Infinity insurance st petersburg Videos

By the way, here's what I got in my computer simulation. I did 100 000 tosses. The number of heads 1 time in a row - 12 439, 2 times in a row is 6246, 3 times - 3174, 4 times - 1605, well you get the idea.

That's what the probability is, which is basically the relative frequency "in the long run", that is when N goes to infinity. That is why the probability of getting let say heads is 1/2, beacause when you throw a coin an infinite number of time the relative frequency goes to 1/2, but you never get this number when you throw a coin a finite number of times. Anyway you can see for yourself what the probability of getting x heads in a ROW actually is if you do a computer simulation of tossing a coin. Just count how many heads you get, lets say, two times in a row and devide it by the total number of tosses. You'll see that this ratio will be about 4 times lower that your formula predicts, it'll be about 0,0625, rather than 0,25. 

The P(H=x) given here is the probability of getting x heads in a ROW. So if the chance of getting one head is 1/2 the chance of getting two heads is 1/4 and so on. This would be more obvious if you draw a tree diagram. The equation n=P*N doesn't actually hold unless you repeat the experiment a large amount of times (i.e as N approaches infinity). This is the reason why if you were to get two tails in two coin tosses you cannot conclude that P=0.

Quick question, how did we know to choose log($)?

I have a python script at sdrv.ms/180eSjz. My plot shows that you need ~1 mln games to have average revenew of 10 and about 10 times more games to increase your average income +1. That is, you need exponentially more time for the lower frequencies to appear. The lower frequencies contribute as any other higher frequency but you cannot expect them to occur in just few games.

very cool, where can I download the excel spreadsheet itself?

Thank you for uploading this!