Waiting for Aces

If you are waiting for aces, what are the chances you get them with X hands left? What about waiting for QQ or better?

The probability of getting AA in a hand is 1/221, so the probability of not getting it is 220/221, and the probability of not getting it in x hands is (220/221)^x. This means that if we can solve for the probability of NOT getting it in X hands we can determine that the remaining percentage we DID get it at least once over X hands.

For example (220/221)⁶⁰=~.761771. Probability of getting aces is then 1-.761771=~.238229

 What about Aces OR kings.
(2/221) or (119/221)⁶⁰=!0.579576102. 1-0.579576102=~.420424.


Action is information. You could run some math to figure out what the odds of one of your opponents getting aces, but it would probably not be as relevant as the odds BASED upon how they act. You could easily define their rasing range on hands they would play in that manner based upon history and be reasonably confident and more accurate...

Define a hand range as 10%, then 3bet range as 4%, and of the top 4% of hands, aces is .4524% of that, which makes it about an 11.3% chance that an opponent who reraised you with that kind of range has aces. It could be higher or lower. Realistically you aren't betting probabilities but probability ranges. You might statistically depending on the sampling size be able to say that you can be 90% confident opponent has between a 8.3% and 14.3% of aces. You could say that about ANY specific pocket pair, so the chances that you are ahead with QQ in that spot is probably about 77.4% Although the chances opponent has AK is 1/82.875=1.2% which gives you about a 30% chance of being in a race, and combine that with a 22.6% of being way behind and suddenly QQ doesn't look great... Especially if you have to put in another bet that opponent may just fold if he has less than KK. Folding actually in this spot may not be a terrible option if you have faith in opponent's 3bet range. However, calling and avoiding flops like AKx, Axx, while trying to keep pot smalls on flops like JTA, and possibly shoving with very few king high flops (since opponent will have to respect YOUR range which would rarely shove there with less than a king), and some AAx and KKx flops and trying your best to get opponent to try to bluff and get all the money in on Queen high flop or lower.

But if the shove is all in preflop, you probably would want to call unless you feel table is weak and can pick away at small pots and pick your spots a little better in a tournament.

Take the time to construct a table which uses the math to determine the probability. Look at the range in which you'll expect a hand in that range 50% of the time as a good range to plan on as an all in hand, but adjust it as you become more and more short stack as you approach fewer and fewer hands left. Be willing to raise all in with 1.5x that hand range since you don't always get action (I actually go for 2x the range I can wait for as I don't want to wait until I am short stacked if I can help it... Exception is when I am deep enough in tournament and want to be even more patient and wait on hands which are less than 50% likely to come because they way I can fold my way up the money and THEN develop the tight image and make up for it with extreme aggression once blinds go higher and fewer people with fewer hands are in.).

You can develop an entire strategy based upon how many hands you can wait for, provided you take the blind structure into account.