Poker starting hands, scored properly with the Chen formula

What is the Chen formula?

The Chen formula, developed by mathematician and professional player Bill Chen, converts any two-card Texas hold'em starting hand into a single points score without running a full equity simulation. It's a mental-arithmetic shortcut built to be usable at the table, not a solver, it doesn't know who you're playing against or what position you're in, it just rates the raw strength of the two cards themselves.

How do you calculate a Chen formula score?

The score builds up in four steps, applied in order:

• Base value from the higher card. Ace scores 10, King 8, Queen 7, Jack 6, and any card 2 through 10 scores half its rank (a 9 scores 4.5, a 6 scores 3).
• Pairs double the base, with a floor of 5. A pair uses its own card's base value doubled, so pocket sevens (base 3.5) doubles to 7, while any pair below fives is bumped up to a minimum of 5 points, since even a weak pair has real value.
• Suited adds a flat 2 points. Any non-pair hand where both cards share a suit gets +2, reflecting the extra chance of making a flush.
• Unconnected cards lose points for the gap. Count the cards strictly between the two you hold: a 1-gap hand (like J-9) loses 1 point, a 2-gap (J-8) loses 2, a 3-gap (J-7) loses 4, and 4 or more gap loses 5. If the gap is 0 or 1 and the higher card is a queen or lower, add back 1 point for the extra straight potential of a low, tightly connected hand.

Worked example: J-9 suited

Take jack-nine suited. The higher card is the jack, which has a base value of 6. Because the hand is suited, add 2, bringing it to 8. The gap between jack and nine is exactly one card (the ten), a 1-gap, so subtract 1, bringing it to 7. Finally, since the gap is 1 or less and the high card (jack) is queen or lower, add the connector bonus of 1, landing on a final score of 8, comfortably in the "strong" band. Try it in the calculator above to see the same result come out the other end.

Reading the score

• 10 and above, premium: raise from any position, hands a solver opens nearly 100% of the time.
• 8 to 9.9, strong: raise from most positions, strong enough to three-bet in many spots.
• 6 to 7.9, playable: fine to open late or call a single raise, weaker the earlier you act.
• 4 to 5.9, marginal: speculative, worth playing cheaply, in position, or as an occasional bluff-raise.
• Under 4, fold: below the line for almost every seat at a full table.

Here's how some common starting hands score, from the same formula the calculator uses.

s = suited, o = offsuit, T = ten. Scores are rounded up to the nearest half point.

What doesn't the Chen formula account for?

A single number can't capture a decision this situational. The formula rates a hand in a vacuum: it has no idea whether you're first to act at a nine-handed table or on the button against one limper, no idea how deep the stacks are, and no idea whether the table is playing tight or loose. Two hands with the same Chen score can be worlds apart in real value depending on those factors. It also says nothing about how a hand performs against a specific opponent's likely holdings, which is a different question entirely, and exactly what the equity calculator on this site is built to answer. Here's a quick illustration from our own equity calculator: AK suited scores 12 and pocket queens score 14, yet when the two meet all-in before the flop, the queens win only about 53% of the time. The scores rank the hands correctly, but they hugely overstate the gap. Think of the Chen score as a fast first pass, not the final word. For how position changes what a hand is even worth opening, the solver page has a simplified opening range chart by seat.

From score to strategy

The Chen score is a starting point, not a full strategy.

• Use it to build a tight, consistent preflop range, then adjust for your position at the table.
• Check how your hand runs against a likely opponent with the equity calculator.
• Once preflop feels solid, read how poker solvers approach later streets.