Pocket Pair Decay

[DukeOfDeath]

3 weeks since any strategy has been discussed is a little sad, so here goes another thing floating in my head. What is the value of pocket pairs in NLHE?

Everyone knows AA is the best, KK is "unfoldable preflop", QQ is great but beatable if not careful, and JJ is cursed. It was kind of weird to me that AA and KK cluster and there's such a drop off before QQ and JJ. In my opinion either QQ should be given more credit or KK less credit.

I guess the logic is that AA has to be beaten by AT LEAST 2 pair, so, since that is rare for a random single hand, AA is quite dominant.

KK can also only be beaten by 2 pair or better or someone having an A (less than 24% chance) AND hitting the flop (barely more than 1/3 of the time) or sticking around to turn or river and hoping to hit a 14:1 shot on either street.

I guess the reason QQ drops in value is people's love of AK, which has 3 more (twice as many) outs agains QQ than against KK (and which is also 33% more likely to be dealt than AA or KK combined).

In black and white terms, AA has no starting hand ahead of it. KK has 6. And QQ has 12 that are ahead plus 16 that are tied. It gets more complicated as you go down the list, so I decided to chart out different starting pocket pairs' value based on how many other opponents face it:



The y-axis is the percent chance the pocket pair will win against x number of opponents. At first I just looked at the pocket pairs I talked about earlier and 10s. And it looked kind of boring, like it was just evenly spaced between hands. But then when I added all the pocket pairs I noticed something and made this graph to look closer:



As you add players to the hand, AA decreases linearly whereas 22 decreases quadratically. So basically the change in value in pocket pair starting hands is relatively consistent with less people at the table and drop exponentially in value with more people at the table. Likewise the higher the pair the stronger it "resists" the decay in value by adding others to the hand:



So, I know this is a bunch of lines and math and boring words, but for those of you that are visual learners like me, I thought this might be helpful. Also the first graph is nice because you can equate starting hands by seeing where a horizontal line crosses a trendline. For example, pick 70%: 8s or less never are more than a 70% favorite, 99 and 10s are so only heads up, JJ is on the bubble between 1 and 2 opponents, QQ and KK are 70% against 2 opponents, and AA doesn't drop below 70% until a 3rd opponent is added. From here you can learn interesting things like AA 6-way and 22 heads up are both coin tosses. Or 77 heads up and QQ 3-way are even (never would have guessed that).

Anyway, just thought I would try to wake the beast of strategy. Hope you all enjoy (or have discussion to add).

[tattmando]

i wasn't serious about the chinese arithmatic m8. lol jk

[DukeOfDeath]

Originally Posted by tattmando

i wasn't serious about the chinese arithmatic m8. lol jk

lol. Yeah the Omaha equivalent of this might never happen.

[reaper1569]

m8 i feel ur painn u must b on bad runn 2..3 week 4 me now it crazy i call crap n win n great cards lose i giv up 2..

[DukeOfDeath]

Originally Posted by reaper1569

m8 i feel ur painn u must b on bad runn 2..3 week 4 me now it crazy i call crap n win n great cards lose i giv up 2..

yeah reaps. I was just talking about the MATH of omaha. The luck is a different story. Some law saying every hand I hit is second best and every hand I fold would have been the nuts.

[reaper1569]

was playin it 2 day budd the the pre flop betts were silly

[phattP]

Thanks Duke ( or should I call you Death?)..
This is interesting reading and helpful too.. good one..

[DukeOfDeath]

Originally Posted by phattP

Thanks Duke ( or should I call you Death?)..
This is interesting reading and helpful too.. good one..

You can call me Cool Hand Duke . Haha. Thanks and glad I could help.

[akatiger]

another good post duke,very informative,keep postin

[OP66fozzy]

[QUOTE=DukeOfDeath;474133]
From here you can learn interesting things like AA 6-way and 22 heads up are both coin tosses. Or 77 heads up and QQ 3-way are even (never would have guessed that).
QUOTE]

AA 6-way is a coin toss ?? How do you figure that out ? I accept it is true, but am very interested in the math behind it...

[jamholdm]

Great post. Well done.

[DukeOfDeath]

Originally Posted by OP66fozzy

AA 6-way is a coin toss ?? How do you figure that out ? I accept it is true, but am very interested in the math behind it...

Well the complete math is complex because you have to indivdually consider all 2651 hands all 5 of your opponents could have and consider over a quarter billion boards that could come up for each and weigh out how often Aces hold. I'm not gonna do that. Roo will win 3 WSOP bracelets by the time I finish that math. But as a shortcut, if you accept AA as 85% against any one hand, just multiply .85 by itself 5 times. (.85)^5 is .444 or 44.4%. It's actually 48.77% (and .56% to tie), but 44.4% gets you close with minimal math.

So yeah take away is that how many opponents you have (or at least how many see more streets) is as big a factor as how big your pocket pair is.

Thanks all for the kind words. If anyone wants to mail me a better calculator I can PM you my mailing address (lol just kidding)

[CherryPie]

The graphs are great

i like it A LOT

[DukeOfDeath]

Originally Posted by CherryPie

The graphs are great

i like it A LOT

Good ole MS Excel Thanks!