Guess the PRWhat is a good PR in backgammon?
PR, short for Performance Rating, is the standard measure of how well someone played a backgammon match. It is the equity a player gave away per decision, compared with a strong bot. Lower is better.
On OpenGammon's scale, a PR of 2.75 or lower is Super Grandmaster level, up to 4.75 is Grandmaster, up to 7.5 is Master, up to 12 is Advanced, up to 18 is Intermediate, and anything above 18 is Beginner.
The scale
| PR | Level | OpenGammon levels |
|---|---|---|
| 2.75 or lower | Super Grandmaster | S0 to S3 |
| 2.75 to 4.75 | Grandmaster | G0 to G3 |
| 4.75 to 7.5 | Master | M1 to M3 |
| 7.5 to 12 | Advanced | A1 to A3 |
| 12 to 18 | Intermediate | I1 to I3 |
| above 18 | Beginner | B1 to B3 |
The bar is drawn on the same scale as the game's guess slider, linear in the logarithm of PR + 2. That scale treats the step from 3 to 6 as about as big as the step from 12 to 22, which matches how differently those players play.
Every level
OpenGammon splits each family into levels. A PR belongs to the last level whose threshold it is above, so exactly 3.00 is G0 and 3.01 is G1.
| Code | Level | PR |
|---|---|---|
| S0 | Super Grandmaster | 2 or lower |
| S1 | Super Grandmaster 1 | 2 to 2.25 |
| S2 | Super Grandmaster 2 | 2.25 to 2.5 |
| S3 | Super Grandmaster 3 | 2.5 to 2.75 |
| G0 | Grandmaster | 2.75 to 3 |
| G1 | Grandmaster 1 | 3 to 3.5 |
| G2 | Grandmaster 2 | 3.5 to 4 |
| G3 | Grandmaster 3 | 4 to 4.75 |
| M1 | Master 1 | 4.75 to 5.5 |
| M2 | Master 2 | 5.5 to 6.5 |
| M3 | Master 3 | 6.5 to 7.5 |
| A1 | Advanced 1 | 7.5 to 8.5 |
| A2 | Advanced 2 | 8.5 to 10 |
| A3 | Advanced 3 | 10 to 12 |
| I1 | Intermediate 1 | 12 to 14 |
| I2 | Intermediate 2 | 14 to 16 |
| I3 | Intermediate 3 | 16 to 18 |
| B1 | Beginner 1 | 18 to 20 |
| B2 | Beginner 2 | 20 to 24 |
| B3 | Beginner 3 | above 24 |
How PR is computed
A bot analyses every decision of the match: each checker play, each double, take and pass, and each resignation. For every decision it measures the equity lost, the difference between the best play and the one made, in fractions of a point.
PR = 500 × total equity lost / number of decisions
Only real decisions count. A forced move, or a roll with only one sensible play, is not a decision, and neither is a cube action nobody would consider. Without that rule, a match full of easy moves would dilute the errors and flatter the player. The factor of 500 puts typical values between about 2 and 30.
OpenGammon PR and XG PR
The best-known PR is the one from eXtreme Gammon (XG). OpenGammon analyses its games with GNU Backgammon and counts decisions with XG's rules, so its PR is comparable with XG's but not identical: the two bots do not always agree on the best play, or on how much an error costs. Guess the PR calls it simply "PR".
Why one game says little
In one game a player often makes only 10 to 30 real decisions. A single blunder in such a short sample can double the game PR, and a game that turns into a simple race leaves little room for errors at all. Over a whole match those swings even out. That is why Guess the PR asks for the match PR, and shows the game PR only after the reveal: the gap between the two is part of the lesson.
Test your eye
Can you tell a Master from an Intermediate by watching them play? Guess the PR shows you one game from a real match and asks you to guess each player's PR.
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