Intro to Combos

Combinations (combos) are a way to judge the relative frequency of various hands.

There are 52 * 51 = 2652 ways to be dealt two cards. Half of those sequences are duplicates (for example 8 of hearts 6 of clubs is the same hand as 6 of clubs8 of hearts). Dividing by two gives 2652 / 2 = 1326 possible starting hands.

The likelihood of being dealt any starting hand is the number of combos of that hand divided by the total number of combos. For example, there are six combos of pocket aces:

A of spadesA of hearts

A of spadesA of clubs

A of spadesA of diamonds

A of heartsA of clubs

A of heartsA of diamonds

A of clubsA of diamonds

On average, you’ll be dealt aces 6 / 1326 = 1/221 hands. Each other pocket pair is likewise 1/221. There’s a 1/17 chance of being dealt any pocket pair in a give hand. There are 16 combos of each non-paired hand, 4 of which are suited.

The most basic insight that combos offer is that it’s hard to have a good hand, and it’s really hard to have a really good hand. Thus in situations where your opponent is representing a very specific, very strong hand, they only need to be bluffing with a small percentage of their other hands to make the overall chance that they’re bluffing rather high. There are simply way more ways to have nothing than to have a very strong hand.

At the same time it’s important to remember that combo reasoning only applies to the hands that are consistent with your opponent’s actions. Some players never bluff, ever, so when they bet a certain way they’ll invariably show you exactly the hand they’re representing, no matter how improbable it is.

Thinking about combos can lead to more specific strategies as well. For example, suppose we’re playing an opponent whose range for 4-betting and calling a 5-bet all-in preflop is AA, KK, and AK. There are more combos of AK (16) than AA and KK put together (12 total). Therefore, hands that have good equity against AK are good candidates for 5-bet bluffing. Pocket pairs have about 50% equity against two over cards, so if this opponent is 4-bet bluffing reasonably often (meaning he’ll be folding to our 5-bet all-in), 3-betting small pocket pairs with the intention of going all-in over a 3-bet could be a very profitable strategy.

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One thought on “Intro to Combos

  1. […] time running diamonds will give me the nut flush. Having a seven in my hand reduces his possible combos of 77 from three to one: he’d need to have both of the remaining 7s in the deck, extremely […]

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