EPC Estimation Methods
The information below is provided by Art Benjamin
| Abbreviation | Name | Variance | Checkers | Restrictions | Formula | Author |
|---|---|---|---|---|---|---|
| 5-Flat | 5 point board six empty |
10+ | f = 0 a,b,c,d,e ≥ 2 |
E=PC+10+2(a-2)+(b-2)+(c-2)/2+h/2 | Art Benjamin | |
| 5.5-Flat | 5 point board six blot |
11+ | f = 1 a,b,c,d,e ≥ 2 |
E=PC+9+2(a-2)+(b-2)+(c-2)/2+h/2 | Art Benjamin | |
| 6-Flat | Closed board | 12+ | a,b,c,d,e,f ≥ 2 | E=PC+10+2(a-2)+(b-2)+(c-2)/2-0.5(If(e,f>2)) | Art Benjamin | |
| abc | Abc pippish | Pippish | 9+ | a,b,c ≤ 2 | E = PC + 7 + a + b/2 | Art Benjamin |
| .2M | Count Your Misses | 5+ | d + e + f = 1 c = 0 |
7N + 1 + 0.2M. See notes below. | Art Benjamin | |
| Fast | Fastimate | Intermediate | 9+ | e + f > 0 | E = PC + 4 + 2a + b + c/2 + 1.2g | Art Benjamin |
| MCG | MCG Estimate | Intermediate | 9+ | e + f > 0 | See MCG formula description below | Matt Cohn-Geier Art Benjamin |
| MM8 | Modified Matussek | 4 to 8 | e + f > 0 | E=PC + 4 + 2a + 1.3b + 0.8c + 0.4d + 0.2e + 0.7(g–2) + 0.3(h–2) | Joachim Matussek Art Benjamin | |
| MM8- | Modified Matussek Minus | Not Rollish | 6 or 8 | e = f = 0 a or b = 1 |
E=PC + 3 + 2a + 1.3b + 0.8c + 0.4d + 0.3(h – 2) | Joachim Matussek Art Benjamin |
| NNM | Nearly No Miss | Rollish or (e + f = 0) |
Any | Gapless | E=7N+1+S; where S=2G–2.8, when G≤2 and S=4G–7, when G>2 |
Walter Trice Art Benjamin |
| NNM5 | Nearly No Miss Five | Not Rollish | 5 or more | e + f = 0 c or d ≥ 5 |
E = NNM + 0.5 if h = 5; add 1 if h > 5 | Art Benjamin |
| NNM+ | Nearly No Miss Plus | Rollish | e + f > 0 a ≥ 4 |
E = NNM + a / 20. Use 0.8 if a ≥ 8 | Art Benjamin |
MCG formula description
E = PC + 10 + 2(a – 2) + 1.25(b – 2) + 0.75(c – 2) + 0.3(h – 3) + 0.2(d – f) plus penalties for high gaps and semi-gaps.
The penalties for gaps on the 4, 5, and 6 points are, respectively 1.5, 1.5, and 1.
We incur a penalty of 0.5 for each semi-gap (consisting of a single checker) on the 4, 5, or 6-point.
With 14 or 15 checkers, the gap penalties are 2, 2, and 1, respectively, and we should subtract 0.4 from the above estimate.
We can also apply MCG when a, b, or c is less than 2.
If a = 1 or 0, subtract 1.5 or 2.5 respectively.
If b = 1 or 0, subtract 0.75 or 1, respectively.
If c < 2, subtract 0.25.
.2M Notes
With an even number of checkers, M is the number of non-doublets that do not remove 2 checkers plus doublets that do not remove 4 checkers.
With an odd number of checkers, M is the number of non-doublets that remove 0 checkers plus doublets that do not remove 3 or more checkers.
With an even number of checkers and a = 4, double-1s is considered to be a missing number.
This method applies to positions of the form 1000ba, 100ba, 10ba, 110a, 200a, 20a, 10a, and gapless 5-checker positions.
| Symbol | Meaning |
|---|---|
| E | EPC estimate |
| PC | Pip count |
| a | Checkers on ace point |
| b | Checkers on deuce point |
| c | Checkers on three point |
| d | Checkers on four point |
| e | Checkers on five point |
| f | Checkers on six point |
| g | Number of empty points |
| h | Checkers on tallest point |
| G | PC/checkers for even positions or (PC/checkers) – 0.5 for odd positions |
| M | Number of immediate misses |
| N | Number of non-doubles to bear off all checkers |
Additional information
For more details, see the following Math Overboard columns by Art Benjamin in PrimeTime Backgammon, published by the US Backgammon Federation.
Short Pippish Races, Summer 2022
EPC Estimation: Primarily Pippish Positions, Fall 2022
EPC Estimation: Reasonably Rollish Positions, Summer 2023
7N + 1 Variations, Fall 2023