Roulette Maths Help Please
December 28th, 2015 at 3:36:19 PM
permalink
Hi everyone
Can some one with more maths ability than me please tell me how many repeats numbers
can be mathematically expected to occur within 300 spins of a fair European Roulette wheel.
Thanks in advance
Pando
Can some one with more maths ability than me please tell me how many repeats numbers
can be mathematically expected to occur within 300 spins of a fair European Roulette wheel.
Thanks in advance
Pando
December 28th, 2015 at 4:30:43 PM
permalink
Assuming you mean how many times in 300 spins will the number be the same as the previous number:
If you limit it to 1 spin, it's 36/37 x 0 + 1/37 x 1 = 1/37
If you limit it to 2 spins, it's (the number expected in the first 2) + (the number expected in the next 1)
= 1/37 + (36/37 x 0 + 1/37 x 1) = 2/37
And so on, so the number expected in 300 spins is 300/37, or about 8.108.
Of course, if the first 292 spins have zero repeats, this does not mean the next 8 will all be repeats, or that any particular repeat will be any more likely. On a European Roulette wheel, the probability that a particular spin's number will be the same as the previous number is always 1/37.
"Mathematically expected to occur" and "actually occurring" are two entirely different things - otherwise, the following system would work every time:
(a) Watch the wheel for 36 spins.
(b) Since every number from 0 to 36 is "mathematically expected to occur" once in every set of 37 consecutive spins, bet on the number that hasn't come up yet.
(c) On the spin after that, the number that came up 36 spins earlier has to come up again - otherwise that number will not have been in the most recent set of 37 spins. (For example, if the numbers 0 through 36 come up in order, the next spin "has to be" 0, as otherwise 0 will not have come up in the set of 37 spins that started with the second spin.)
Of course, if this was true, then the expected number of repeat numbers would be zero, as a set of 37 spins would not have every number appear once if a number appeared twice in a row.
If you limit it to 1 spin, it's 36/37 x 0 + 1/37 x 1 = 1/37
If you limit it to 2 spins, it's (the number expected in the first 2) + (the number expected in the next 1)
= 1/37 + (36/37 x 0 + 1/37 x 1) = 2/37
And so on, so the number expected in 300 spins is 300/37, or about 8.108.
Of course, if the first 292 spins have zero repeats, this does not mean the next 8 will all be repeats, or that any particular repeat will be any more likely. On a European Roulette wheel, the probability that a particular spin's number will be the same as the previous number is always 1/37.
"Mathematically expected to occur" and "actually occurring" are two entirely different things - otherwise, the following system would work every time:
(a) Watch the wheel for 36 spins.
(b) Since every number from 0 to 36 is "mathematically expected to occur" once in every set of 37 consecutive spins, bet on the number that hasn't come up yet.
(c) On the spin after that, the number that came up 36 spins earlier has to come up again - otherwise that number will not have been in the most recent set of 37 spins. (For example, if the numbers 0 through 36 come up in order, the next spin "has to be" 0, as otherwise 0 will not have come up in the set of 37 spins that started with the second spin.)
Of course, if this was true, then the expected number of repeat numbers would be zero, as a set of 37 spins would not have every number appear once if a number appeared twice in a row.
