Showdown Win Percentages Against Legitimate Callers

by Daniel Kimberg | Published: Feb 27, 2004

Against seven random hold'em hands, pocket aces will turn out to be the best hand at showdown about 39 percent of the time. Pocket kings win 33 percent, and queens 29 percent, while at the other end of the spectrum, 7-2 offsuit weighs in at 7 percent. Although these showdown win percentages don't tell you everything you need to know about the playability of these hands, they do convey a lot of information about your hand's value.

Unfortunately, we don't often get to play at tables full of opponents who play random cards. So, on those occasions when we do see many callers, it's safe to assume some of those players have decent hands, and the usual showdown percentages may be misleading. It's worth doing a bit of work to find out how showdown win percentages should be adjusted when you know a number of your opponents' hands are legitimately playable.

One way of attacking this problem is to examine the showdown values of hands against non-random opponents. As a first approximation, I've chosen a pretty extreme but still plausible example. What happens when you're on the button and five of six solid players ahead of you call with playable hands? Of course, this doesn't happen too often – the chances of five or more players all having legitimately playable hands is generally small, so when you see that many callers, it's generally fair to assume someone's feeling lucky. But situations like this do come up occasionally, and when they do, it's important to have some sense of how the value of your own hand changes.

In order to answer this question, I wrote a short computer program to run a large number of simulated hold'em hands. For each deal, the program examined the hands of the six players to act before the button. A given deal was included only if exactly five of the hands were playable according to Lou Krieger's starting charts (thanks again, Lou!), liberally assuming two players in each of early, middle, and late position. A deal was also excluded if any of these players held A-A, K-K, Q-Q, or A-K. This was an expedient to reflect the fact that when five players all flat-call, these hands tend not to be in the mix. The blinds, however, were allowed to come along with their random hands, for a total of seven opponents. A total of 200,000 such simulated hands were tallied. For each of these deals, the exact winning percentage of the button hand (our hero) was calculated by dealing out all possible boards, given the remaining deck. From these results, average win percentages for each of the 169 distinct starting hands in hold'em were calculated. These results are not exact, since 200,000 hands is still a relatively small number. But the true winning percentages should be close enough to what's listed below to make no difference.

First, let's look at the hands that are playable strictly on the basis of win percentage. Here are the hands that win their fair share or better – 12.5 percent, or odds of 7-1 against winning. For purposes of comparison, I've listed them alongside their showdown win percentages against random hands.

Strikingly, this is exactly the list of the 13 pocket pairs. Baby pocket pairs are the biggest winners, with threes through sixes exceeding even A-A and K-K. If you compare the win percentages to their performance against random hands, you get a better sense of what's happening. The baby pocket pairs are gaining only a little bit of equity, while the medium and large pocket pairs lose a lot. In effect, we see that few hands do well against five legitimate callers plus the blinds, and the result is that there's little range between the best and the worst of the profitable hands. The baby pocket pairs approach 5-1 odds against winning, while J-J rounds out the list at just north of 7-1.

Another striking pattern emerges if you look at the next 15 hands, after the pocket pairs: 6-5 suited, 5-4 suited, 7-6 suited, 7-5 suited, 6-4 suited, 5-3 suited, 8-7 suited, 8-6 suited, A-5 suited, 6-4 suited, 4-3 suited, 9-8 suited, A-4 suited, 10-9 suited, and 7-4 suited. All of these hands are suited, all but two are connected or one-gappers, and all mesh well with small-card boards. They range in win percentages from 9.9 percent down to 7.9 percent, so none of them are playable strictly on the basis of win percentages, and even the best is a sharp drop-off from the pocket pairs. But if you're going to play a marginal hand against opponents you believe you can outplay, these might be better choices than some of the premium starting hands.

And what about those premium hands? What happens to some of the unpaired big-card hands you may be used to thinking of as playable or even worth a raise on the button?

These hands have gone way down in showdown value, with some of the strongest starting hands in hold'em the biggest casualties. Most strikingly, these hands now win far less than their fair share in an eight-way showdown, the best being A-10 suited with odds against winning of almost 13-1. While it's no secret that unpaired big cards have liabilities in multiway pots, the steep drop-off in win rates is striking. The unsuited big cards all win less than half their fair share, with A-K actually the worst of them. Although folding A-K on the button is not something many of us do routinely, these results suggest that in some situations, it's practically mandatory.

Of course, many caveats apply to the use of simulated numbers in making actual game decisions. And these simulations reflect only the fairly unusual case in which you believe all of the callers have legitimate hands. Still, I think these results are striking enough to suggest that some fairly dramatic adjustments are in order when multiple solid players call ahead of you. It would be worth knowing how these numbers change as a function of the number of solid calls, but that's a simulation for another day.

In case you'd like to know more about how I calculated these numbers, I've put my code, along with the full results, on my web site, at www.seriouspoker.com. As in the past, it's based on the free hand evaluation code available at pokersource.sourceforge.net. It probably won't be that helpful to you unless you can do some programming, but it does work. I got the percentages against random hands from Percentage Hold'em, by Justin Case. The software written by Steve Jacobs to generate the tables for that book is now available free from ConJelCo, at www.conjelco.com. You can also generate similar tables using my code, although it can take a while.