Misadventures with sets

Set-mining describes a play in no-limit hold’em in which a player smooth-calls a pre-flop raise with a small pair, hoping to catch a set and thereby stack the original raiser. There is an oft-repeated rule among no-limit hold’em players regarding the proper odds that one needs in order to set-mine. The rule is that the raiser should have a stack-to-call ratio of at least 10/1. So, if you were playing a $1/$2 game and someone raised to $8, and you wanted to call with a pair of fours in the small blind, the raiser would need to have $70 remaining. This would give you $70 to $7 or 10/1. In this article, I’m going to explain why this rule is a bad one, and I will also suggest a replacement rule.

THE 10/1 RULE

To begin, let’s figure out where this rule came from. Your odds of catching a set on the flop are roughly 7.5/1, so why isn’t this the rule? Well, as you might have guessed, you will not always stack an opponent when you catch a set. Sometimes your opponent will have A-K or similar and miss the flop entirely. Sometimes your opponent will have Q-Q and simply fold to pressure when an Ace hits the flop. And sometimes your opponent will also catch a set and you will be the one getting stacked. To account for these other situations, a higher ratio is needed.

In their book Pot-Limit and No-Limit Poker, Stewart Reuben and Bob Ciaffone advocate calling raises only if the initial bet represents 10% or less of the effective stack sizes; that is, a 10/1 ratio. Now, Reuben and Ciaffone are not advocating this for set-mining purposes alone, but for any hand you might be inclined to call a bet with, and they also advocate playing your positional advantage. The true set-miner plays ‘fit or quit’ on the flop. Either you hit your set and try to stack your opponent or you miss and fold. Building on Reuben and Ciaffone’s advice, online forums have popularised a 10/1 rule for set-mining.

WHAT’S WRONG WITH THIS RULE?

While the 10/1 rule correctly rejects simply playing your odds of flopping a set, it fails to allow for enough of the times that you do not win your opponent’s stack. In other words, the 10/1 ratio is not high enough for profitable set-mining.

Let’s consider an example of this failure. Say you are in a $0.50/$1 game and your opponent raises to $4 from middle position. The action folds to you in the small blind with pocket threes. The raiser has been playing sparingly and has seldom raised. You estimate her raising range to be Q-Q+ and A-K. She has $35 remaining, so you follow the rule and call. The big blind folds.

Now let’s consider what happens when your opponent has Aces. You will catch a set 12.23% of the times you call against this opponent (this is slightly higher than what you will find in most odds charts, but here we are stipulating that your opponent has Aces, so we actually know more of the cards, which increases your chances of flopping trips). I will make a further simplifying assumption that all the money goes in on the flop when you hit a set. This is the best possible scenario, as you will always get paid off when you hit.

So, 87.77% of the time you miss your set and lose $3.50 each time. The remaining 12.23% of the time you hit your set. Ignoring flushes and straights, you will run into a set over set or be redrawn on the turn or river 2.01% of the time (or 16.47% of the times when you hit your set). Assuming a $3 max rake, your winnings are only $23.31 for that 12.23% of the time.

Let’s make things a bit more concrete. Say we run this scenario 10,000 times:

8,777 TIMES YOU LOSE $3.50 = -$30,719.50
201 TIMES YOU LOSE TO A BETTER HAND = -$7,839
1,022 TIMES YOU WIN HER STACK = +$37,814
TOTAL: A LOSS OF $744.50 OVER THE 10,000 CALLS

What all this means is that you are losing money on this call over the long run – about seven cents for each call. It is therefore a poor call, but not by much. What stack size would you need to make this profitable against Aces? Just under $40 pre-flop, so just under $36 left when the action gets to you. That’s a stack-to- call ratio slightly over 10/1, but as you might imagine you will lose money with that ratio when the rest of your opponent’s range is included.

In order to determine a proper ratio, we need to see what happens against the other hands in your tight opponent’s range. For Q-Q and K-K let’s make the simplifying assumption that your opponent continuation-bets every flop for the full pot amount, but mucks once you raise if there is an overcard. So, versus K-K, if there is an Ace on the flop, your opponent will bet the pot and then fold when you raise. Once again, you will miss your set 87.77% of the time and lose $3.50. Of the times you do hit, an Ace will flop 24.14% of them, and you will win only $12 (assuming a $1 rake). Against Q-Q an Ace or King will flop along with your set 31.45% of the time, and again you will win only $12. The same percentages as for A-A redrawing on you apply to both K-K and Q-Q. This means that holding K-K, this particular opponent must have a $49.68 starting stack, and holding Q-Q a $54.51 starting stack. This gives us stack-to-call ratios of 13.2/1 and 14.6/1 respectively in order to break even on our calls.

As for A-K, this hand will fail to catch a pair on 75.86% of the flops when you hit your set. Thus you will win only $12 in those cases, as your opponent will fold in the face of a raise. The most profitable situation, then, is the 22.76% of the time she hits only one pair. This is followed by the roughly 1.4% of the time she hits two pair or trips. You will get redrawn in those situations a non-negligible amount of the time (17-23%). Running the numbers again for A-K, we arrive at a required starting stack of $67.86. This means that the stack-to-call ratio must be 18.4/1 in order to break even on our calls.

KEY POINT

The accepted wisdom when set-mining is that your opponent should have a stack of at least ten times the amount required to call the bet before the move becomes profitable, but our examples show that this 10/1 ratio is too low

THE GOLDEN RATIO

So what can we do with all these ratios? Each of the pairs has six combinations and the A-K hand has 16 combinations. Properly weighting these possibilities produces a break-even stack size of $57.35 or a stack-to-call ratio of 15.4/1.

Of course, we don’t want to just break even. We want to make money with our calls, so against this particular opponent, you might require a $60 starting stack (a stack-to-call ratio of just over 17/1). Generalising this to other blind amounts, you’d want to be facing a stack of at least 60 big blinds.

You should also keep in mind your position when applying the new rule. In the big blind, you will need a slightly higher ratio, as only the small blind will offset the rake. Similarly, you can call with a slightly lower ratio when outside the blinds, as both blinds will now offset the rake. If you are playing without rake, such as in a tournament, you can get by with a slightly lower ratio.

Also keep in mind that my calculations are for a player with a very tight pre-flop raising range, capable of folding to pressure on bad flops. Players with a wider pre-flop raising range are less easy to read and will tend not to stack off easily. Set-mining against these players will require much greater stack sizes as fewer flops will be safe and much of their range will play like the A-K hand. Things change for the better when you find an aggressive player who wants to win every pot, but these situations can get rather complicated with varying ranges and levels of aggression.

However, the main thing you can take away from all this is that profitable set- mining requires fairly decent stack sizes – considerably more than the 10/1 ratio suggests. If you are the one doing the mining, pay attention to the stack of your opponent rather than simply calling because you have a pocket pair and can flop a monster.

If, on the other hand, you are the one trying to avoid having your big pair cracked, one way of combating this would be to play half-stacked. You would not avoid running into sets, but you would ruin the profitability of your set- mining opponents who mistakenly call your pre-flop raises operating on the 10/1 ratio. The best option, however, is to learn some restraint and not stack off easily simply because you have a big pair. This is easier said than done, but it is nonetheless a requirement for improving as a no-limit hold’em player.

KEY POINT

Instead of using the 10/1 ratio, look for effective stacks of 60 big blinds or more if you’re thinking about set-mining. However, it’s too simplistic to rely on rules of thumb, and you need to take into account position and your opponent’s range when gauging a speculative call