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Nov 27, 1994, 11:24:49 PM11/27/94

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I find the most difficult part of the game is the doubling cube. I read a

book and have the following question.

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.

--

Nov 28, 1994, 8:47:59 PM11/28/94

to

Craig Connell (con...@sun490.fdu.edu) wrote:

: I find the most difficult part of the game is the doubling cube. I read a

: 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

Nov 29, 1994, 5:02:50 PM11/29/94

to

In article <1994Nov28.0...@sun490.fdu.edu>

con...@sun490.fdu.edu "Craig Connell" writes:

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

------------------------------------------------

RECREATE THE EXCITEMENT OF A DAY TRIP TO LONDON

AT HOME: simply sit in your car with the engine

running, and occasionally sound your horn.

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