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Jun 13, 1995, 3:00:00 AM6/13/95

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In article <3rj763$a...@newsbf02.news.aol.com> usro...@aol.com (USRobots) writes:

>In various postings recently I've seen the terms

>"Gammon Rate" and "Gammon Price". Can somebody explain them?

>In various postings recently I've seen the terms

>"Gammon Rate" and "Gammon Price". Can somebody explain them?

Gammon rate generally refers to the percentage of one's wins which

are gammons (including backgammons). Typically it refers to cubeless

results, though this need not be so. If no other context is provided,

it generally refers to the gammon rate of the opening position between

two equal players.

For example, a gammon rate in the opening position of 22% would mean

that 22% of each player's wins would be gammons, so that the

cubeless results would be (ignoring backgammons):

Player 1 wins plain game: 39%

Player 1 wins gammon: 11%

Player 2 wins plain game: 39%

player 2 wins gammon: 11%

Another example, not the opening position:

Player 1 wins plain game: 60%

Player 1 wins gammon: 15%

Player 2 wins plain game: 22%

player 2 wins gammon: 3%

Here player 1 has a 20% gammon rate (15/(60+15)) and player 2

has a 12% gammon rate (3/(22+3)).

The consensus is that the opening position has a gammon rate in the

low to mid 20's. I think Kit Woolsey's analysis of games from

Hal Heinrich's match database gave a gammon rate of 21 or 22%.

Rollouts with Jellyfish have reportedly given a gammon rate of

around 26%. Roy Friedman has argued for a gammon rate in the

mid 30's. Expert Backgammon rollouts have given gammon rates in

the mid 20's (PC version) and low to mid 30's (Mac version).

The opening gammon rate is important for constructing match

equity tables. Consider the score -1:-2 Crawford. How often

will the trailer win? Well, the trailer will win whenever

he or she wins a gammon, plus half the time when he or she

wins a plain game. So, with a gammon rate of 20%, the trailer

will win 10+1/2*40=30% of the time. With a gammon rate of 36%,

the trailer will win 18+1/2*32=34% of the time.

Note that the gammon rate depends on the match score, the relative

strengths of the players, and players' styles. Thus it is somewhat

inaccurate to speak of the gammon rate of a particular position

without addressing these features, but this is what is commonly

done.

The gammon rate can also refer simply to the probability of

winning a gammon, unadjusted for the probability of winning, if

it is clear that this is what is meant by the context.

------

The gammon price refers to value a gammon has beyond that of

a plain win, relative to the difference between winning and

losing a plain game. That is:

(Equity from gammon win)-(Equity from plain game win)

Gammon Price = --------------------------------------------------------

(Equity from plain win) - (Equity from plain loss)

In money play, we have:

(+2*cube) - (+1*cube)

Gammon Price = ---------------------------- = 0.5

(+1*cube) - (-1*cube)

This is what is meant when people say that gammons are half as

valuable as winning. An important point for match play is that

a gammon price greater than 0.5 indicates that gammons are more

valuable than money play, while a gammon price of less than 0.5

indicates that gammons are less valuable than money play.

The gammon price can simplify the calculations for taking a double.

The procedure is this:

1) Estimate the probability of winning and losing a gammon. Note

that this is *not* the gammon rate, but the unadjusted probabilities.

2) Adjust your take point by adding your opponent's gammon probability

multiplied by the opponent's gammon price, and subtracting your

gammon probability multiplied by your gammon price.

If the gammon prices are the same, as they are in money play, then

step 2 is simpler:

2) Adjust your take point by adding the difference in the gammon

probabilities multiplied by the gammon price.

For example, let's say you estimate the gammon probabilities as:

Opponent wins gammon: 15%

You win gammon: 3%

If your gammonless take point is 22% and the gammon price is 0.50,

then you need to win 22 + 0.50*(15-3)=28% to take here.

Knowledge of gammon prices can also simplify the decision to

play on for a gammon or cash. If your gammons, multiplied by your

gammon price, minus your opponent's gammons, multiplied by their

gammon price, exceed your losing chances, then you should definitely

play on for the gammon. In money play, this simplifies to checking

whether your excess gammons (your gammons minus your opponent's) are

at least twice your losing chances.

Calculation of gammon prices in match play uses the match winning

chances (mwc) at different scores. For example, consider the score

-2:-4.

With the cube on 1, the relevant mwc are (using Woolsey's table):

Leader wins gammon: 100%

Leader wins plain game: 85%

Trailer wins plain game: 60%

Trailer wins gammon: 50%

The leader's gammon price is (100-85)/(85-60) = 0.60.

The trailer's gammon price is (50-40)/(40-15) = 0.40.

Now consider with the cube on 2:

Leader wins gammon: 100%

Leader wins plain game: 100%

Trailer wins plain game: 50%

Trailer wins gammon: 0%

The leader's gammon price is (100-100)/(100-50) = 0.00.

The trailer's gammon price is (100-50)/(50-0) = 1.00.

As can be seen here, the gammon prices in match play can vary

a great deal based on the score and the cube position. Doubling

may raise or lower both players' gammon prices, and this can play

a big role in the correct doubling decisions. For example, at

-2:-4, the leader has a big incentive not to double in a position

that is at all gammonish, since it lowers the leader's gammon price

from 0.60 to 0.00 while raising the trailer's gammon price from

0.40 to 1.00. Conversely, the trailer should double very aggressively

if there is much chance for a gammon -- in fact, at this score the

opening position is not far from a double for the trailer.

Typically, the gammon price on 2 is much more important than the

gammon price on 1, because the cube usually will get turned, and

at that point it is the gammon prices on 2 that matter, even if

the cube is not taken. The gammon price on 1 is significant

primarily for deciding whether or not to play for a gammon.

Gammon prices can be used to help guide doubling and taking

decisions in match play as well as money play, but extra care

must be taken due to fact that the gammon prices change with

each cube turn. When both players are far from victory, the

match gammon price is around the money play value of 0.50.

David Montgomery

monty on FIBS

Jun 13, 1995, 3:00:00 AM6/13/95

to

Greetings,

In various postings recently I've seen the terms

"Gammon Rate" and "Gammon Price". These are not in

Woolsey's "Tournament BG" or any other book I

have. Can somebody explain them?

Thanks,

USRobots

usro...@aol.com

Jun 14, 1995, 3:00:00 AM6/14/95

to

David Montgomery (mo...@cs.umd.edu) wrote:

: In article <3rj763$a...@newsbf02.news.aol.com> usro...@aol.com (USRobots) writes:

: >In various postings recently I've seen the terms

: >"Gammon Rate" and "Gammon Price". Can somebody explain them?

: In article <3rj763$a...@newsbf02.news.aol.com> usro...@aol.com (USRobots) writes:

: >In various postings recently I've seen the terms

: >"Gammon Rate" and "Gammon Price". Can somebody explain them?

[long and detailed explanation deleted]

Thanks for the explanation . I think it should go into the faq .

: David Montgomery

: monty on FIBS

muni .

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