A brain teasing probability puzzle

btw if someone knows how to calculate the average payout I'd like to see it. I think it'd be a summation from 1->infinite with x^2 and 0.5 mixed in but I don't really know how to do it.

Szlia_sl said:

Did you run it just the once? I would expect avgVal to be all over the place considering the expected result is infinite and the deviation not a lot smaller.

expectedResult = (1/2)*1 + (1/4)*2 + (1/8)*4 + ... + (1/2^n)*2^(n-1) + ...

since (1/2^n)*2^(n-1) = (2^(n-1))/(2^n) = 1/2 expectedResult does not converge.


As to the question of whether or not a casino would run such a lottery... just imagine Loki is running the casino as a practical joke or something and that he is creating money out of thin air.

Click to expand...

I ran it 100000000 times (literally, check out the while(i<100000000) { } statement, that's C++ code for "Run this shit 100000000 times bro" as long as you're increasing i each time it goes through.)

Szlia_sl said:

A good sign rand() is fubared is that you getexactlythe same results as Tuco at the 100000000 mark even though the values are not converging.

Click to expand...

Hehe, that's exactly how rand() is supposed to work, it's not fubared.

fromrand - C++ Reference
This number is generated by an algorithm that returns a sequence of apparently non-related numbers each time it is called. This algorithm uses a seed to generate the series, which should be initialized to some distinctive value using function srand.

This means that if you seed it with the number 5 and call it a 1000 times it will return the same 1000 numbers. This makes it very useful for certain simulations (Because you can have a semi-random but repeatable simulation).

If you want some more random you can seed it with a different number before you start calling it. Giving it a timestamp is popular because you'll never give it that seed again:
srand (time(NULL));

You could also hash the time() value if you're afraid it won't properly cast to unsigned int, you could use the C++ random (- C++ Reference) and there's probably other random libraries to use.


output:
avgVal:[11.69] avgIt:[ 2.00] max:[ 8388608] maxTimeToTails:[ 24]
avgVal:[15.24] avgIt:[ 2.00] max:[ 16777216] maxTimeToTails:[ 25]
avgVal:[11.55] avgIt:[ 2.00] max:[ 8388608] maxTimeToTails:[ 24]
avgVal:[12.51] avgIt:[ 2.00] max:[ 8388608] maxTimeToTails:[ 24]
avgVal:[10.95] avgIt:[ 2.00] max:[ 4194304] maxTimeToTails:[ 23]
avgVal:[11.17] avgIt:[ 2.00] max:[ 8388608] maxTimeToTails:[ 24]
avgVal:[12.16] avgIt:[ 2.00] max:[ 8388608] maxTimeToTails:[ 24]
avgVal:[14.22] avgIt:[ 2.00] max:[ 16777216] maxTimeToTails:[ 25]
avgVal:[13.13] avgIt:[ 2.00] max:[ 8388608] maxTimeToTails:[ 24]
avgVal:[13.18] avgIt:[ 2.00] max:[ 8388608] maxTimeToTails:[ 24]


Now the reason why you see so much variance in these is because it's sort of emulating a lottery. If you were look at the counts of who won what times you'd probably see very few at the high end.

I couldn't help myself:
Note that those win counts are over all ten games. So in one game that guy that won 24 times skewed the whole fucking result a bunch. If he didn't win that time it'd be way over.

Another cool observations that are intuitive if you think about it is each win count is roughly twice that of the next win count. So 5million suckers lost their first time, but only 2.5 million suckers lost their second time. And if you were to tabulate up the people who didn't lose their first time you'd get 5 million people! This is pretty basic stuff but if you're a nerd it's a little beautiful.

Theoretically if you increased the thing to run for a very long time (overnight etc) in most random systems you'd see them settle around a number. However because the payout increases exponentially this game is very resilient to that. If you were to cap the maximum to 10-20 you'd probably see things stabilize much more.

Here's a max of 15:
funs over, time to get some real work done

Tuco_sl said:

This means that if you seed it with the number 5 and call it a 1000 times it will return the same 1000 numbers. This makes it very useful for certain simulations (Because you can have a semi-random but repeatable simulation).

If you want some more random you can seed it with a different number before you start calling it. Giving it a timestamp is popular because you'll never give it that seed again:
srand (time(NULL));

Click to expand...

No wonder I keep getting the same Minecraft maps!

Put a cap on the # of flips you get and the game could be very profitable for casinos. It's a very basic gambling game though, and the odds are so plain that people would be harder to fool into various gambler's fallacies.

For those that follow NFL you'll know the NFC won 14 straight coin tosses:
Super Bowl 2013: Coin toss odds, tails is best bet - SBNation.com

You're right. Any other HOS candidates? I really haven't felt like any threads have met the bar.

You mean HoF