11-17-04, LearnTexasHoldem:

Heads Up Odds Races

Question: I recently had an argument with a player online. He went all-in with Queens and had two callers who created a side-pot. I had AJ. I don't know what the other guy had because he folded soon afterwards. I wound up getting running Aces on the turn and river to win the hand. He immediately started complaining how lucky I was.

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I tried to explain to him that Queens was not a mortal lock as long as I had one overcard and straight potential. I tried to explain that with two callers, he was the favorite but also an overall dog - especially if the other player had at least a King. He wasn't buying it.

I know a few things from watching WSOP when it comes to the odds of winning in a race. For example, if I recall correctly, a pair against two overcards is a 53% favorite head's up (virtual coin flip); the higher of two pairs is an 80% favorite head-to-head. I seem to recall these from WSOP broadcasts, but please correct me if I am mistaken.

I heard from the guy who runs the house game I play at that the worst starting hand (72) against the best (AA) will win about 12% of the time

- a huge number when you consider that this is the worst hand (which nobody will ever call) against the best (which few are fortunate enough to have).

I tried looking online for stats that discuss these things to make my point and I couldn't find any. A lot of pages with odds but none on what to me seems pretty important: The odds your hand will have in a head's up race.

So maybe you can help? What are the odds of QQ against AJ as outlined above? My educated guess is about 65%.

I know you can't address every situation, but you can possibly list some simple concepts based on common races with regard to pairs and over/undercard match-ups with the percentage chance for the favorite to win?

Answer: I'm not sure what the flop was so I can't give you exact odds for what your chance of winning was but if you were both all-in preflop the odds of AJ beating QQ is around 30%. I think you may be applying what you learned on the WPT incorrectly. When they talk about a race situation they are referring to situations where the players won't make any more moves; the money is all-in preflop. For example, take 55 versus AK.

If one person was all-in preflop, then it would be a race situation (coin flip). If on the other hand both players still had chips post flop, it isn't considered a race situation and if the AK missed, it would be a big underdog to catch. You can't look at the hand holistically (preflop to river) unless you are all-in. Holdem isn't won by just picking the best hand preflop and then going till the river based on some stats. Take another example like A7 versus AK.

The AK is a huge favorite but if the flop comes back with a 7, the AK is now a huge underdog (in most cases a bigger underdog than the A7 started out preflop). The point is that the flop changes everything and your hand strength is based on how it relates to the flop, not how it shaped up with the opponents hand preflop. If you were to take that approach, you would get hammered.

Let me give you an example that uses coins instead of cards to illustrate my point. Let's say that I was going to bet you some cash that I could beat you flipping a penny. We get one point if we flip heads and if you get to 5 first you win, and for me to win I have to get to 7. That's a safe for you to take, you should beat me, right? Would you double the money if after a number of turns I was already at 5 and you were only at 2?

You could very well say to yourself, "yes I will double the bet because if I look at the numbers I should win." Well that's the funny thing about odds though is that it takes a lot of data before the theoretical probability is represented. The more we turn cards or flip coins, the more we can see how the hand will shape up and your odds for winning keep changing. I can't say whether it was ok for your to call in the hand you sent in but if it was ok to call it would have been an issue of pot odds because you knew you were behind in the hand.

For the sake of completeness, let me throw out a few odds/probabilities for preflop hands (flop till river). I'm not going to use any suited cards, just unsuited:

* Two connected overcards versus two connected undercards: JT vs 45 - ~65% to 35%

* If the two connected over cards using one of the undercards: JT vs T9 - ~70% to 30%

* Large pocket pair versus smaller pocket pair: KK vs 44 - ~80% to 20%

* Large pocket pair versus smaller undercards: KK vs 78 - ~82% to 18%

* Pocket pair versus hand with one overcard: QQ vs AJ - ~70% to 30%

* Two cards versus dominated hand: AK vs AJ - ~73% to 27%

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