Shut the box analysis

One of my Livejournal friends cananian has a very interesting series of posts about a dice game called Shut the Box. Even though I am not a math major, unlike Adam, I find mathematical analysis of games and strategies for playing games to be very interesting, especially when the results are counter-intuitive:

In previous entries I’ve been discussing the mathematics of the game “Shut the Box”. I first asked about good strategies which were simple enough for a human to use.

One obvious intuitive strategy is to chose tiles to flip down such that your score is as low as possible after each turn. I turns out this is an extraordinarily bad choice: against an optimal 2nd player, the 1st player can expect to lose xy% 75.3% of their stake in each game, and against an optimal 1st player, a second player following this strategy will lose 70.8% of their stake (first player shuts the box 9.5% of the time and wins 71.5% of the rest of the games).

A better strategy is the opposite: flip tiles so that your score is as high as possible after each turn!

C. Scott Ananian’s continuing analysis of this game that I had never heard of before makes me want to play it! Now I just need to find my dice.

In a related question, should this blog cover gambling games / games of chance? I know Adam was interested in poker in the past and I’ve become interested in it recently myself, but ALASSCA hasn’t covered games of chance much in the past, preferring games that are further towards the “pure skill” end of the spectrum. My personal feeling is that any games we create ourselves or unusual/unpopular games that we discover should be within ALASSCA’s purview, regardless of the degree of chance involved in the game. What say you, Adam and any other readers we might have?

UPDATE: Another interesting question is, why have I never heard of this game? Apparently it was popularized by a TV show that last aired when I was 4 years old, High Rollers, so I would never have seen it. Perhaps the game is better known among older people, but it may still be worth reviving old games for our generation who may otherwise be ignorant of them.

1 thought on “Shut the box analysis

  1. I fixed the ‘xy%’ in the above; the actual number is 75.3%. (I’d generated the number in one of my runs and remembered it as being “above 70%” but not saved the output; I had to rerun my script to regenerate the exact number.)

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