There are 7776 possible rolls for first roll


Five numbers the same = 6 combinations

Four = 6*5*5 = 150

Three = 6*25*6 = 900

Two = 6*100*10 = 6000

All different 6.5.4.3.2= 720


If two or more the same we have 11/36 chance of each dice pairing the ones we keep in the next two rolls.


Chances of winning in this scenario are:

6/7776 + (11/36)(150/7776) + (11/36)^2(900/7776)

+(11/36)^3(6000/7776)

=3.95%


If all different, we throw again, same combinations, but now we only have 1/6 for last roll, so

720/7776 of the time we get:

6/7776 +(1/6)(150/7776) + (1/6)^2(900/7776)+

(1/6)^3(6000/7776)=1.08% but we need to multiply

through by 720/7776

which is approx 0.01% (i lost figures in rounding)


and the remaining chance is

720/7776 * 720/7776 *6 /7776 = not much


total therefore is 3.96% +/- 0.01% due to operators lack of calculator skills