Re: An open-ended maths/backgammon problem

On Aug 20, 6:24 pm, Philippe Michel
<philippe.mich...@xxxxxxxxxxxxxxxxxxxxx> wrote:
If you do not assume theoretical optimal play then I think the answer
is all real numbers.

That seems impossible. The games (or moves) are countable, so the possible
equities have to be as well. Don't you mean all rational numbers ?


But can you play 3/2/off 1/pi of the time, for instance ?- Hide quoted text -


If a random strategy is not allowed then I agree that it would not
be all real numbers. I don't think
though that all rational numbers would be possible.

There is nothing about probability theory that precluds irrational
numbers. Here is one practical way to do a task
that gives a success with probability of 1/pi. Write the decimal
expansion of 1/pi in this case .318309...
Draw a natural number randomly from 0 to 9. If it is less than 3, stop
and declare a success. If it is 4 or higher stop and declare a
failure. If it is a 3 continue on by drawing a second value. If it is
a 0 stop and declare a success. If it is 2 or higher stop
and declare a failure. Only if it is the second digit in the expansion
( in this case 1) is the outcome in doubt. Continue on
until the outcome is decided one way or the other.

Bob Koca




.

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