THE PIP-COUNT OF MONTE CRISTO
Part 3
THE THORP COUNT
This method was invented by the famous Edward O. Thorp for making doubling decisions in pure race games. It is a modification of the basic pip count which takes into consideration some elements of checker distribution. Here's what you do:
- Total up your pip count using your preferred method.
- Add 2 pips for each checker you have left on the board.
- Add 1 pip for each checker on the 1-point to get a total amount.
- Deduct 1 point for each point you occupy in your home board.
- Add 10% to your total if it is more than 30 to get the Thorp Count.
Now do the same for your opponent, but do not add 10%. Then compare so:
- Double any time your count does not exceed the opponent's by more than 2.
- Redouble any time your count does not exceed opponent's by more than 1.
- Accept if your count does not exceed doubler's by more than 2.
In this next example the pip counts for each are, White 31, Black 29; so, in a pure count it is very close ... or is it? Let's do a Thorp Count:
 Diagram 18
White on roll
Cube Action?
The count is as follows:
|
White |
Black |
| Pip count |
31 |
29 |
| 2/checker |
22 |
22 |
| add 1/ace |
5 |
7 |
| minus 1/home point |
6 |
3 |
| Total so far |
52 |
53 |
| add 10% White |
5 |
|
| Thorp Count |
57 |
53 |
So, it isn't a double, but it is a take. JellyFish 3.5 confirms, No Double/Take. As far as I am aware the Thorp Count isn't 100% accurate but it is useful to have in your counting repertoire.
Our next method is one devised by Bob Hoey, he's called it ...
THE HALF ROLL METHOD
The half roll count to is to determine the equity in a race and is not an accurate pip count; nonetheless it is effective for determining who is leading in the race. Bob uses the average roll to work out the count.
 Diagram 19
Since the average roll is about 8.3 or thereabouts, once could say that any checkers on the 7- to 10-points are half a roll from coming in. Checkers on the 11- to 14-points are a roll each from coming in. Checkers on the 15- to 18-points are a roll and a half from coming in. Checkers on the 19- to 22-points are two rolls from coming in and a checker on the 23-, 24- or the bar-points is two and a half rolls from reaching home. It is a much quicker calculation as to who has more half roll to get home. Having determined the race to home by this method, then one has only to consider the distribution in the home board. Also take a half roll from my your opponent's count if he is on roll (if he were doubling, that is).
Another method is one (probably) devised by Mark Denihan. This one uses crossovers and sixes (and blocks) to determine the count. Mark calls it . . .
THE CASTING OUT CROSSOVERS METHOD
The fundamental idea is that to move a checker from one quadrant to the same position in the next quadrant takes six pips. So if you count all of the crossovers needed to bring all your checkers into your home board and multiply this number by six you have reduced each quadrant into a home board position with pip count values of 1 to 6. Then you need to recognise patterns of ten pips; such as two checkers on the 2-point and two checkers on the 3-point, and just keep adding these tens onto the first number you obtained when you multiplied by six. Finally add on the few extra pips that did not fit conveniently into the patterns of ten. That's it. Gone is the problem of trying to multiply and add or subtract different groups of numbers or keep mental shifts in your memory. It’s easy for us humans to increment by tens.
Finally, here's one method that seems so simple; that is until you're hit and placed on the bar. This is ...
THE RUNNING TOTAL DIFFERENCE METHOD
Look at the starting position:
 Diagram 20
Don't bother doing a pip count, trust me; the pip count for each player is 167 pips. All you have to do in this method is keep a running total of the difference between you and your opponent. For example, you roll 31, therefore you are four pips ahead; your opponent rolls 65 and you drop down to seven pips behind, you roll 55 and go into the lead with 13 pips; and so on and so on. Now, you might just think that this is by far the best method you've come across; it's so easy, all you need to do is add and subtract; and the biggest number you'll have to deal with is thirty-six. Don't fall for it. It is nigh impossible to keep up to date; being hit back onto the bar, dancing with half a roll, both of these will complicate matters - but if you don't believe, have a go! Another method using the starting pip count is ...
THE RUNNING TOTAL METHOD
Just like the method above except this time you keep your own pip count in your head rather than the difference. Not much use and far more difficult than the difference method. Don't even try this one!
There are no doubt other short cuts to pip counting, and, if and when I come across them I'll add them to this article but for the moment there should be enough here for you to develop a system that suits you. No one system is better than the others, the best system is a hybrid of one or more methods; find the one that suits you the best and then practice, practice, practice.
So, you've mastered counting, but have you figured out how to keep the score in your head whilst counting your opponent's pips? This is perhaps the hardest thing to do; you get your own count, you get your opponent's count, and then you find you've forgotten your own count! As it is illegal to write down the pip count devious methods have been invented by some clever people using an aid that no-one can take away from you - your hands! Here are three examples:
PALM UP - PALM DOWN
Place your right hand face down on your leg and count 1 to 5 with 1 being your thumb; turn your hand over and count 6 to 9 starting with the little finger and ignoring your thumb. Do the same for the tens with your left hand. To record your pip count all you need do now is identify your tens finger and your singles finger and there you are. Perfectly legal.
THE CURLY FINGER
Count one side, and then store the answer on your fingers in your lap to save having to remember it while counting the other side. It’s really easy to do this. Record the tens on your left hand, one finger down for 10, two for 20 etc.; one down curled up for 60, two for 70, etc. Same for the units on your right hand. Once again to record your pip count all you need do now is identify your tens finger and your singles finger and there you are. Another easy one. Finally . . .
THE BOARD & FINGER
This sounds like one of those trendy pubs that have mushroomed up in the last few years (awful places in my opinion). But this is a really easy method and you don't have to contort your fingers in the process. Quite simply make use of the points on the board. Use a thumb to indicate tens and a finger to indicate units; so for a pip count of 86 place your left thumb near the 8-point (80) and your right finger near the 6-point (6); and there you are, eighty-six. When the count is greater than 129 (thumb near 12-point, finger near 9-point) then use your knuckle to indicate tens and keep the finger for the units. With this method there isn't any need to cross your hands over for awkward counts just keep fingers for units and thumbs or knuckles for tens and you can go up as high 252 (knuckle near 24-point, finger near 12-point).
So, we are now at the end of this lesson in pip counting. If you've followed and understood what I've been on about, counting over the board will become second nature to you. It really isn't difficult and is very worthwhile - especially if you know how to do it and your opponent doesn't. Before we finish, here are a few tips and extra short cuts.
Tips
- When pip counting start at the high end; it’s easier to do 3 x 23 and then add on 4 x 4; than do 4 x 4 and then add on 3 x 23.
- Two checkers on each home board point totals 42 pips. Or, put another way ...
- A six-prime block is 42 pips.
- Checkers on the bar are 25 pips each.
- Two checkers on each of the 13- and bar-points total 40 pips.
- Turn off the pip counter in JellyFish and Snowie and practice counting positions and then confirm accuracy by turning it back on again.
- Your opponent's 5-point is 20 pips away.
- Your opponent's bar-point is 18 pips away.
- Keep calm when counting and don't get distracted.
- Practice, practice, practice.
I would like to acknowledge the following for their assistance: Robin Clay, Paul Magriel & X22 Publishing, Richard Howes, Edward Thorp, Patti Beadles, Bob Hoey, Mark Denihan, Stephen Turner and Tom Keith.
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