Poker Math Lesson 301: Starting Hand Odds

In this part of my poker math series we'll discuss various starting hands and their odds of beating other starting hands in a show down. This information can be put into a form that is surprisingly easy to remember. I think it is essential for every player to know these numbers. They will come up most in tournament play, especially in the late stages of an event when contested pots tend to go to show down and when most of the betting is done before the flop. Understanding these numbers is crucial to heads up play as well.

Starting Hands

You're going to learn how different types of hands play against each other in an all-in confrontation. Expect some surprises. Some of the hands that many players value a great deal, such as AK just don't win as consistently as you might think against some random holdings, particularly small pairs. A plethora of factors need to be considered when gauging the overall strength of a starting hand. This article will tackle one. Many of the hands that are playable when the blinds are small diminish in value as the blinds increase. For instance, most players value JTs over K3o when playing No Limit Hold 'em, however, king three off suit is actually a favorite against jack ten suited in an all-in confrontation. The appeal of "speculative" hands such as KQs and suited connectors like JTs comes from the hands' "post- flop" playability. Hands like AXs and small pocket pairs are valued in cash games and early in tournaments because of their "implied value". The hands are easy to play after the flop and have the potential to flop monsters. When you strip away the post- flop play, such as when a tournament gets to the final stages and the blinds and antes inflate, few players really understand the transition that occurs in hand rankings. Hopefully, this article will give you a bit of the insight that all the top tournament players use to finish at the top.

The information I'm about to share has a great deal of practical application, most of which we will not discuss here. After reading this article and setting a few basic ideas to memory, you will be able to determine the win percentages of any two starting hands instantly. Sound hard to believe? It's a lot simpler than it sounds. There are tons and tons of two card combinations and setting to memory the exact percentages of every match up would be nearly impossible. All of these match ups can be grouped into 8 simple categories and you can know within a few percentage points exactly what the numbers are for every conceivable combination just by remembering these eight match ups.

Starting Hand Match Ups

The match ups are:

  • 1) Pair vs. pair
  • 2) Pair vs. two under cards
  • 3) Pair vs. two over cards
  • 4) Pair vs. one over and one under card
  • 5) Two over cards vs. two under cards
  • 6) One over card and one under card vs. two middle cards
  • 7) One over card one middle card vs. two split cards
  • 8) Dominated hands

Pair vs. Pair

In a pair vs. pair confrontation, the larger pair is a huge favorite to win the showdown. The farther apart the pairs are from one another and the closer to mid value the small pair is, the better its chances are of winning. As a rule of thumb, the larger pair will win about 80% of the time. That makes it a 4 to 1 favorite, and it doesn't get much better than that.

Pair vs. Two Under Cards

When one player has a pair and is up against two under cards, for instance; AA vs. 76, the under cards are in just a little worse shape than the under pair. The pair can be as great as 88% to win the hand and can't be much less than 76%. As a rule of thumb, the two lower cards are about a 4.5 to 1 dog.

Pair vs. Two Over Cards

The classic "coin flip" situation occurs when all of the money goes in before the flop with one player holding a pair and the other, two over cards. It's actually not quite a coin toss, usually the pair has a small edge, it's about 53% to win depending on how close it is in value to the two "live cards" (a card is "live" when hitting it on the board will give you a winning hand). It's actually possible for two higher cards to have a very small edge if they are suited connectors and separated by a large gap from the pair. JTs is a very tiny favorite against 22. All in all, just consider these confrontations to be about even money, 1 to 1.

Pair vs. One Over and One Under Card

Often in the late stages of a tournament, players are willing to push it all in with any hand containing an ace, particularly when they are short stacked. When the match up is one high card and one low card against a medium pair (A2 vs. KK, K5 vs. 66, Q9vs. JJ, etc.) the medium pair will win about 70% of the time. The pair is a bit better than 2 to 1 to win.

Two Over Cards vs. Two Under Cards

In the case of two high cards against two lower cards the exact percentages will vary, but the two high cards will generally win about 60% of the time. Even a match up like AcKh vs. 7c2h will leave the seven deuce about a 35% chance to win the pot. In general the two high cards are about a 3 to 2 favorite. It might come as a surprise that trash hands like 87 are only a 3 to 2 dog to the coveted "Big Slick", but most of the time whichever player pairs one of there whole cards will win the showdown.

One Over Card and One Under Card vs. Two Middle Cards

One high card and one low card against two middle cards is another example where the player who pairs the board will usually win the pot. A match up like A3 vs. T9s is essentially in a coin flip with a small edge going to the Ace high hand. The hand with the higher card will usually be between 52-60% to win the race. Most of the edge that the high card hand has comes from those times that neither player pairs the board. Most of the confrontations will be 3 to 2 in favor of the high card hand.

One Over Card One Middle Card vs. Two Split Cards

The next situation requires some explanation. One over card and one under card with two spit cards refer to races such as T4 vs. 82. One hand has a high and a low card and that hands' low card falls in between the other hands' two cards. (A5 vs. K2, T8 vs. 97.) These percentages can vary a bit from situation to situation but, in general, the hand that contains the high card is about a 3 to 2 favorite. The situation is only slightly different than one high and one low card vs. two middle cards.

Dominated Hands

The last situation is referred to as "domination". When two hands share one card the hand that contains the lower second card is said to be "dominated". Situations like this arise often with two hands that contain an ace, AK vs. AQ, for instance. The hand in the dominating position is nearly a 3 to 1 favorite in most instances; it will win in a show down almost 75% of the time.

Knowing starting hand odds is very useful in no limit hold 'em poker, particularly in the final stages of a tournament. When the blinds reach a certain point most pots that are contested go to showdown. During the late stages of a tournament, when most of the betting is done before the flop it is crucial to understand how your hand shows down against other hands that may be out against it. Good "luck"!

Poker Math Series by Dead Money

Poker Math

Poker Math 101: Pot Odds and Counting Outs
Poker Math 201: Drawing Hands vs. Made Hands
Poker Math 301: Starting Hand Odds
Poker Math 401: Application of Knowledge
Poker Math 501: End Game Mathematics

♣ Back to the series of articles on poker hand analysis or poker strategy.