Re: [pbmserv] yacht strategy?

[Andrew Schepler <schepler@msu.edu>]

On Fri, Dec 26, 2003 at 03:09:16PM -0600, Douglas Zander wrote:
> so, for example is you rolled 1 2 3 3 6  and you have one roll left
> do you go for a large straight or try to build up your threes?
> (assuming you can go for either a large straight or threes)
> if you reroll 126 you have a 7 in 216 (roughly 1 in 30 chance) of rolling
> at least one more three. 

Er, no.
P(at least one 3) == 1 - P(no 3s) == 1 - P(each die not 3)^3
 == 1 - (5/6)^3 == 91/216 (about 0.42, nearly 3 in 7 chance).

> if you reroll 36 you have 2 in 36 (1 in 18)
> chance of getting a large straight.  so it would be better to go for
> the large straight.  (that sounds counter-intuitive)  

The 3s give a bigger probability of improving, but you could also 
consider that you get at least 6 points for 3s even if you fail, 
while the large straight is more points but all-or-nothing.  If you 
haven't scored small straight (I know, ignoring the assumption), keeping 
123 also gives a decent 11/36 chance of hitting that one.

-- schep