Wednesday, May 07, 2008

AA and 44-66 Expectation Value Graphs

I have refined a bit the Expectation Value graph and have ended up with what is below.

Expectation Value in Percentage for AA
This was data collected over 13k hands at FullTilt 1/2 NL Holdem. 63 instances of AA for the above graph. The vertical bar shows the percentage chance of the result each time you are dealt AA. Each bar represents 5% of your stack size. This shows that 33% of the time you will win 0-5% of your stack size (steal the blinds), and about 5% of the time you will win 45-50% of your stack size. I am also three times more likely to get stacked than to double up with AA based on the 63 hands. Keep in mind that this is my chart for how I play AA. Other player's charts will look different, but in general should show a similar shape. The blue line is a guess at what the long term results would average to if I had bigger sample size. Overall I win 7.5% of my stack size or about $15 on average when dealt AA at a 1/2 NL cash table. You win tons of small pots with it and have a significant chance of winning a decent pot. You only actually lose money on the hand about 13% of the time you are dealt it.

Below is the chart for 44-66 the semi-dangerous low to middle pair. Again this is for 1/2 NL Holdem at Full Tilt. In this case 180 hands are shown.

Expectation Value in Percentage for 44-66

For the small to middle pairs a full 66% of the time I am dealt them I will lose 0-5% of my stack. This is me limping in with them, and getting either bet off preflop or missing the set. About 4% of the time I will call a raise preflop, miss, and lose 5-10% of my stack. 15% of the time I will win 0-5% of my stack. This probably includes some late position plays where I am not limping or limp/calling the hand preflop. Outside of that I will win a bunch of decent sized pots, and not really lose too many big pots. Overall I will increase my stack size by 1.1% or $2.20 on average each time I am dealt 44-66.

Where am I going with all this? Its going to be a different way of looking at MTT results. If you take a chart like above and rotate it 90 degrees it becomes an operator on your chip stack. I want to build a few more of these charts before I get there, but you can take whatever your MTT chip stack is and then take the expectation value chart for the hand that you are dealt and line up the 0% mark on the Expectation Value axis with your stack size. Then rather than just give you the +7.5% in EV for AA you would get some result between +100 and -100% of your stack based on the likelihood of each occurrence. You can then simply map out your MTT chip stack size based on the hands you are dealt. This all sounds a bit crazy, but I think this is actually a very solid model of how MTTs work. The key is that each player has their own EV curves for each hand they are dealt in an MTT. They are also free to manipulate how they play certain hands to influence the EV curves as necessary. When you get into push or fold mode late in an MTT the curve for 44-66 will look a bunch different, but that is how you may want it to look late. Ultimately, I think this will show why we are more of a slave to the cards in an MTT than many would want to admit. Sure we can play each hand slightly better then the next guy, but is that enough to overcome the threat of elimination on any hand in an MTT significantly?



At 4:11 PM, Blogger $mokkee said...

cards play a big factor obv but, IMO stack sizes and position in the hand play a way bigger factor in the late stages of an MTT. you may be able to wait around for AA then dubble if you're lucky enough not to get cracked. but, building your stack by punishing weaker players in later stages is what separates the men from the boys in MTT's.

bigger stacks are raising a wider range of hands taking down uncontested pots. that's the best way to accumulate chips.
winning races like a drunken irishmen doesn't hurt tho. :)

these graphs serve better in a cash game.

At 4:11 PM, Blogger Neilc999 said...

i read this post and started getting wierd images in my head of you having phone sex with sklansky.

At 4:31 PM, Blogger $mokkee said...

Blinders has a cat.

just sayin'

At 11:40 AM, Blogger Hammer Player a.k.a Hoyazo said...

I'm still trying to wrap my arms around you being 3x more likely to get stacked with AA than to double up with it. Dam girl you need to work on your postflop play!

At 10:03 AM, Blogger Blinders said...


Its a limited sample size, but I would guess for most people you are more likely to get stacked than to double through with AA. This is more than made up for by all the medium sized pots you will win with AA. Keep in ming that you will be raising and c-betting a bunch with AA giving your opponents plenty of chances to get out of your way. When you AA is beaten, you will probably get only one chance to release it, and may not actually fold. More charts to come later this week.


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