Rounds and Skill Progression

After looking a quite a number of analyzed brackets, I’m finally beginning to see some patterns that should have been obvious long ago. I now begin to think that I can explain why the bracket shift works for some events, and not for others.

I’ve been distracted by the question of bracket balance. Balance is, to be sure, important, and I’m not going to lighten up on my crusade against bad drops and grouped byes. But two other features are more important: the number of rounds in the path to success, and the progression of skill levels.

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Follow the Money

Today, a different kind of analyzed bracket.

Most of the brackets posted here have shown the prospects of the player occupying a certain line in terms of the chance of winning the tournament as a whole from that line. In this new bracket, the outlook is couched in terms of expected prize money – the player’s aggregate chance of winning any of six prizes.

The bracket I’ve analyzed is one of the possible brackets for the main even at this weekend’s Viking Classic backgammon tournament in Minnesota. The analysis gives me a chance to show a few new things besides the money, also.

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Fairness ($)

For some time, I’ve been a little unhappy with my fairness measures. It’s time, I think, to try something new.

Something along these lines:

Fairness (D): Fairness is the correlation between the skill level of the player, and the player’s mean reward.

The reward could be expressed in dollars and cents if it is evaluated in terms of prize money (hence fairness ($) in the title to this post). But I’d like to to be a little more flexible than that – to cover situations where the reward is couched in terms of ranking points, the opportunity to play additional matches, or prize money, or whatever else, including various combinations.

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Beware printyourbrackets.com

I’m planning to play Viking Classic backgammon tournament in Minnesota next weekend, and contacted the director to see if he needed any brackets. He allowed as how he thought he had things well in hand because he’d found what he needed on printyourbrackets.com.

After some back and forth, he’s decided to let me draw some brackets for the tourney. The stuff he’d found on PYB was pretty awful.

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All That Luck

In Skill and Luck in Backgammon, I described the process by which I settled on the parameters tourneygeek should use to simulate backgammon tournaments. The result was that the luck factor should be set to three, which implies that backgammon is 75% luck, and only 25% skill.

This does not mean, however, that backgammon is an easy game – a game in which a few small, easily learned heuristics will allow you to play at a high level. Open any of the many more advanced monographs on backgammon strategy and tactics, and you’ll soon see that there’s an enormous body of knowledge that expert players have and others do not. There’s plenty of skill in backgammon, it’s just that this skill is regularly overwhelmed because there’s even more luck.

Is there really that much luck in backgammon? How do players cope with it?

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More Better Bad Byes

In More Bad Byes, I looked at the consequences of grouping byes together in a bracket rather than spreading them evenly according to the conventional seeding pattern. Today I’ll follow up on a couple of suggestions that were made in the comments to that post.

Kevin H. suggested a format with the byes grouped just enough to allow the second round to start immediately. His bracket would equalize in the third round, rather than the second as happens with fully spread byes. As might be expected, his bracket does better than one with fully-grouped byes, but not as well as with a full spread.

Sean Garber, the author of the grouped-bye design that was the centerpiece of the analysis, mentioned that he had revised the drops for that design, and sent the new ones. His new drops made a modest improvement in fairness (C), but actually hurt fairness (B) a little, and increased the number of repeated pairings. I, guided by the pattern Sean established, uses the technique described in Getting the Drops Right, Part II to derive another new set of drops, which improved fairness (C) and reduced the number of repeats.

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In Praise of Games

In Playing Games I offered my definition of game play, and suggested how that definition might help explain how it is that some games are good and others are not. In Kissing and Contract Bridge, I used that interpretive framework to show why a hypothetical kissing game was not a good game, and why contract bridge was, at least as played by my mother’s generation, also a bad game.

I’m concerned that, by focussing on those examples of bad games, I might be suggesting that playing games is a bad thing. It’s not, of course. If I didn’t have a deep affection for games and game play, I wouldn’t bother with this blog. I like to think that tourneygeek is, at its heart, my way of expressing thanks for the benefit of a lifetime of playing games.

I know many people who feel this way about a particular game or sport. One reason that I’m trying to make tourneygeek relevant to a wide range of games is that I have, at different times, benefited from playing a lot of different ones. Chess, fencing, darts, bowling, golf, bridge, cribbage, backgammon … at one time or another, each of these has been important to me.

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