Understanding The Advantage Of Flopping The Best Hand

by Bob Wilson & Mike Gilbert

(Bob Wilson founded Wilson Software in 1989. He joined Mensa in 1966 and has been playing poker and working with computers for more than 30 years. Mike Gilbert has many years of professional poker experience and works as a prop player in Los Angeles.)

How often should you expect to win when you flop the best hand in hold’em?
This is really a 2-part question:

This article examines situations when the flop has no pair. It contains previously unpublished information on the significant advantage enjoyed whenever you flop the best hand.

How to read the table: Each row shows the data for a specific number of players that see the flop. The columns show the different type of hands. When 3 players see the flop, no pair is the best hand 16% of the time, 1 pair is the best 69% of the time, etc. Therefore, a pair or less is the best hand 85% of the time (16% + 69%). Note: whenever there was a tie for best hand (which does not occur with great frequency), the data was excluded.

Table 2 clearly shows the powerful advantage of flopping the best hand. When 3 players see the flop, if 1 pair is the best hand, it wins 68% of the time; trips, when the best hand, hold up 90% of the time. Note: win rates do not include split pot wins.

The information shared here will help you to reasonably forecast your chances of winning when you have flopped the best hand. We’ll review two examples that show how to do this. (The values shown throughout this article are averages. Often, the action before the flop may reveal the strength of an opponent’s hand and adjustments should be made.)

Example 1: Suppose that you flop trips versus one opponent. Table 1 tells us that when 2 players see the flop, trips or less will be the best hand 98% of the time. Table 2 tells us that trips as best hand will win 93% of the time. If we combine these, we can see that you’re favored to win 91% of the time (.98 times .93 = .91).

Example 2: Suppose that you flop 2-pair versus three opponents. Table 1 tells us that when 4 players see the flop, 2-pair or less will be the best hand 90% of the time. Table 2 tells us that 2-pair as best hand will win 76% of the time. If we combine these, we can see that you’re favored to win 68% of the time (.90 times .76 = .68).


These 2 examples are very straightforward. When we want to forecast win rates for a pair as the best hand it gets a bit more complex. To do this 3 additional factors must be considered:

First, we’ll look at the effect of the flush potential:

A 3-flush on the flop reduces the chances that a pair is the best hand, particularly as more players see the flop. With 2 players seeing the flop, the pair’s chances fall from 90% to 81%, a 10% drop in value. With 4 players, the pair’s chances fall from 83% to 63%, nearly a 25% drop in value.

A 2-flush and a 3-flush both reduce the win rate; again more so as the number of players that see the flop goes up. The effect is small when 2 players see the flop. We see a drop of 2% for a 2-flush and about an 8% drop for a 3-flush. When 4 players see the flop we see a drop of 9% for a 2-flush and about an 11% drop for a 3-flush. (The drop percentages are relative.)

The straight potential of the board has an effect similar to that of the flush potential, although it is less dramatic. The specifics are not included in this article.

The most significant factor is the relative strength of the best pair. On a no-pair board, there can be 7 different types of pairs. Depending on the board, one or more of the 7 may not occur. The 7 are best shown by example:

Board: Q 9 4

For pairs, the data in Tables 1 and 2 needs to be replaced with data specific to the type of pair held. What you really need to know is “when I flop a pair, how often is it likely to be the best hand”. To determine this, we ran special tests, which counted how often each type of pair occurred, how often it was the best hand and how often it won. Again, this data is for an unpaired flop.



Here’s how the 7 different types of pairs measure up:

When 2 players see the flop, pocket overpairs score 89%, nearly equal to the 90% from Table1. The small drop off is due to the infrequent occurrence of multiple overpairs. Top pairs run into both overpairs and top pairs with better kickers. The effect of this drops the top pair score to 83%. The pairs below top pair get outflopped still more often and drop further in value.

When 4 players see the flop, we see a growing separation in the relative value of the different types of pairs. Pocket overpairs and top pairs retain a lot of strength but the lesser pair types really drop in value. The kicker value for top pairs has a greater impact as the number of opponents increase and you must factor this into the evaluation of your hand. In addition, lower rank top pairs run increased risk of overpairs and of being out drawn. The values shown in Table 6 are averages. In using the data, you should adjust upwards for higher rank pairs and downward for lower ones.

Here’s one more example showing how we to use the pair data:

Example 3: You flop top pair versus three opponents. Table 6 tells us that when 4 players see the flop, top pair will be the best hand 66% of the time. It also tells us that top pair as best hand will win 70% of the time. If we combine these, we can see that you’re favored to win 46% of the time (.66 times .70 = .46). These are averages and should be adjusted up or down based on the strength of your kicker and the rank of the top pair. In addition, if the flop is 2-suited, the net win rate needs to be reduced by about 10%. For a flopped 3-flush, it should be reduced by about 2.

This article contains a lot of information; information that is valuable when used the right way. It helps you judge the likelihood that you have flopped the best hand and the chances that you’ll emerge as the eventual winner. When you judge that you haven’t flopped the best hand, it gives you a sense of the odds you must overcome and whether you should hang in or hang it up.

Turbo Texas Hold’em for Windows was used for this analysis. The program includes two sets of charts:

Tests of 1,000,000 hands each were run to gather the data for this article. The best hand effect is so consistent that similar numbers can be obtained from tests as short as several hundred hands. Enhancements, which will be incorporated into a future version of the program, allowed the data gathering for the flush and pair analysis.