## More ArticlesMatthew Hilger

This column contains excerpts from the upcoming book The Math of Hold’em, by Collin Moshman and Douglas Zare (available from Amazon). This is Part I of a three-part series that looks at set-mining.

Sets are disguised monster hands that can win large pots against strong hands or against multiple opponents. Set-mining means playing a pocket pair primarily for the chance to flop a set and win a big pot. Ideally, you make a small investment preflop, and then play a big pot as a huge favorite after you connect with the flop.

Set-mining is a classic example of implied odds. You may call a raise preflop as a big underdog against a higher pair, even though you might be getting only 2-1 or worse current odds. The odds against flopping a set are roughly 7.5-1; that is, you will flop a set roughly one time in 8.5. You will rarely get odds that good on a preflop call, but your hope is that you will win not only the pot, but your opponent’s stack when you hit. Set-mining will often not be a large component of your play, but studying it will help you to understand implied odds in more general situations.

## What Can Go Wrong?

Sets are very profitable. However, winning players are often surprised to find that they lose money with small pocket pairs, even though they associate pairs with sets. How effectively you can set-mine depends on your opponent’s range. In most poker situations, you should prefer being up against a weaker range, but this is often reversed when you rely on implied odds. If you are playing mainly for the chance of flopping a set, you want your opponent to have a tighter range, so that he is more likely to pay you off in a big pot when you do hit your set. Let’s look at what can go wrong.

## Not Getting to See a Flop

When you call a raise preflop while not closing the action, you are not paying to see a flop. You are paying for the chance that the remaining players let you see the flop. That possibility significantly reduces the probability of flopping a set, increasing the implied odds that you need. The probability that someone will raise behind you depends on the number of players left to act and with what ranges they will reraise. In certain situations, it is quite possible that calling will enable you to see a flop only 65 percent of the time or less.

## Behind With a Flopped Set

Set-over-set situations are rare in hold’em, but they are not negligible relative to the chance that you’ll flop a set. If you have pocket fives against pocket aces, you will flop a 5 and be outflopped by a set of aces about 12 percent of the time. And against non-pair hands, your opponent could flop a straight or a flush.

## Not Getting Paid Off

One possible problem is that your opponent doesn’t like the flop and gives up if you show any strength. Another possible problem is that your opponent is willing to stack off, but the effective stack depth is low. To get paid off, both your stack and your opponent’s stack must be large in relation to the size of your preflop call.

A player with A-A will like almost all flops enough to put a lot more money in. A player who has revealed that he has A-A is likely to offer good implied odds.

A player with K-K will like most fl ops without an ace, but usually won’t stack off if there is an ace on the flop. Although at least one ace comes 23.4 percent of the time when you have 2-2 against K-K, an ace is less likely when you flop a set of deuces, only 16.6 percent. More than 80 percent of the time, a player with K-K will still have an overpair when you flop a set. A player with queens or jacks is less likely to have an overpair, and when J-J is an overpair, there tends to be more straights possible.

How about A-K offsuit? A set is a crushing favorite over top pair with top kicker, since top pair with top kicker needs to catch two perfect cards to beat you. However, someone with A-K is not as good a target for set-mining.

On average, when you have 3-3 against A-K, at least one ace or king is in the flop 33.6 percent of the time — 5,816 flops out of 17,296. However, when there is at least one trey in the fl op, it’s harder for A-K to hit the flop, as there is at least one ace or king on 516 fl ops out of 2,116, or 24.4 percent of the time. When you fl op a set against A-K, about three-quarters of the time, it will be against A-K unimproved.

A hand like Q-J offsuit will flop a pair just as often as A-K offsuit. However, Q-J will never flop top pair with top kicker, and many of the pairs will be second pair.

Connectors and low to medium pairs are poison for set miners. They rarely pay off sets, and they more commonly beat sets in big pots. If an opponent is raising a wide range, including many speculative hands, you need to count on bad play to set-mine profitably.

## Being Outdrawn

An overpair against a set on the flop has two outs twice. That’s worth about 9 percent, and an overpair usually has at least that much equity against a set. However, overpairs often have more ways to win from flushes, straights, or counterfeiting the set.

On a board of 7 6 3, the 3 3 can be outdrawn by the A A in more ways than just catching an ace. Running spades would give the A A a flush. After a turn 6 and river 6, the low full house would be counterfeited, and the 3 3 would lose to sixes full of aces. A turn 5 and river 4 would produce a split pot, since both players would play the straight on the board. On this flop, the A A has 13.6 percent equity against bottom set. On a flop of Q 10 3, the A A has 35.6 percent equity. On average, you get outdrawn one way or another about 12 percent of the time that you flop a set against an overpair.

It’s harder to get outdrawn by top pair with top kicker, but when you get action from a flush draw or open-end straight draw, you lose about 25 percent of the time. Backdoor draws can be worth a few percent.

There are many reasons why you might be reluctant to set-mine. However, set-mining can be profitable under the right conditions. In my next column, I’ll discuss the ideal and favorable conditions that can make set-mining profitable.

This article first appeared in Card Player magazine.

Matthew is the owner of Dimat Enterprises, “Publishing Today’s Best Poker Books”. The Math of Hold’em by Collin Moshman and Douglas Zare is available now at pokerbooks.InternetTexasHoldem.com.

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