) 5%. Since you are getting (at least) 6:1 you should always make this call.

The problem really comes with your preflop decision. Since you know in advance that every hand you enter is going to require multiple bets to see a showdown you should very rarely be seeing flops with unpaired middle cards. Calling a single bet from BB is about the only scenario where I could justify playing something like JT or J9 against a maniac, and these hands should usually be discarded on the flop unpaired since HU you probably won't even have odds to call a single sb on a straight or flush draw.