So, I was reading a text the other day and the hand played out where hero had KK and he put in a bet and a nit with a low 3-bet percentage 3-bet him. According to the author this put him on a range where he would either have AK suited, AA or KK. Obviously KK is most likely a chop, you are a favorite against AK suited and you are a dog when it comes to AA.

The author said that made his kings a 2:1 dog. However, since KK is a favorite to AK suited and a dog to AA then shouldn't he be a 3:1 dog. I am saying this because there are two combinations of AK suited and 6 combinations of AA.

I believe that the author is correct. I just want to know where my logic is incorrect. Any help would be appreciated, thank you.

You don't work out how big a dog you are by just counting the combinations you beat and don't beat. You average your win% versus each hand, weighting by number of combinations.

For this hand this works like this:

KK v AKs: 65.9%, 2 combinations
KK v AA: 18.1%, 6 combinations
KK v KK: 50%, 1 combination

((65.9 * 2) + (18.1 * 6) + (50))/9 = 32.3%

So your KK wins 32.3%, i.e. a 2 to 1 dog. If you can learn to think in percentages instead of odds, it makes the maths a lot easier.

Also even though when you're against KK it's neutral EV, you can't leave it out of the calculation. Imagine if you knew that out of 1000 times he was going to have AA once and KK 999 times. You can't just disregard all the KKs and say that you're a 4 to 1 dog there. You have to include all the KKs which puts you close to 50%.

Lastly, get www.pokerstove.com and it will do these calculations for you.

Thanks that clears it all up.