How Many Preflop Callers Should You Expect?

In my last column, I wrote about some simple simulations I ran to answer some questions about the distribution of hold'em hands when it's folded to you on the button. I couldn't resist playing with the simulation code a bit more, so I decided to try to get some idea of just what preflop play would look like if everyone played "by the book." In this case, the book is Lou Krieger's Hold'em Excellence (and More Hold'em Excellence), using the starting-hand requirements from inside the back cover.

This time, I had the computer deal out a table full of random hands and check to see how many of those hands would be considered playable in their position, according to Krieger's tables. To get a good estimate of the average number of callers, the computer dealt out 10,000 random deals. The hitch is that, in addition to using the tables correctly (what I'm calling the "standard" setup), I also ran separate simulations with different numbers of players in different positions. For example, one of the simulations had six late-position players and one each in early and middle position. Obviously, there can't actually be six players in late position. But there can be a table where, on average, six players are playing that way.

Here are the results for various full-table (eighthanded) configurations. Note that I've omitted the blinds, so we're considering only the number of players to call the big blind voluntarily.

The "standard" setup is 3-3-2, where everyone plays roughly according to his actual position (at least on average). If all the early-position players acted as though they were in late position, that would be 0-3-5. It's worth keeping in mind that these are averages – if only one player at the table ever follows the early-position guidelines, on average there will be 0.375 early-position players, because that player will actually be in early position for only three of the eight positions.

I've included a variety of table setups, most of which are looser than standard, including three tables where all the players play the same, which you can think of as tight, medium, and loose games in which none of the players are sensitive to position. For each table setup, you can see the expected (average) number of callers as well as the standard deviation.

The most obvious pattern, if not the most surprising, is that as players drift toward later positions, the expected number of players seeing the flop goes up, as does the variability in the number of callers (some caution should be used in interpreting the standard deviations, because the distribution of callers is non-normal). The looser the table, the greater your uncertainty of the number of players you expect to see the flop.

What I find most striking about this table is the fact that even the most extreme setup, with eight players all acting as though they were in late position, seems well within the range of what I might expect to see at my local cardroom. If I had to pick out the distribution of callers that seems most typical of the games I've played in (mostly midlimit, generally loose games), it would be somewhere between 2-2-4 and 1-1-6; in other words, a table at which the pattern of preflop calling suggests something between moderate and gross insensitivity to position.

Of course, failing to consider position is only one reason a player could see the flop more often than Krieger recommends, but it's a reasonable way of describing loose play. Certainly, some players also play hands that are not considered playable in any position, and those hands do contribute to the number of callers at loose tables. This is obvious from the simulations, as well. A table that played like 0-0-8, with five players (including the blinds) typically seeing the flop, would certainly seem like an action table. But it wouldn't be the most extreme action table anyone's ever seen, or even close. Truly loose tables invariably have at least a few players playing hands that are not on anyone's start charts.

These simulations are only a rough approximation of what we would expect from real players. The most obvious source of error is that they ignore action. For example, they assume the button will play K-10 for any number of bets, whether there are eight callers or none. Lou Krieger certainly doesn't advocate that you play this way, but it was the best I could manage in writing this simple simulation (perhaps when I have more time, I'll endow my simulated players with more realistic preflop strategies). On the whole, the simulations probably overestimate the number of by-the-book callers you should expect. The error is greater at tables with more preflop raising, and at tables where players will adjust to a raise. But I think they are a decent first step toward a sense of what you should expect from a table full of players who are playing more or less by the book, and indirectly toward estimating how many preflop errors players are making, on average, at your table.

The code for these simulations is freely available (although it will take some technical know-how to get it working), and can be found at my web site, www.seriouspoker.com. The libraries upon which the code is built can be found at http://sourceforge.net/projects/pokersource. Daniel Kimberg is the author of Serious Poker, and he maintains a website for serious poker players at www.seriouspoker.com.