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What total do zero score players get when they lose if they play forever?
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skrumgaer wrote
at 3:12 PM, Sunday September 2, 2007 EDT
The thread "I am in math heaven" seems to be irretrievable so I will give the answer to the math homework I assigned there in this thread.
The question was, if there are only 7 players, and they play each other only, and they play forever, what will their average scores be? Will it be infinite? Answer: Infinity, yes. I don't have the math skills to work it out directly, but I set up a simpler problem on a spreadsheet. Suppose you flip a fair coin over and over. For each head, you gain one point, for each tail, you lose one point, but if your total score falls below zero, it is restored to zero. I ran this for 12,000 iterations on a spreadsheet and found that you have a positive score about 98 percent of the time. So every 50th toss, on average, you will go into negative territory and be given one point. So, your score will roughly be 200 points for every 10,000 interations. In other words, unbounded. In kdice, will the average player have a positive score 98 percent of the time? It remains to be seen. |
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Boomshank wrote
at 6:21 PM, Sunday September 2, 2007 EDT Skrumager - I think the mistake you've made is that you've taken a position (everyone being equal at zero) and then extrapolated that situation into infinity.
In reality, what's happening is that when someone loses that has a zero score, a point is given from the 'bank' because their score can't fall below zero. As more and more points are added to this closed system, the chances of someone losing that has zero points becomes less and less. Unless I'm reading this all wrong. |
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skrumgaer wrote
at 6:41 PM, Sunday September 2, 2007 EDT It's not a mistake...it's the problem at hand. "If they play forever".
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Elithrion wrote
at 7:12 PM, Sunday September 2, 2007 EDT It's kinda sad that you both don't understand the distinction between "infinite" and "arbitrarily large" (or choose to ignore it), and can't even understand (or possibly just read correctly) Boomshank's argument.
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skrumgaer wrote
at 8:04 PM, Sunday September 2, 2007 EDT I think that the expression "arbitrarily large" refers to the domain of a value, not the value itself. Since I didn't use it, I don't have to defend it.
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Tommen wrote
at 8:24 PM, Sunday September 2, 2007 EDT Boomshank, it doesn't matter. Yes it takes longer for people to go bankrupt when there is so much wealth to spread around, but it is a theorem that someone will always, eventually go bankrupt. Over infinitely many games the bank will pay out an infinite amount of points.
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integraI wrote
at 11:29 PM, Sunday September 2, 2007 EDT where's my sandwich when I need it.
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SodaPop wrote
at 6:30 AM, Monday September 3, 2007 EDT Soda speaks.
7 players play forever. the amount of real points after each game can only go UP or Remain stationary therefore dont listen to skrumager |
