### An Introduction to the Effective Pip Count (epc)

First, what is the effective pip count? The effective pip count is defined by the number of rolls required to bear off all your checkers multiplied by the average pip value of a roll. (49/6 or 8.167) A player's effective pip count is equal to his actual pip count plus the wastage of the position.

What is wastage? If you don't know what wastage is already here's an extreme example:

 is Player 2 score: 0 pip: 15 Unlimited GameJacoby Beaver pip: 15 score: 0 is Player 1
XGID=-O-----------------aaa----:1:1:1:00:0:0:3:0:10
on roll, cube action?

Here both players have the same actual pip count and the bottom player is on roll, would you rather be the bottom player?! Of course not. Even though the actual pip count is the same the bottom player wins about 0% of the time here. This is because we need a better tool to compare the players' positions. Every time the bottom player rolls he's going to be wasting pips. If he rolls a 65 he bears off two checkers but his actual pip count only decreases by 2 pips. The rest of the roll is said to be 'wasted'. This is where the effective pip count comes in.

On average the bottom player's position takes about 7 rolls to bear off all his checkers. We know that the average roll is 49/6 so according to our definition we ought to be able to get the effective pip count by multiplying those together. (49/6) * 7 = ~57. If you have XG2 you can toggle on the effective pip count and see for yourself. (options >> settings mode) If you don't have the latest version of XG I recommend getting it but you can survive without. GNU also provides you with the effective pip counts. In XG you need to create the bear off database and you can extend that clear out to the 12 point. (analyze >> create bearoff database)

There are many general rules we should know to get better at estimating the effective pip count. The more accurate our estimates are the more accurate our cube decisions will be. The first thing we need to do before jumping into epc cube actions is do a lot of work on estimating epcs. Let's jump in to the 3 rules we absolutely need to know.

 Rule 1:  For an N-roll position, the EPC is 7N + 1.

 is Player 2 score: 0 pip: 15 Unlimited GameJacoby Beaver pip: 15 score: 0 is Player 1
XGID=-O----------------------o-:0:0:1:00:0:0:3:0:10
on roll, cube action?

In other words in our example above of 15 checkers to bear off on the ace point otherwise known as a pure 8 roll position the effective pip count would be 7n+1 where n equals the number of rolls. Substituting the values we get 7(8)+1 or 57 pips as our epc. If you were to average the number of pips it took to bear off having all your checkers stacked on the ace point it would be equal to 57

 is Player 2 score: 0 pip: 12 Unlimited GameJacoby Beaver pip: 14 score: 0 is Player 1
XGID=-FD--------------------dd-:1:1:1:00:0:0:3:0:10
on roll, cube action?

In this example we have the player on roll having a pure 5 roll position with 10 checkers left to bear off. His effective pip count would then be 7(5)+1 or an epc of 36. The top player has a pure 4 roll position with 8 checkers left to bear off. His effective pip count would therefor be 7(4)+1 or an epc of 29. As you can see in the diagram these effective pip counts match up with the epc that the bot reports.

If you extend the formula to look at all pure roll positions here are the epcs:

Here is a chart rounded to the nearest full percent of your cubeless winning chances in any pure roll v. roll situation.

# of Rolls Effective Pip Count
1
8
2
15
3
22
4
29
5
36
6
43
7
50
8
57

The second rule we need to know for determining effective pip counts can be summarized:

 Rule 2:  Nice positions waste 7 pips.

What is a 'nice' position you ask? A nice position is one where all your spares are on the higher points, the 4, 5, and 6 points. This is where you try to keep your spares when you're bearing in during a straight race as it leads to the least amount of wastage. The optimal position as far as wastage is concerned that you should strive for is the 7/5/3 position shown below.

 is Player 2 score: 0 pip: 79 Unlimited GameJacoby Beaver pip: 79 score: 0 is Player 1
XGID=----CEG------------gec----:0:0:1:00:0:0:3:0:10
on roll, cube action?

This is what we would consider a 'nice' position. With positions like this you start with the regular pip count which is 79 in our above example and then according to Rule #1 above, we add 7 pips for wastage and get an epc of 79+7 or 86. You can again double check this against the epc that XG or GNU reports. (being off by .1 or .2 is not important) Let me show a couple more nice positions along with their effective pip counts displayed so you have a better idea of what a nice position is.

 is Player 2 score: 0 pip: 54 Unlimited GameJacoby Beaver pip: 50 score: 0 is Player 1
XGID=----CDC------------cdd----:0:0:1:00:0:0:3:0:10
on roll, cube action?

In the example above both players still have all their spares on the higher points in a smooth distribution. To determine the effective pip count of the bottom player we start with the regular pip count, 50, and add 7 per Rule #2 again for wastage. So 50+7 or an epc of 57 as the bot again confirms. For the top player the regular pip count is 54 and we add 7 for the wastage of a nice position again and get an epc of 61.

The third and final rule in our introduction to the effective pip count is:

 Rule 3:  Flat positions waste 10 pips.

 is Player 2 score: 0 pip: 43 Unlimited GameJacoby Beaver pip: 42 score: 0 is Player 1
XGID=-BBBBBB------------acbcba-:0:0:1:00:0:0:3:0:10
on roll, cube action?

The bottom player here has the prototype of a flat position. Again we start with his regular pip count which is 42 for a closed board and per Rule #3 add 10 for wastage giving us an effective pip count of 52. The top player is close to a flat position and I would still use this rule as a reference here so his normal pip count is 43 and then adding 10 for wastage we would get an epc of 53.

There are now a few more general rules I'd like to point out that aren't as important but will help you in understanding and estimating effective pip counts.

• The wastage of a single with 4 or more pips to go is usually between 4 and 5 pips.
• Per rule #1 of an N roll position, the epc = 7N+1, we can further improve on this. This formula tells us that it costs 7 pips either to miss or roll a non working double. 1/36 is about 1/35 and 1/35 of 7 pips is 0.2 pips. This means if a particular double does not work for one roll it will cost 0.2 pips. So if you can estimate the missing doubles you can get a more exact epc.
:insert examples:

Another good way to adjust the epc for close to pure N roll positions is as follows.

Even   Odd
1 2.0 2.6
2 2.3 2.9
3 2.6 3.2
4 2.8 3.4
5 3.0 3.6

How to read the above table. The numbers under Even and Odd refer to the average pip count per checker. The numbers in the left column from 1 to 5 tell you how many pips to add to the 7n+1 formula. Take the example below where you have 10 checkers totaling 20 pips. This gives you an average pip count per checker of 2.0 and is near a pure N roll position. You have an even number of checkers left so the formula tells you to add 1 effective pip to the 7n+1 formula. Since the number of rolls here equals 5 we would normally have 7(5)+1 = 36 as your epc. Given our more accurate modification using the above chart we know to add 1 more effective pip to our total and come up with an epc of 37. The difference between even and odd is because you can afford to miss with an odd number of checkers but not with an even number.

 is Player 2 score: 0 pip: 20 Unlimited GameJacoby Beaver pip: 20 score: 0 is Player 1
XGID=-CDC-----------------abcd-:0:0:1:00:0:0:3:0:10
on roll, cube action?