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landmark Inner circle within a triangle 5194 Posts |
As long as there are a finite number of flips, any distribution of heads and tails might occur. Some of those distributions (such as all heads and no tails) are highly unlikely. But by definition, the "luckiest" and "unluckiest" people in the world are precisely those who flip and happen to get unusual distributions.
Or to put it another way--if we knew nothing else about the two players, then in the long run, the distribution of heads and tails would be even. But we do know something about the two players--they are the luckiest and unluckiest players in the world. Note I'm not referring to their past reputations--because that does not affect their present throws (although in the real world it does, but I won't get into that now)--but if indeed they are the essence of lucky and unlucky, then we can expect anomalies.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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LobowolfXXX Inner circle La Famiglia 1196 Posts |
There are actually two issues in play; one I've brought up, and the other I haven't. Here's the one I haven't mentioned - the greater the number of trials, the more the percentage of heads vs. tails flattens out (NYC Twister's point). Granted. However The expected difference between the number of heads and tails doesn't flatten out - it spreads out.. And in the example where one guy is paying the other, that's the number we care about - how much is guy X going to pay guy Y. That number INCREASES with additional trials. For instance, if they flip the coin ten times, the loser will pay the winner two dollars or they'll break even almost 2/3 of the time (6-4 or 5-5 just over 65% of the time). HOWEVER, if they flip it twenty times, the loser will probably (just over 50%) pay the winner three dollars or more. And so on.
Getting back to what I was saying last night - I was defining the unluckiest person as the one who loses the most on the coin flip. Let's call the amount the loser loses the "swing." - that's the difference between the number of heads and the number of tails. What I was saying is this - let's say I call myself the luckiest man in the world. I flip the coin a hundred million times against everyone in the world. I start against you: we flip a hundred million times, and we call the difference "swing one.". Then I flip a hundred million times against Landmark, and we call the difference "swing two.". And so on, up to "swing 7 billion and change.". The person with the greatest negative swing is by my definition the unluckiest person in the world - he lost more than anyone else on a series of coin flips. What I was saying is, flipping 7 billion different sets is going to produce in the most extreme case a much greater difference than in one random set. For instance, going back to ten-flip sets, if I flip a coin ten times, the most likely result is 6-4 one way or the other. But I flip a coin ten times against everyone in Los Angeles ((let alone the world), I'm not going to get out of the first city before I find an "unluckiest man in Los Angeles" who goes 0-10. So if we define "unluckiest" a posteriori, then the 7 billion = more flips and a bigger swing. If we define "unluckiest" a priori, the. Yes, we have only one set of a hundred million, and the seven billion isn't a factor. However, we still have the first issue: more flips = bigger (absolute) swing, not smaller.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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LobowolfXXX Inner circle La Famiglia 1196 Posts |
To put it another way, if you were a gambling addict with five dollars in your pocket and you going to bet against a mafia guy who would break your legs if you didn't pay, would feel safer agreeing to a 10-flip set or a 100-flip set?
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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NYCTwister Loyal user 267 Posts |
The variance shrinks the greater the number of flips, and will do so regardless of whether a person considers themselves lucky or not.
They pay the difference after all the flips are finished.
If you need fear to enforce your beliefs, then your beliefs are worthless.
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LobowolfXXX Inner circle La Famiglia 1196 Posts |
The disparity between the number of heads and tails increases the greater the number of flips. 13-17 or worse is more likely than 3-7 or worse. It's only the percentage of flips that gets closer to 50-50 with more iterations, not the number of flips.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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NYCTwister Loyal user 267 Posts |
Two people, one the luckiest, one the unluckiest flip a coin for a predetermined, large number (10,000,000) of times. They pay at the end of all the flips. According to you the difference between the heads and the tails increases the greater number of flips?
If you need fear to enforce your beliefs, then your beliefs are worthless.
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LobowolfXXX Inner circle La Famiglia 1196 Posts |
Correct.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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LobowolfXXX Inner circle La Famiglia 1196 Posts |
This is pretty easy to see on a small scale. If they flip twice, it's 50-50 that they'll be dead even. If they flip 4 times, it's 37.5% that they'll be dead even. If they flip six times, it's 31.25% they'll be dead even. You think there's a realistic chance they'll be dead even after a hundred million flips?
On the other end of the scale, a difference of 20 is extraordinarily unlikely after twenty flips. After a hundred million flips, who would be surprised if someone was +20? And so on. More flips = wider spread. It's only the percentage that gets closer and closer to 50-50. Two guys flip ten times; two others flip a thousand times. The second pair is more likely to be closer to 50-50. But they're also more likely to have one guy owe the other more money than the first pair.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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landmark Inner circle within a triangle 5194 Posts |
Quote:
On Mar 31, 2014, NYCTwister wrote: Ah, but it's not about whether they consider themselves lucky, we were *told * (by some omniscient force) that one of them was lucky. Otherwise, what Lobo said.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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