Dice game followup

In the post on a dice game, I didn't explain the meaning of the graphs.

A player has about a 50/50 chance of winning some points in her turn. That's in a good range--not too rare, not too often. But one attractive feature of the "losing turn" is that it isn't a one-and-done. There's a little tension: "I missed once, will I miss the second time too?" It makes the game a trifle slower, but the dramatic advantage should compensate for that. Clever.

Getting multiple points in a turn is common enough to make that something to hope for--and even getting a winning throw isn't so rare that the women wouldn't see it every few games. This also helps cultivate a little drama.

The more biased the chips are, the more likely early players are to win, but the effect isn't that dramatic for reasonable estimates of unfairness. If the chips are dramatically unfair, players will notice and quit using them. So it seems to be a pretty fair game.

The prize (some yard goods that she would give to a man in exchange for something of equal value) was something easily provided by the other women, something the man had to supply, and an exchange which emphasized the reciprocal obligations of men and women in the tribe. And--probably now and then an unmarried winner used it for signaling interest.

I'll work up some estimates for how many women can play the game before it gets too unfair. If there are 1000 women playing, the winner will appear in the first few hundred and the last ones will pretty much never get a turn. If you've only got 2 players, the odds are close to even for them both.

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UPDATE:

Actually, this is a terrible game. Below see the table for the number of women playing and the relative odds of the last woman in the group to those of the first woman in the group. If you can randomly pick who goes first, who second, and so on, you're OK, but otherwise the first players have quite an advantage.

# players	win rate ratio of last to first
2	0.86
3	0.78
4	0.73
5	0.66
6	0.62
7	0.58
8	0.53

UPDATE:

The easiest way to fix this is to skip the "first past the post" rule, and allow points to keep accumulating. The first past woman with 10 or more points marks the final round, which continues until all are done; then the woman with the highest number of points wins--with tie-breaker rounds as needed. Of course, that's a different game then, but probably similar enough.