The 50% Rule of Poker

The 50% Rule of Poker (a.k.a Pinnock's Razor) states that in no-limit games, in a heads-up pot, on any street, the player who is out-of-position (OOP) should attempt to construct their checking and betting strategy in such a way as to force the player who is in-position (IP) to bet or raise at most 50% of the time.

The 50% Rule has many interesting consequences for the range construction of both players:

  1. OOP should always ensure that their checking range is strong enough that IP should check back at least 50% of the time.
  2. If OOP does not have enough strong hands in their range to prevent IP from betting more than 50% of the time when OOP checks, then OOP should check their entire range.
  3. If OOP has a betting range, and if OOP checks, then IP should check back more than 50% of their range.

On the River, with stack sizes larger than the pot, the 50% rule holds most strongly. In other words, in any River spot with the SPR > 1, IP will check back at least half the time when OOP checks. IP will attempt to bet as often as possible, which means that IP's betting frequency will be close to (but still less than) 50%.

Let's look at some example lines. Note that IP checks back at least 50% in all of these River scenarios.

Example 1.1

Folds to Hero/BU who opens to 2BB.
SB folds.
Villain/BB calls.

Flop (4.5BB) .
Villain checks.
Hero bets 1.1BB.
Villain raises to 4.5BB.
Hero calls.

Turn (13.5BB) .
Villain bets 13.5BB.
Hero calls.

River (40.5BB) .
Villain checks.
Hero?

Example 1.2

Folds to Hero/BU who opens to 2BB.
SB folds.
Villain/BB calls.

Flop (4.5BB) .
Villain checks.
Hero checks.

Turn (4.5BB) .
Villain checks.
Hero checks.

River (4.5BB) .
Villain checks.
Hero?

Example 1.3

Folds to Hero/BU who opens to 2BB.
SB folds.
Villain/BB calls.

Flop (4.5BB) .
Villain checks.
Hero checks.

Turn (4.5BB) .
Villain bets 2.25BB.
Hero calls.

River (9BB) .
Villain checks.
Hero?