Pip Counting
 High FivesA new method for counting pips Pierre Viau (Peyo)February 2011

Introduction

I really wanted a counting method where I could work board-by-board. This counting method is clearly inspired from Naccel (Nack Ballard), and the Five-Count (Sho Sengoku; great name by the way), but they don't quite use the full boards, and that always bothered me. The method also draws inspiration from the Half-Crossover (Douglas Zare), but it uses full boards (only four numbers to add) rather than half-boards (eight numbers).

It is based on:

• the multiplication by 5, which is trivial (for the maths-impaired: multiply by 10, then divide by 2 :-)
• making an approximate trivial count, then making small count adjustments
• working board by board; actually staying inside each 6-points board, no shifting, no distortion; this hopefully limits errors through the cleaner visualization (it does for me anyway)
• NB: this is at the expense of a little more count adjustment; however this is usually mitigated by the symmetry considerations found in many counting methods

The Method

1.  Count men in each board and use appropriate weighting factors before adding up.

I prefer to start from the furthest board, but this is a matter of taste.

• bar (don't forget): counted men × 5
• opponent infield: counted men × 4
• opponent outfield: counted men × 3
• own outfield: counted men × 2
• own infield: counted men × 1

2.  Add all up, multiply by 5.

This is your approximate count = (S1 + S2 + S3 + S4 + S5) × 5.

Use the "5-points" as reference in each board:

• own infield: 5-point
• own outfield: 10-point
• opponent outfield: 15-point
• opponent infield: 20-point

Make count adjustments in each board:

• Add pips for men trailing the reference 5-point.
• Substract pips for men ahead of the reference 5-point.
• NB1: Use symmetry around the reference 5-point inside a board to remove the need for some count adjustments.
• NB2: Use symmetry across the board to remove the need for some count adjustments (in particular across outfields).
• NB3: The bar is your 25-point, and is only one point, so no count adjustment there, obviously.

Board-specific issues.

Opponent infield:

• the reference point (20-point) is lopsided (not near middle of board)
• this (statistically) requires more count adjustments
• not a real issue since there are usually very few men in this board

Opponent outfield:

• the reference point (15-point) is more central (not perfect)
• this (statistically) means simpler count adjustments
• it is sometimes possible to cancel the need for some count adjustments by symmetry inside the board
• it is often possible to cancel the need for some count adjustments by symmetry with own outfield

Own outfield:

• the reference point (10-point) is more central (not perfect)
• this (statistically) means simpler count adjustments
• it is often possible to cancel the need for some count adjustments by symmetry inside the board
• it is often possible to cancel the need for some count adjustments by symmetry with opponent outfield

Own infield:

• the reference point (5-point) is lopsided (not near middle of board)
• this (statistically) requires more count adjustments
• this is somewhat an issue since there are usually many men in this board
• this is really an issue later in games when more men move in, and move deeper and deeper in (away from the reference 5-point)
• however there are better ways to count such late positions (e.g., my own Sweet-Fifteen :-)

Do not worry about men already off: they count for 0 each.

And let's not forget: it is quite easy to forget men on the bar. If you did, just add 25 pips each at the end ...

Example 1.

Example 2.

Example 3.