Value combos vs bluff combos
What a range has made on a board, counted — the arithmetic behind bluffing frequencies.
7 minute read
Put a range on a board and evaluate every live combination. What comes out is the shape of the range on that board: how many combinations are two pair or better, how many are one pair, how many are draws, how many are nothing. Those counts are what 'value' and 'bluff' mean in numbers.
Range TT+, AQs+, AKo, KQs, JTs, T9s, 98s, 87s on Q♠ J♥ 7♦: 60 live combinations.
| Made hand | Combos | Share | Mostly |
|---|---|---|---|
| Three of a Kind | 6 | 10% | QQ JJ |
| Pair | 30 | 50% | AA KK TT AQs KQs JTs |
| High Card | 24 | 40% | AKo AKs T9s 98s |
| Flush draws | 0 | 0% | four to a suit using a hole card |
| Open-ended straight draws | 4 | 7% | two ranks complete a straight |
| Gutshots | 20 | 33% | one rank completes a straight |
Computed by evaluating every live combination on the board. The sample range is an educational example.
The bluff break-even frequency from the pot odds module tells you how often a bluff must work. Combinatorics tells you how many bluffs a range can afford: to bet half pot with a balanced range, roughly one bluff for every two value hands (the opponent needs 25% to call, so 25% of the betting range can be bluffs).
Bluffs per value bet at break-even indifference
bluffs ÷ (value + bluffs) = call ÷ (pot + bet + call)
Half-pot bet: 25% bluffs. Pot-sized bet: 33% bluffs.
Educational, not prescriptive
These ratios describe a range that makes the opponent indifferent. Whether you want that depends on the opponent. The counting is exact; the strategy built on it is a choice.
Quick check
A range has 24 combinations of two pair or better on a board and bets pot. About how many bluff combinations would make a caller indifferent?
Show answer
Pot-sized bet → 33% bluffs → bluffs ÷ (24 + bluffs) = 1/3 → 12 bluff combinations.