I played 190 spins at a roulette table.... 3 vs 4 which number is better? Law of large..

[d_u_guy]

...number test? we are testing the law of large numbers, after 5 sets of 38 spins which = 190 spins total only one number never came 3, and the number 4 came up the most..... Which numbers is better to play 3 or 4?
we are testing the law of large numbers, after 5 sets of 38 spins which = 190 spins total only one number never came 3, and the number 4 came up 8 times the most..... Which numbers is better to play 3 or 4?

 

[efqy]

There are two possibilities: *either* the table is effectively fair (i.e. where the differences in probability are far too small to be picked up by such a small sample size), or the table is unfair enough to be picked up by a small sample. SInce casinos invest a lot of effort in making the outcomes equally likely (anything else compromised the profits), the first is generally a good bet.

In either of the above two possibilities, there's no reason to choose 3 over 4 (either 4 is equally as good, or 4 is better).


If you're interested in whether or not there's enough evidence to conclude 4 is actually better, the question you need to consider a question like "in 190 spins of a fair wheel, could the difference between the most and least frequent outcomes reasonably be at least as big as 8?"

So you calculate the probability of a difference of 8 or more between the most and least frequent categories in 190 spins.

If that probability is small (considering the costs of the two types of error in order to determine how small is "small"), you conclude that the wheel is not fair in the sense that 4 is really more likely than 3.