Re: Heads up with when you know ONE of opponents cards - best strategy
DEEP STAKES
In deep stakes you can out play him... Any ace you can get away from. You can hit 2 pair against an ace and he might think you also have an ace. If you haven't done anything for awhile, you can also even make a very bold move with an ace on board... it won't make sence to him why you're doing it, and he might assume he's beat giving you valuable chips and taking away a pot that you might have no chance of winning.
Either see a bunch of cheap flops and try to chop away at him. If he lets you do this, a move with an ace on the board probably isn't neccesary. If he's being too aggressive just wait for the goods. If he gives you room you can play back at him after the flop, of course if his other card hits, you won't know it. If he pushes too hard you can get yourself in a dominating position. Pocket pairs are a slight favorite and will win money in the long run... If he's being a maniac and pushing every hand hard, you can get these all in.... but 1/17-1/18 he will have pocket aces, so preferably wait for 8s or better to push so your ++EV against A2 through 7 makes up for your --EV when he has aces, since it's more rare that he'll have pocket aces If you're playing once or if you think your advantage is greater than 51% over him you can just keep it small and not take those risks. I see it being pretty hard if he's just playing preflop poker and going all in with A9 or better to defend against in any other way, but even so most times you'll be in a coinflip as a slight favorite, but there will still be situations where he has AA and this will kill your EV, and you'll have to wait for good hands which could take awhile.
SHORTER STAKES
A random ace vs a random hand the ace is favored about 60/40. However if you play the top 22% of hands, you're favored slightly. Then, if he plays about 20% of the top ace hands, it goes back to him being the big favorite... So obviously your advantage is going to come after the flop, but shorter staked you don't have as much room. You HAVE to make some steals early with junk if he'll let you so you actually have a slight advanatage, and a way to get action when you hit your hand. No more than 3 steals with garbage hands that you wouldn't normally play. you could play any ace and hope to pair your kicker, but shorter stakes you don't have room... he can tighten up and play one out of 5 hands and he'll be playing AA, AK, AQ and AKs-AJs. I wouldn't mess around with hands with aces in them unless it's AA AK or AQ. Play suited connectors. If you're going to advertize, do it with high cards. Show him KQ when it's low cards on the board. Perhaps play any king to advertize. You want to be able to represent the high cards too. He'll assume you play some low cards, but you want to Represent every signle hand, as well as draw out there. Flush draw, represent (just as long as it isn't the spade draws... toss all spades, unless you have a pair) If he's tight stay away from brodway hands, they're too easily dominated AT and AQ will both dominate QT and AK puts it into a 35% dog. 46 suited you have 2 live cards
This is where the pairs really comes much more into place. If he thinks he has a great advantage, he might not call an all in. But that's really a lot to know here. If he does, you're 40/60 maybe closer to 47/53. If you don't think he'll call an all in with any ace, you might want to move in with junk especially if he just completes the button. This will set yourself up later and when you move in with a pair he'll figure you've moved in too often and you might even be a situation like TT vs A8. Obviously idealy you want AA vs A7 or A6. If you do this for a few times, he figures, well if he's going to do this I'll wait for aces. The key is just to do this a couple times to set yourself up. Now you're waiting for quite awhile and he figures you might have done it with decent hands I think with shorter stakes you can actually push all in more
If he's not going to call you with ace high then obviously it'd be great if you know that he only pushes you around with A8 or higher because low cards on board=push. 2 low 1 mid=push. This is assuming you get a good percentage of your chips in preflop.
Now if it's shorter staked you can either criple him early by betting a huge portion of his chips (ALMOST a third, then push him all in. You'll have to wait for a pair or AQ or higher to start with, and as your stack gets down there open it up. A pair is always at least a 51%+, where as if you do AJ or higher he can exploit it by waiting, depending on how much he puts into the pot for a raise.
Keep in mind he only will hit a third of the time... You should bet no more than about 3 times the potsize, if it's slightly more for all of your chips push because you have chance to draw out. Get a third of your money with a pair preflop. If he goes all in that's fine, but if he calls a third of your chips where he'll hit a third of the time(where you'll hit your set 10%, and given that you dont you'll suck out about 5%), that's better EV than 51-55% favorite. I doubt you have much fold equity in shorter stakes.
I actually prefer shorter stakes where you can make a move on him once or force him to take a coinflip (where you have a pair and are favored) The element of suprise could really get him burried if he raises big and all of a sudden you pull a stop and go type play on him.
Anyway, mathmatically having an ace gives you a 60/40 favorite over a random hand. I think knowing he has an ace is a HUGE advantage and makes up for the 60/40, but the fact that he knows that you know that helps him as well.
Sounds like a great idea, is having the math favor you, or knowledge more important?
Let me know how it goes!
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