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Peter Fankhauser wrote:
> Just, what exactly is the famed "gammon price"?
> I've heard this term now quite often, but neither Kit Woolsey's
> monography on Tournament Backgammon, nor Tom Keith's pages on
> cube strategy in matches (nor his glossary btw) use this term.
> Although the market-window-tables (takepts for both players)
> for different gammon rates in TK's pages might be a different
> perspective on this.
>
> If anyone knowledgeable cares to post doubling window table
> (that's the easy part) + a definition of gammon prices + a
> few hints how to use this stuff (that is how to adjust the
> doubling window according to the gammon price) I'd be very greatful
> (and I assume lots of others too:)
The gammon price represents the relative value of a gammon swing vs a
win-loss swing. In money games, the gammon price is always 50%. It's
computed as:
GP = (equity from winning a gammon - equity from winning a plain game)
divided by (equity from winning a plain game - equity from losing a plain
game)
or GP = (G-W)/(W-L)
For money (G-W) is one unit, (W-L) is 2 units, so GP is 50%.
This figure is used in a couple of ways:
1. To adjust the take point to account for gammons. If I expect to get
gammoned x%, I need to add x% times the gammon price to my basic take
point. So for money, if I expect to be gammoned 20% of the time, I need an
additional 10% wins over the basic 25%, or 35%, to take.
2. To calculate play decisions. If I'm considering taking extra risks to
win a gammon, I can take the risk as long as my extra losses are no more
than 50% of my extra gammons. Conversely, if I'm risking losing a gammon
in order to try for the win, I must make sure that my extra wins are more
than 50% of my extra gammon losses.
(As far as computing the minimum doubling point, I don't know how to use
the gammon price. People seem to estimate a % of gammons and factor that
into the normal calculations.)
In match strategy, the gammon price can vary from 0 to 100%. For example,
at Crawford-odd, the trailer's gammon price is approximately zero; at
Crawford-even, it's 100%. (The leader's gammon price is zero in both
cases)
At a score of 2-away, 4-away, for example, you need to know the gammon
price for both players, with a 1-cube or a 2-cube.
Leader, 1-cube: GP = (100 - 83)/ (83 - 60) = 74%
Leader, 2-cube: GP = (100-100)/(100-50) = 0
Trailer, 1-cube: GP = (50-40)/(40-17) = 43%
Trailer, 2-cube: GP = (100-50)/(50-0) = 100%
(There are some extra variables too, like what happens if both players have
significant gammon chances? For money, you can use net gammons times
gammon price to compute the offset to the take point. But in matches,
where each side's gammons are worth different amounts, it gets complicated
and I'm not really sure what the formula is.)
Ron
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