Bet Size, MDF & Value-Threshold
Every number a bet size implies — what the caller needs, what a balanced bettor's bluffs must be, and what streets of pressure filter a range down to. Throughout, b is the bet as a fraction of the pot.
What a bet size buys
Each derived quantity is a one-line function of the bet size.
| Bet | Caller needsb/(1+2b) | Alphab/(1+b) | MDF1/(1+b) | Bluff shareb/(1+2b) | Value : bluff(1+b) : b |
|---|---|---|---|---|---|
| 1/6 potb = 0.167 | 12.5% | 14.3% | 85.7% | 12.5% | 7 : 1 |
| 1/4 potb = 0.25 | 16.7% | 20.0% | 80.0% | 16.7% | 5 : 1 |
| 1/3 potb = 0.333 | 20.0% | 25.0% | 75.0% | 20.0% | 4 : 1 |
| 1/2 potb = 0.5 | 25.0% | 33.3% | 66.7% | 25.0% | 3 : 1 |
| 2/3 potb = 0.667 | 28.6% | 40.0% | 60.0% | 28.6% | 2.5 : 1 |
| 3/4 potb = 0.75 | 30.0% | 42.9% | 57.1% | 30.0% | 2.33 : 1 |
| Potb = 1 | 33.3% | 50.0% | 50.0% | 33.3% | 2 : 1 |
- Caller needs — equity required to call: the call risks b to win 1+2b.
- Alpha — the fold frequency that makes a pure bluff break even; if they fold more, any two cards profit.
- MDF — minimum defense frequency, 1 − alpha. They must defend at least this much of their range or you can bluff any two.
- Bluff share — the bluff fraction of a balanced, polarized river betting range; Value : bluff is the same number as a ratio.
The caller's required equity and the bettor's balanced bluff share are the same number — laying X : 1 on a call mirrors bluffing 1-in-(X+1). A pot-sized bet lays 2 : 1, the caller needs 33.3%, and the balanced bettor arrives with 33.3% bluffs: two value bets per bluff.
SPR and the call-down ladder
Betting on n streets against an opponent defending at MDF leaves MDFn of the range that saw the flop at showdown.
| Streets of pressure | 1/4 potMDF 80.0% | 1/3 potMDF 75.0% | 1/2 potMDF 66.7% | 2/3 potMDF 60.0% | PotMDF 50.0% |
|---|---|---|---|---|---|
| 1 street | 80.0% | 75.0% | 66.7% | 60.0% | 50.0% |
| 2 streets | 64.0% | 56.3% | 44.4% | 36.0% | 25.0% |
| 3 streets | 51.2% | 42.2% | 29.6% | 21.6% | 12.5% |
Potting three streets means the range that calls you down is ~12.5% of where it started — your hand must beat that range, not the flop range.