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The only things to consider are:
- Your estimation of your win percentage (you said 99 % of the time... would you keep that same estimation wether you check and he bets enough to put you all in?), which should be fairly high (but not as high as you estimated, I think) since a few hands can beat you (Ad+X, Q+6, Q+5, Q+2, 3d+4d, 66, 55, 22)
- The probability he'll fold if you bet all your money
- The probability he'll bet enough to put you all in if you check
I wouldn't consider any amounts less than your stack, since it's not even half of the pot (you have 4,70 $ left for a 10,70 $ pot).
Just estimate those numbers, and calculate your EV. That's the best way to get the answer to your original question.
If you're convinced you have a 99 % win rate, you're better off betting, even more so if you estimate he's the kind of player that'll bet back at you more often. Even with a lower win chance, you're probably better off this way, because of the gain you do when he folds (the extra 4,70 $ you can gain if he calls isn't enough compared to the 10,70 $ already in the pot... that's the money you're after, really).
Another reason to bet instead of checking is that, if he checks after you, you still stand with your 99 % (or slightly less, but still very strong) chances of winning the pot. But if he bets for your remaining money, he's probably announcing a stronger hand, giving him a much higher win percentage (probably as high as 40 %), forcing you to fold more hands which you probably don't wanna do at that point.
So, by being the agressor, you don't have to worry about his hand more than necessary. And you'll give him 4,7:15,4, or 1:3,28 pot odds, so he needs to beat you more than 23 % of the time to make it worth his money.
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