## Hot & Cold Hand Odds In Holdem And Domination

### Limit Texas Holdem, No Limit Texas Holdem, Strategy

October 10, 2007

A key concept in holdem, especially in NL, it “hot and cold” comparison of starting hands – namely the the odds of each pair of hole cards winning in a two hand matchup that always goes to the river. While it’s not important to memorize these odds exactly (and I’m not even going to bother calculating them exactly here – that’s what poker stove is for), it is important to know them in an approximate sense because a lot of correct preflop strategy in holdem is a direct result of this concept.

It should be noted that hot and cold comparisons are only a useful measure of relative hand strength when you expect that the hands will both always go to the river. This situation arises most often when someone is all-in in NL holdem, but can happen in other circumstances too. Here are the basic matchups and the relevant odds:

Pair v. Pair

When both hands are pairs, the higher pair has a huge advantage – roughly 4:1 depending on the exact pairs involved. This is because the lower pair has to hit one of 2 outs, or several cards to a 4-on-board straight or flush to win. That’s drawing pretty slim.

Pair v. Unpaired

When a paired hand goes against unpaired cards, it depends where the pair falls relative to the unpaired cards. If it’s higher than both, then the pair is a prohibative favorite since the unpaired hand has no single card outs to win. Depending on the exact ranks of cards involved it’s often about 7:1. If the pair is between the unpaired cards (ie. KK vs. AQ) then it’s usually about 2:1 in favor of the pair wining. If the pair is below the two unpaired cards, the odds are almost exactly even, which is often called a race in tournament parlance. If the pair is of the same rank as one of the unpaired cards, the pair is a big favorite – about 10:1 if it pairs the top card and about 2:1 if it pairs the bottom card.

Unpaired v. Unpaired

When two unpaired hands are run, and they share no ranks, the odds are surprisingly even. The exact odds depend on how the cards interleave and the ranks involved, but the hand with the highest card (which usually wins if neither hand improves) is usually between a 5:4 and 4:3 favorite. Something more interesting happens when two unpaired hands contain cards of the same rank. The hand with the higher rank for the other card is a big favorite. How big depends on the exact ranks involved, but it’s usually in the ballpark of 2:1.

Domination

There’s a common theme running through all this: a hand that’s behind and has less than 6 outs to improve is a big dog. Otherwise any two hands are pretty even. This situation where a hand is behind and has insufficient outs to improve is called “domination” or the weaker hand is said to be dominated.

Minor Stuff

It’s worth noting that it doesn’t make much different to these hot & cold runs whether a hand is suited or connected. Those things change the results by few percent, but that’s it. When running two hands hot and cold, the likelihood of making a wining pair is the primary deciding factor in relative hand strength.