Probability Question

[Sean81]

I have a general probability question for those in the know that is mostly conceptual in nature.

Suppose three people, A,B, and C are competing for a prize that will be determined based on a lottery format. For whatever reason, it is determined that person A should have a 50% shot at the prize and persons B and C 25% each respectively. Two lottery formats are given in which person A gets to choose. 100 balls numbered 1-100 and half of the numbers represent player A, and one is drawn, or a 0-9 format drawing system with 10000 unique 4 digit numbers in which half represent player A.

My argument is player A should always choose the first format because even though the win rate over time is equal either way, the variance around the expected 50% win rate is larger in the second scenario over smaller sample sizes.

Is this logic correct?

Thanks

[sharpcat]

I think the second option is better because of the variance, whereas if you have a 50% chance of winning compared to their 25% 4 draws is going to benefit you more than 1 draw.

[noober]

I don't see why there should be any difference.

[sharpcat]

This is a matter of preference no matter what you have a 50% chance and they have a 25% chance my first post misunderstood the question.

[Grind-It-Out]

What's a 0-9 format drawing system?

[Sean81]

Thanks for the responses. In the second scenario, think of a lottery where all of the balls are numbered 0-9 and 4 are drawn, thus making 10000 unique combination's. sorry for the confusion

[Grind-It-Out]

There is zero difference if only one number (or one sequence of numbers in the second example) is being pulled. Both have exactly a 50% likelihood of happening, and variance is a non-issue.

[thebayareabeast]

variance does not exist here.