a clarification on how the maximum score (#2) is attained:
you first throw five 6s, and score them a yahtzee. you then throw five 3s (these early ones don't matter what you throw five of, but only that you throw five of each once) and put them on your threes. then five ones, and you put those on your ones. remember, though, that each subsequent yahtzee is worth 100 bonus. then come five fives; put them on your fives. another five ones, which you can ue as a joker; put them on large straight. five fours follow, and they go on fours. your top score is now 65, so you rack up your 35 bonus. you throw five threes again, putting them on small straight. five twos for the 2s, five more fives for full house (ironically, they score the same whether taken as full house or four of a kind). then five sixes, which go on sixes. your top score is now 105 plus bonus. you keep throwing nothing but sixes until all spaces are filled, thus getting 30 for each of three and four of a kind and chance. your scorecard will show:
5, 10, 15, 20, 25, 30, 35 bonus, 30, 30, 25. 30, 40, 30, 1250 (fifty for the first yahtzee adn 100 for each after that).
total is 1575.
the odds against such a feat are so astronomical that it is reasonable to say that it won't be achieved even if every person and every computer in the world played the game continuously for millennia!
look at it this way: the odds of throwing a yahtzee with one roll is one in 1296 (6^5, with six different possiblities); with two, between one in six and one in 1296; and with three, i think, one in between six and 216. since some are specific rolls (one each of ones through fives and four sets of sixes), those are one in 7776 each but placed anywhere in the sequence of turns, so i'm taking those at 12 in 7776^9 or two in 6^44. you can see where this is a huge number!
there are other factors involved, of course, but that will do for now.
how do you get 301 with no yahtzees? simply throw four each of ones thrugh sixes for a top of 84 plus bonus, get your straights and full house, and throw 29 (56666) for each of three and four of a kind and chance. the scorecard then shows: 4, 8, 12, 16, 20, 24, 35 bonus, 29, 29, 25, 30, 40, 29, 0, for 301. also highly unlikely; the best i've done in thousands of games is 282, in which i got the three 29s but could manage only 65 on top.
doesn't anyone else play this fun little game and know how to get the combinations i'm referring to?