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I am in math heaven
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skrumgaer wrote
at 9:42 PM, Saturday September 1, 2007 EDT
New rules! New scoring! New math!.
The TAPL will still be around since Ryan is continuing to publish the percentage stats. (For those who are new, the TAPL is explained in a comment on my profile page). But what I am interested in right now is how much money (how many diamonds) is being generated in the system per game. Consider the very first game. It has seven players, each with 0 points. At the end of the game, first probably got about 20 points, second 5 points, and third broke even. The other four should have lost a total ot 25 points but since you are not allowed to go negative, the game results in a net 25 point increase in the money supply. Suppose the same seven players play a second game. The leader cannot go bust (since he has 20 points and the loss limit is 15)but it is possible for the second place player to go bust and it is likely that at least three of the five still at zero will lose points but have them restored. So the second game will contribute more to the money supply but not as much as the first game. Suppose the same players play a third game, fourth game, etc. Eventually all the players will have some finishes in the money. Homework assignment: Suppose the seven players are the only players in kdice and they keep playing games forever. What is the expected value of the total money in the system (the sum of all their diamonds)? Is it finite or infinite? |
Replies 1 - 4 of 4
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Elithrion wrote
at 10:46 PM, Saturday September 1, 2007 EDT Pfft.. obviously depends on the probability of victory. With an entirely equal probability of victory for each, it's finite (but entirely random, so theoretically, given enough time you could get arbitrarily large values), otherwise I'm pretty sure it's infinite.
Basically, as long as it's likely that the same people will lose over and over again, money will keep flowing in, while (if money in=money out, which it should) no money can ever flow out. Plus you basically have to get 1st to get anything, so it's rather likely that some people will never have points. Also, notably, in this system players at 0 are the only ones who generate new points in the game, meaning that points will have to trickle up the food chain to the high ranked players, meaning that we're likely to end up with increasingly large gaps between the points of leaders as their amount of points goes up. Just sayin'. Oh, also, this means that a chunk of the players will have to always end up on 0 since there aren't enough points around for them to scrounge as all the points flow upward (well, this last one isn't entirely mathematical, but I suspect it's the case. |
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Ryan wrote
at 12:00 AM, Sunday September 2, 2007 EDT With elo, were points generated by anyone other than new players? no.
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mugambo wrote
at 4:24 AM, Sunday September 2, 2007 EDT But with ELO, the scores were weighted against each other and it wasn't worth playing lower ranked players. The new system runs under a different economy.
As for the homework assignment, if they played forever, the expected total value would be infinite (don't ask me which one has it. Now if you were allowed to go under zero, that would be a mind bender... |
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skrumgaer wrote
at 4:25 AM, Sunday September 2, 2007 EDT Under elo, new points would have been generated by non-new players if their elo's were automatically reset to 1500 whenever they fell below it.
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