On Sunday, October 15, 2023 at 12:09:40 PM UTC+1,
peps...@gmail.com wrote:
On Sunday, October 15, 2023 at 1:08:18 AM UTC+1, peps...@gmail.com wrote:
If you've really got absolutely nothing better to do, you might like to think about all three possible symmetric races where:
1) The on-roll player has the cube.
2) The pip count for each player is 7.
3) Each player has exactly two checkers.
If the checkers are on the points 6 and 1, it's a pass.
Otherwise it's a take.
With the checkers on 5 and 2, it's a bigger take than with
the checkers on 4 and 3. Note that with the checkers on 5 and 2,
it's a redouble whenever the on-roll player doesn't immediately bearoff. All positions need 3 rolls to bear off iff the first two rolls are 21,
1 roll to bear off if the player immediately bears off (duh!)
and 2 rolls to bear off otherwise.
This means that the EPC depends only on the number of out shots.
There are 19 outshots in the 5, 2 position, 17 in the 4, 3 position
and 15 in the 6, 1 position.
So the higher the EPC, the worse for the off-roll player.
This seems paradoxical to me but I recently had a croissant and two
fried eggs for breakfast and used the croissant to mop up the left over yolk,
so I may not be a reliable source of info.
Paradoxical because in a symmetrical position, a person might naively expect that the longer the race, the more chances the underdog has.
But these three positions go in exactly the other direction.
Thanks for listening. And thank you just as much if you didn't listen at all.
Paul
Above, I tried to change the title of the thread to "Three Symmetrical Races".
Not sure if it worked.
BTW "might not be interested" means the same (to me) as "might be interested". After all, if something might happen, then it also might not happen (and vice versa).
It's intended as a logical/mathematical joke.
Paul
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)