doubling

[Craig Connell]

I find the most difficult part of the game is the doubling cube. I read a
book and have the following question.

The author said that you should accept a double if your odds of winning are
25% or more. His logic is that if you played 100 games in which your odds of
winning were 25% and you conceded them all, you would lose 100 points. If
you accepted them all you would lose 150 points (75 X 2) and win 50 (25 X 2)
for a net loss of 100 points. Therefore, 25% is the break even point. Makes
sense to me.

He next says that you should offer to double when your odds of winning are
66% or greater. He does not explain his logic and I do not understand this.
If I apply the same logic as above, 50% would be the break even point and at
51% I should double.

I am guessing that the higher winning percentage is required to offer to double
because you turn contol of the cube over to your opponent. But it seems to
me that this disadvantage is less important as the game goes on.

Can someone explain why such a high perecentage is required to offer to double.

--

[Kit Woolsey]

Craig Connell (con...@sun490.fdu.edu) wrote:
: I find the most difficult part of the game is the doubling cube. I read a

: book and have the following question.

: The author said that you should accept a double if your odds of winning are
: 25% or more. His logic is that if you played 100 games in which your odds of
: winning were 25% and you conceded them all, you would lose 100 points. If
: you accepted them all you would lose 150 points (75 X 2) and win 50 (25 X 2)
: for a net loss of 100 points. Therefore, 25% is the break even point. Makes
: sense to me.

: He next says that you should offer to double when your odds of winning are
: 66% or greater. He does not explain his logic and I do not understand this.
: If I apply the same logic as above, 50% would be the break even point and at
: 51% I should double.

: I am guessing that the higher winning percentage is required to offer to double

: because you turn control of the cube over to your opponent. But it seems to

: me that this disadvantage is less important as the game goes on.

: Can someone explain why such a high percentage is required to offer to double.

: --

You've got the right idea, Craig. If it were the last roll of the game
(i.e. if you didn't double now you would never have a chance to double),
then it would be correct to double with a 51% advantage. The reason it
may not be right to double with an advantage greater than 50% is that you
relinquish the opportunity to double later (if you already own the cube
then there is even more cost to doubling, since in addition to losing the
chance to double later you are giving your opponent the opportunity to
double which he did not have). So, why should we double now when we can
double later? The answer, of course, is that after the next exchange of
rolls (that is we roll, he rolls) we may shoot over the 75% mark so our
opponent will have a proper pass. This is called losing our market. If
this happens, clearly we wish we had doubled. So, our motivation for
doubling depends not only on our chances of winning from the given
position but on the volatility of the position. If the position is a
very static position (such as a holding game or a long race) it is not
likely we will lose our market by much, so we would want to be near the
75% mark before we turned the cube. On the other hand if the shit is
about to hit the fan on the next roll we would need much less in winning
chances, since if things go our way we would lose our market by a lot.
Naturally the last roll of the game is the most volatile position of all.

The 66% figure you read does not have any mathematical validity. It is
simply the author's estimate of when on average it would be correct to
turn the cube. As I have shown, the real question is how volatile the
position is -- that is just as important as the winning chances. Hope
this helps to answer the question -- it is really a very complex subject
and there has not been any adequate written material on doubling.

Kit

[Julian]

In article <1994Nov28.0...@sun490.fdu.edu>
con...@sun490.fdu.edu "Craig Connell" writes:

> He next says that you should offer to double when your odds of winning are
> 66% or greater. He does not explain his logic and I do not understand this.
> If I apply the same logic as above, 50% would be the break even point and at
> 51% I should double.
>
> I am guessing that the higher winning percentage is required to offer to double
> because you turn contol of the cube over to your opponent. But it seems to
> me that this disadvantage is less important as the game goes on.
>
> Can someone explain why such a high perecentage is required to offer to double.
>
> --
>

Control of the cube is usually worth something; it is most important to
consider that value in positions where if you double, you are likely to
be redoubled after one bad roll; if you keep the cube then you deny
your opponent the use of it. These positions seem to occur *more*
towards the end game, however. Incidentally, if the cube is in the middle
then you can't deny your opponent access to it anyway.

Now, when you decide whether to take or drop a double, you have no choice
as to the timing of the double. If you are ahead then you can pick your
moment... and the most *effective* time to double is around the 75% mark.
(It gains an average of 0.5 points - a double at 51% chance of winning
gains 0.02 points on average)
--
------------------------------------------------
Julian Hayward
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