Tuesday, May 22, 2007

Poker Flop Probability - Continuation Betting Against Opponents Who Love Ace-Rag!! (A Post for Lower Stakes Players)

Time to bring a couple of the recent thoughts together... by looking at a fairly common scenario - you have KK and raise pre-flop in a SNG / MTT, you are called and the flop comes Axx... this post is for lower stakes players who often face opponents who think A5o is the nuts pre flop!

The approach I wanted to take is to look at someone who loves Ace-Rag too much and go into the poker hand probablilty math - if we take someones entire range we should be able to come up with a ratio of Ace-Rag / Pair hands this way, this in turn should show us how confidently we can continuation bet the KK on an Axx flop against such an opponent.

So we start with some simplification, just one opponent who will call our raise pre flop with any pair, and aces up to ace-X (going to use different measures for X). What is the distribution of hands when he calls?

Well, if we have KK there are 6 ways of being dealt any non-KK pair and 1 way of being dealt KK. So (12*6) +1 = 73 ways out of 1326 that he could have been dealt a pair pre-flop or an approximate 1 in 18 chance = we will use 5% to keep the numbers round.

Now the chances of being dealt an Ace-X hand rise significantly the more X's you add... for example there are 12 ways of your opponent getting dealt AQ, 12 for AJ and so on (there are only 6 for AK as you have 2 of the K's). So the number of calling hands for the various Ace-X's is as follows

AK Only - 6
+AQ - 18
+AJ - 30
+A10 - 42
+A9 - 54
+A8 - 66
+A7 - 72
+A6 - 84
+A5 - 96
+A4 - 108
+A3 - 120
+A2 - 132

So if our lower limit opponent will call with any pair + Ace-x then the chances he called with each are in a ratio of 72/132 he is more likely to have the ace by 1.8 / 1, he is almost twice as likely to have an ace than a pair... but hold on - in our example an Ace has appreared on the flop, that is one less to put into our pre-flop calculations then...

Well, there are now only 9 ways of getting dealt each Ace-X hand (less for AK). If we take the A2+ scenario then instead of a 72/132 ratio we now have a 72/99 ratio - 1.37 / 1 in favour of our opponent having an Ace rather than a pair.

All very nice but how can this be used by readers in those $3 SNGs?

Well we have established that our opponent has that ace 58% of the time in our simplified scenario after the flop if he calls raises with any ace (you can work it out for A5+ or A8+ by removing these from the list and looking at the new ratio).

To show a profit with a half-pot continuation bet we need to win 1 in 3 times (for example we bet 100 into a 200 pot - if we lose our extra 100 twice but win the 200 pot once we break even, if we win the 200 pot any more than this we show a profit on our bet).

Following this logic through our opponent would need to have the ace 66% of the time (and raise us out of the pot) to make our continuation bet unprofitable. This is not the case even for the loosest Ace-x player.

Of course real-life is never that simple... my parting thought here for the lower level players is to look for opponents who love Ace-rag too much and look for spots where you are likely to dominate them (with a pair over their kicker or a strong ace). They will pay you off soon enough!!

GL at the Tables,

Mark

2 comments:

Cell 1919 said...

Thanks for this, aimed as it is towards my end of the market.

It's long been a concern of mine that (understandably) a lot of poker theory is based on having rational opponents who you can read with a degree of consistency.

This type of post is very useful for those of us who, due to bankroll considerations, have to play at micro-limits instead of advancing up the ladder.

Cheers :)

Scott said...

Thanks-Mark
Have a feeling this was directed at/inspired by my insane ranting during my downswing. Anyways thanks for your advise you kept me focused and I turned around in a big way!!!

Check my progress at:
http://acefilleddreams.blogspot.com