Note: Not at the old Poker1 site. A version of this entry was originally published (1987) in Poker Player Newspaper.
Rediscovered, updated, and added to Poker1 in 2015.
Good afternoon. Do hold ’em beginners fail to appreciate the difference between big-pair starting hands and small-pair starting hands? Yes. They fail to appreciate. Do hold ’em beginners fall in love with medium-pair starting hands? You bet. They fall in love.
Is it a fact, Mad Genius, that hold ’em beginners unwisely favor insignificant pairs over high non-paired cards as starting hands? Sure. They unwisely favor them. And will hold ’em beginners be battered brutally forever and ever because of these unfortunate misconceptions? Yep. They will be battered.
You and I know that a pair of aces is awesome and a pair of deuces is disastrous. Well, that isn’t always true, is it? In rare situations a pair of deuces isn’t quite so bad. If you’re playing against just one opponent, then a pair of deuces can almost hold its own against ace-king. In fact, that pair of deuces will win more than its fair share of pots, if dealt to the showdown. It will often lose money, anyway, during the betting process. But, at least, it’s competitive heads-up. Unfortunately, in the real world, against a table full of players, the ace-king triumphs. And it isn’t close. And we know it. And universal justice includes no mercy for those who do not know it.
Your chances
Still, it’s interesting to know your chances of liking a flop when you invest money on various pairs. It’s hard to define a general set of rules for whether or not you like the flop. Suppose you have A-A and the flop is A-K-K. Looks like a great happenstance, but are you perfectly safe? Obviously, a pair kings held by any opponent will make you miserable. How likely is it that an opponent holds both remaining kings. Depends. If you bet and the opponent folds, there’s almost no chance whatsoever that kings was the opposing hand. If the other player didn’t raise before the flop, kings would usually be less likely (although with some tricky opponents, exactly the opposite is true). We can make powerful and profitable estimates about what opponents hold, but we can seldom know for sure.
But this we can calculate, this we can know for sure: If we don’t take previous events into consideration and include only our pair of aces and the flop in our appraisal, then the odds are 11-to-1 against any opponent holding one king and something else. And the odds are 1080-to-1 against both kings being held.
That’s interesting, but not especially useful. Maybe the following will help you know how often to expect an unfavorable flop. It tells you how frequently the flop will not provide you with at least one more of your rank (thus making three-of-a-kind or rarely four-of-a-kind) AND, at the same time, the flop will contain at least one card higher than your pair. In other words, the chart assumes you want to either make three-of-a-kind (or four-of-a-kind) or flop all cards smaller than your pair.
Misery index
Based on that simplistic and incomplete assumption, this is the “Misery Index” taken from my Professional Hold ’em Report…
Percentage of misery for hold ’em starting pairs after seeing the flop
|
2-2 ………. 88.24% |
9-9 …………. 71.53% |
|
3-3 ………. 88.22% |
10-10 ………. 62.94% |
|
4-4 ………. 87.96% |
J-J ………….. 51.82% |
|
5-5 ………. 87.12% |
Q-Q ………… 37.84% |
|
6-6 ………. 85.39% |
K-K ………… 20.67% |
|
7-7 ………. 82.43% |
A-A …………. 0.00% |
|
8-8 ………. 77.92% |
While that chart is deliberately elementary and ignores many concepts critical to professional hold ’em, it nonetheless illustrates a profound truth. There isn’t nearly as much difference between low ranks as there is between high ranks.
Look at it this way. A pair of kings is much better than a pair of queens (and they’re only one rank away from each other), but there’s a much less dramatic difference (but still an important one — as we’ll explore) between a pair of sevens and a pair of deuces (five ranks apart). Also, notice that, based on the simple premise, you’re probably going to hate the flop unless you hold at least a pair of queens. Jacks often avoid flop misery, but not quite half of the time (48.18% avoidance vs. 51.82% misery).
More misery
Sadly, there’s even more misery associated with hold ’em small pairs.
Let’s think about how a pair of sixes is better than a pair of deuces. The difference isn’t as trivial as believed by most players — even experienced ones.
Here are just a few of the issues:
If a pair of deuces collides with a pair of sixes and no player improves, obviously sixes win.
If a pair of deuces collides with a pair of sixes and both hands make three-of-a-kind, obviously sixes win. And that can be a wagering disaster.
So far, who didn’t know that, right? But, wait. If deuces make two pair with a board like A-A-9-5-5, a pair of deuces is worthless and plays the board, while a pair of sixes still has two pair superior to the board and might win. And that kind of thing happens more often than you might think.
For all these reasons — and more — you should be very reluctant to play the smallest pairs in most hold ’em situations. Often, players group small pairs like sevens down to deuces in a single category. That’s a costly mistake, even though there’s less difference in profit or loss between adjacent pair ranks at the low end than at the high end. As ranks increase, there’s an even bigger difference between each rung up the ladder.
You will fare much better at hold ’em when you become certain of these concepts. They’re important and often-overlooked during the confusion of poker combat. — MC
“A version” and “updated”!!