11- 5-04, LearnTexasHoldem:
Overcards vs Underpair
I have not mastered probablities yet and would like to know if someone can give a definitive answer to this. There are a lot of scenarios to consider it would seem or maybe I am reading to much into it.
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I think the odds of catching one of two cards by the river (A or K) is about 55%...not sure exactly. The odds of the 88 improving to a set is about 15%...if you subtract 15% from 55% you are left with a 40% chance of AK winning. Two pair doesn't really come into play in either scenario. I guess you would then have to add in the odds of AK making a straight, a flush if it is suited, or even a set of A's or K's. At which point you could go on and on with full houses, four of a kind, and straight flushes. Toward the end the odds are getting so small that it probably isn't worth the time doing the math.
If someone is capable of doing this math or it has already been done I would like to know. The numbers I have been told are around 55% that a pocket pair will beat two overcards but I don't know if all of these probabilities have been taken into account. Thank you, Rex.
Answer: Yes, that is correct that two overcards are an underdog to an underpair. It depends slightly on which cards are in play. For example, if you have AsKs versus 8c8d then the odds are around 52% to 48% in favor of the 88. If you have unsuited AsKh then the 88 is 55%. Note though that any two cards that can make a straight have a slight edge over cards that can't. Take 88 compared to A9, the 88 in that case is now around a 57% favorite.
You need to be careful about how much you value those odds when you are on the receiving end of a big raise preflop. AK of course is a great hand, but in no limit cash games, you still need to hit something on the flop. It is easy to look at the entire hand holistically, from deal to river but in actuality, you'll most likely fold on the flop if you miss your Ace or King.
No limit holdem isn't a game of all-ins. Raises are made preflop to build pots and then bets after the flop are usually in relation to the size of the pot. On the same accord as the AK, if someone raises a lot preflop and you have 88, you don't feel that great about calling. This is one of those situations where you are either a slight favorite or a big underdog.
My point with this warning is to not think of no limit holdem in terms of having a slight edge and going all-in; instead, you should think about building pots, using deception and getting value on your hands. The all-in is a move used sparingly either when you are up against the wall or for the occasional tricky play.
The time when you are happy to put all your money in, even if you have a lot of chips and options left, is when you have a dominating hand like AK versus A9 where you are a 75% to 25% favorite, or when you have an over pair versus underpair like AA versus 88 in which case you are an ~80% favorite to win.
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