How can we memorize which Hold'em starting hands to play? Our first problem lies in ranking all 169 possible starting hands. I did this in an earlier post, and showed that the ranking depends quite a bit on how many players are in the hand. In the chart below, you can see the ranking of starting hands for a heads-up game, a 3-player game (in which all 3 showdown every hand), etc. My interpretation is that the 3Way column (for example) is appropriate for any game in which we expect 3 players to see the flop, regardless of how many people were dealt in and how many stay for the showdown.
The Avg column ranks hands using a weighted average of the value of that hand in different sized games, with 50% of the weight given to a hand's value in a 2-way flop, 25% in a 3-way flop, 12.5% in a 4-way flop, etc. I think of it as a correction to the 2Way column, where hands that weaken with more players (like 77) are pushed down the list, while hands that become stronger with multiple players (like KJs) move up.
Our challenge now is to find a formula that helps us memorize the ranking of the most commonly played hands (especially the top third). I considered more formulas than I care to admit. I'll present the best two of these below. Both are very faithful to my hand ranking. The "Simple Feinberg Formula" boasts a very simple rule, but can be difficult to use in practice. The "Easy Feinberg Formula" requires a small effort to memorize, but is extremely easy to apply.
Part 2: The Simple Feinberg Formula
In this formula, A = 14, K = 13, Q = 12, J = 11, T = 10, 9 = 9, and so on. We simply triple the high card, add the kicker, add 3 if suited, and add the number of possible straights (using both cards), as illustrated by the following examples.
KJ: 3 × 13 (high) + 11 (kicker) + 2 (straights) = 52
A7s: 3 × 14 (high) + 7 (kicker) + 3 (suited) = 52
K9s: 3 × 13 (high) + 9 (kicker) + 3 (suited) + 1 (straights) = 52
QTs: 3 × 12 (high) + 10 (kicker) + 3 (suited) + 3 (straights) = 52
These hands have the same score because they're about equally strong in my ranking. For a pocket pair, triple the value and add 34.
Let's see the results.
So, if in a certain preflop situation you felt you ought to raise 14% of the time, you could raise any hand with a score of 52 or higher. (See my earlier post for a discussion of how often to raise preflop.)
This formula exactly reproduces the top 50 hands in my ranking. (In fact, the formula makes only 4 "mistakes" in ranking the top 60 hands, which can be corrected by adding 1 point to the scores of 55, 44, JT, and T9s.) The formula is granular enough that you can adjust your play to your exact position.
Ok, so the scores are rather high, which makes it difficult to perform the necessary mental math quickly. But I claim it's easier than it looks. In most situations, a quick estimate is enough to decide whether to enter a hand. You probably already recognize premium hands like 99, AQs, and AK and trash hands (nearly anything with a high card below a jack), so you can skip the math on these.
AXs = (14 + 1) × 3 = 45
AXo = KXs = 14 × 3 = 42
KXo = QXs = 13 × 3 = 39
QXo = JXs = 12 × 3 = 36
Once you know these, the math gets much easier. Another key is to stop calculating as soon as the score passes the desired threshold (or clearly won't get there). This way you won't have to determine the number of possible straights often.
If you'd prefer to work with smaller numbers, you can reduce the card values without affecting relative card rankings. For example, you might use A=4, K=3, Q=2, J=1, T=0, etc., for the high card (but this requires using negative numbers for hands like 98s).
The Simple Feinberg Formula distributes the top 50% of starting hands into more than 20 hand groups. That sounds great, and it is if you can take advantage of this in your play. But you might not want to memorize a different strategy for each group. The solution is to bundle multiple scores into larger groups.
A simple approach is to round all scores to the nearest multiple of 3 (for example). 50, 51, and 52 would all round to 51, and would therefore all be played the same way. The good news is that this means there's no need to triple in the first place. We could simply add the kicker and number of straights, divide by 3 and round to the nearest integer, then add the high card and 1 more if suited. Now the numbers are smaller, but they're not really any easier to compute. The bad news is that there are good reasons for treating scores of 50, 51, and 52 differently.
A better solution is to group scores into more meaningful ranges. Suppose you consider 41 to be a reasonable threshold for raising heads-up, 47 for raising on the button, and 50 for raising from the cut-off. Now you've got a few hand groups: the 40-and-less group, the 41-46 group, the 47-49 group, and the 50 group. Of course, this approach would require memorizing the numbers 41, 47, and 50, along with how to play such hands. There must be an easier way...
Part 3: The Easy Feinberg Formula
If you'd prefer to work with smaller numbers, you can reduce the card values without affecting relative card rankings. For example, you might use A=4, K=3, Q=2, J=1, T=0, etc., for the high card (but this requires using negative numbers for hands like 98s).
The Simple Feinberg Formula distributes the top 50% of starting hands into more than 20 hand groups. That sounds great, and it is if you can take advantage of this in your play. But you might not want to memorize a different strategy for each group. The solution is to bundle multiple scores into larger groups.
A simple approach is to round all scores to the nearest multiple of 3 (for example). 50, 51, and 52 would all round to 51, and would therefore all be played the same way. The good news is that this means there's no need to triple in the first place. We could simply add the kicker and number of straights, divide by 3 and round to the nearest integer, then add the high card and 1 more if suited. Now the numbers are smaller, but they're not really any easier to compute. The bad news is that there are good reasons for treating scores of 50, 51, and 52 differently.
A better solution is to group scores into more meaningful ranges. Suppose you consider 41 to be a reasonable threshold for raising heads-up, 47 for raising on the button, and 50 for raising from the cut-off. Now you've got a few hand groups: the 40-and-less group, the 41-46 group, the 47-49 group, and the 50 group. Of course, this approach would require memorizing the numbers 41, 47, and 50, along with how to play such hands. There must be an easier way...
Part 3: The Easy Feinberg Formula
Although many people treat all small pocket pairs (66 - 22) the same, we see from our hand ranking that there are surprisingly large differences between the values of these hands.
The Simple Feinberg Formula above asked us to triple pair values, triple high values, and add 3 for suited hands. That leads us to the following key observation. If K8 (a top 30% hand) is about as strong as 44, then A8 (like K8, but with a higher top card) and K8s (like K8, but suited) should be about as strong as 55 (the next pair up). In practice, this trick works impressively well. For that reason, the Easy Feinberg Formula groups hands into "plays like 55," "plays like 66," etc. (The strange kicker values in the Easy Feinberg Formula have been determined empirically, with the goal of faithfully producing the above hand rankings.)
The Simple Feinberg Formula above asked us to triple pair values, triple high values, and add 3 for suited hands. That leads us to the following key observation. If K8 (a top 30% hand) is about as strong as 44, then A8 (like K8, but with a higher top card) and K8s (like K8, but suited) should be about as strong as 55 (the next pair up). In practice, this trick works impressively well. For that reason, the Easy Feinberg Formula groups hands into "plays like 55," "plays like 66," etc. (The strange kicker values in the Easy Feinberg Formula have been determined empirically, with the goal of faithfully producing the above hand rankings.)
Rule #1: The value of pocket pair XX is X.
Examples: The value of 66 is 6. The value of KK is 13.
Rule #2: High card values are 3 for Ax, 2 for Kx, and 1 for Qx. All other high cards are worth 0.
Rule #3: Kicker values are:
Rule #3: Kicker values are:
5 for xKExamples:
4 for xQ, xJ, xT
3 for x9
2 for x8, x7
1 for x6, x5, x4, x3
0 for x2
AK = 3 (Ax) + 5 (xK) = 8Rule #4: Add 1 if suited.
A2 = 3 (Ax) + 0 (x2) = 3
Q8 = 1 (Qx) + 2 (x8) = 3
T9 = 0 (Tx) + 3 (x9) = 3
KQs = 2 (Kx) + 4 (xQ) + 1 (suited) = 7If you can will yourself to memorize the kicker values, the payoff is a formula that's easy to apply and gives the following results, which again are quite faithful to the hand ranking shown earlier.
J3s = 0 (Jx) + 1 (x3) + 1 (suited) = 2
So, if in a certain preflop situation you felt you ought to raise 15% of the time, you could raise any hand with a score of 6 or higher. An easy (but simplistic) rule might be to play 3+ from the blinds (and heads-up), 4+ from the button, 5+ from 1-off-the-button, and 6+ from 2-off-the-button. Note that it's roughly the case that raising your score threshold by 2 will halve your play frequency. So, if you believe someone would raise with a score of 4+, you might reraise them with a score of 6+.
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