I'm sorry, I was being lazy. I mean the expected number of rolls. ie. the sum of the product of the number of rolls and the probability of it taking that many rolls.
I have to think about that for a while. How does that "expected number of rolls" relate to the probability of a certain sequence, ie.
"what is the probability of getting a sequence of at least 11 losses when tossing a fair coin 4094 times?"I have a hunch it would be 50%, and it comes back to the bell-shaped distribution curve, but hunches in this area are often wrong.
but the conclusion is that it takes on average 4094 plays to get a sequence of 11 losses at 50% chance per loss.
This correction went unnoticed for me last round...so it's 4094 and not 2046.
Edit: weird because of the step in the graph. The probabilities that it will take 3 or 4 tosses to get 2 heads in a row are the same:
Yes, there is something that occurs to me mystical at that particular anomalous step
I find it weird when I look at it from another point of view: The probability of heads-heads sequence is 0.25, so you would need on average 4 sequences of 2 tosses.
x x first sequence
x x second sequence
x x third sequence
x x fourth sequence
12 34 5 toss number
4 sequences of 2 tosses can be obtained from 5 tosses total, not 6. Now, why is one of those sequences invalid so you need the extra toss?
I must digest your chart, Fibonacci and the Markov chains referred to in the other thread to get this clear.
In statistics and Quantum Mechanics (which also uses statistics heavily) common sense is useless. The human brain simply fails at understanding probabilities and large numbers.
That's very true. However with hard practise you can understand some of it up to very limited numbers (I'm attempting now the range 1 to 6
). The counter-intuitiveness is fascinating. I would like to craft a game designed around this 2-heads-in-a-row thing when I can understand it. Most people think it's only 4 tosses you need. Without using mathematics too much and through the practical example, I'd say it's 5, but even that is too low.
