RichardSRussell (![[info]](http://l-stat.livejournal.com/img/userinfo.gif){kind=small} richardsrussell) wrote,@ 2005-04-21 15:52:00 |
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Evolution: The Game Is Rigged
Evolution: The Game Is Rigged
By Richard S. Russell • 2005 April 22 (Earth Day)
This is in the public domain. Feel free to reproduce it.
In the imaginary world of role-playing games like Dungeons and Dragons, the workings of fate are simulated by rolling percentile dice. They come in pairs, each of which has 10 sides. Die #1 is labelled 00 thru 90; Die #2, 0 thru 9. You find what percentage you've generated by adding the numbers together. For example, a 50 and a 4 yield 54. If some event has, say, a 75% chance of occurring, any roll of the percentile dice of 75 or below means it's happened.
Let's use these percentile dice in a little game between Randy the Rationalist and Cretin the Creationist. The name of this game is "Evolution". Here are the rules:
(1) Randy and Cretin each get to start with $100.
(2) Each will roll a pair of percentile dice, check the results, and make whatever payoffs are required by these rules. This will keep going until one or the other is broke.
(3) If they both roll the same number, Randy will pay $1 to Cretin, and they will enter that number on the Master List.
(4) If either of them rolls a number on the Master List, Cretin will pay $1 to Randy.
These rules are designed to reflect each player's attitudes toward Evolution. Cretin thinks that Evolution operates by chance alone, so he wins every time chance alone generates a winning number. Randy understands that a more important factor in Evolution is natural selection, so he wins every time a previously successful number comes round again. And the rules emphasize the importance of time in Evolution, as each roll of the dice represents a generation in the history of a species, but it takes a lot of generations to produce a definitive result.
Now, they'll probably roll the dice a lot before they 1st get to invoke Rule #3. (The probability of a match is 1/100, so the expectation is that it'll happen about 50 rolls into the process.) Let's say they both roll 16. At this point, Randy's down to $99, Cretin's up to $101, and the number 16 is entered on the Master List.
They keep rolling. Within about another 25 rolls, Cretin hits 16 again. Now they're even again: Randy $100, Cretin $100.
They keep rolling. Within about another 25 rolls, they both get 73. This number gets entered on the Master List. Randy $99, Cretin $101.
After another 15 rolls, Randy hits 16 again. Randy $100, Cretin $100.
Another dozen rolls, and Cretin hits 73 again. Randy $101, Cretin $99.
Another 10 rolls or so, and they both get 55. Randy $100, Cretin $100.
Another 8 rolls, and Cretin hits 73 yet again. Randy $101, Cretin $99.
Another 10 rolls, and Randy hits 55. Randy $102, Cretin $98.
These 1st few transactions make it look as if the 2 players are reasonably evenly matched. In actual practice, even tho the rules guarantee Cretin the 1st win, Cretin's high-water mark will be only about $101 to $103, because the game is rigged. Cretin's chances of winning remain at 1% per roll forever, whereas Randy's chances of winning get better and better as time goes on. Inevitably, no matter how much money Cretin starts with, Randy will have it all. Even if we vastly reduce Randy's chances by, say, modifying Rule #4 to require Randy alone to roll Master List numbers twice in a row to win, the game is still rigged, and -- over a much longer and more tedious game -- Randy will still get all the money.
This is the way Evolution works. Every roll of the dice is governed by pure chance. But, once the game hits on a winner, it STAYS a winner ever afterward (given a constant environment, which the rules of the game provide). The effects are cumulative. It may take a long, long time for Randy to win ALL of the money (the equivalent of coming up with a whole new species thru a series of tiny incremental changes), but it's as inevitable as the sunrise.
After awhile, you'd think that even the Cretins of the world would realize that the game is rigged.
Teachers:
Excellent game dice available at http://www.chessex.com/.
Monopoly money available at http://www.boardgames.com/monopolym
= = = = = =
Creationism: the theory that Rome WAS built in a day.
By Richard S. Russell • 2005 April 22 (Earth Day)
This is in the public domain. Feel free to reproduce it.
In the imaginary world of role-playing games like Dungeons and Dragons, the workings of fate are simulated by rolling percentile dice. They come in pairs, each of which has 10 sides. Die #1 is labelled 00 thru 90; Die #2, 0 thru 9. You find what percentage you've generated by adding the numbers together. For example, a 50 and a 4 yield 54. If some event has, say, a 75% chance of occurring, any roll of the percentile dice of 75 or below means it's happened.
Let's use these percentile dice in a little game between Randy the Rationalist and Cretin the Creationist. The name of this game is "Evolution". Here are the rules:
(1) Randy and Cretin each get to start with $100.
(2) Each will roll a pair of percentile dice, check the results, and make whatever payoffs are required by these rules. This will keep going until one or the other is broke.
(3) If they both roll the same number, Randy will pay $1 to Cretin, and they will enter that number on the Master List.
(4) If either of them rolls a number on the Master List, Cretin will pay $1 to Randy.
These rules are designed to reflect each player's attitudes toward Evolution. Cretin thinks that Evolution operates by chance alone, so he wins every time chance alone generates a winning number. Randy understands that a more important factor in Evolution is natural selection, so he wins every time a previously successful number comes round again. And the rules emphasize the importance of time in Evolution, as each roll of the dice represents a generation in the history of a species, but it takes a lot of generations to produce a definitive result.
Now, they'll probably roll the dice a lot before they 1st get to invoke Rule #3. (The probability of a match is 1/100, so the expectation is that it'll happen about 50 rolls into the process.) Let's say they both roll 16. At this point, Randy's down to $99, Cretin's up to $101, and the number 16 is entered on the Master List.
They keep rolling. Within about another 25 rolls, Cretin hits 16 again. Now they're even again: Randy $100, Cretin $100.
They keep rolling. Within about another 25 rolls, they both get 73. This number gets entered on the Master List. Randy $99, Cretin $101.
After another 15 rolls, Randy hits 16 again. Randy $100, Cretin $100.
Another dozen rolls, and Cretin hits 73 again. Randy $101, Cretin $99.
Another 10 rolls or so, and they both get 55. Randy $100, Cretin $100.
Another 8 rolls, and Cretin hits 73 yet again. Randy $101, Cretin $99.
Another 10 rolls, and Randy hits 55. Randy $102, Cretin $98.
These 1st few transactions make it look as if the 2 players are reasonably evenly matched. In actual practice, even tho the rules guarantee Cretin the 1st win, Cretin's high-water mark will be only about $101 to $103, because the game is rigged. Cretin's chances of winning remain at 1% per roll forever, whereas Randy's chances of winning get better and better as time goes on. Inevitably, no matter how much money Cretin starts with, Randy will have it all. Even if we vastly reduce Randy's chances by, say, modifying Rule #4 to require Randy alone to roll Master List numbers twice in a row to win, the game is still rigged, and -- over a much longer and more tedious game -- Randy will still get all the money.
This is the way Evolution works. Every roll of the dice is governed by pure chance. But, once the game hits on a winner, it STAYS a winner ever afterward (given a constant environment, which the rules of the game provide). The effects are cumulative. It may take a long, long time for Randy to win ALL of the money (the equivalent of coming up with a whole new species thru a series of tiny incremental changes), but it's as inevitable as the sunrise.
After awhile, you'd think that even the Cretins of the world would realize that the game is rigged.
Teachers:
Excellent game dice available at http://www.chessex.com/.
Monopoly money available at http://www.boardgames.com/monopolym
= = = = = =
Creationism: the theory that Rome WAS built in a day.
