Question

In roulette, the bet on a “split” pays 17 to 1 and there are 2 chances in 38 to win. The bet on “red” pays 1 to 1 and there are 18 chances in 38 to win. Compare the following two strategies:

A: bet $1 200 times (independently) on a split

B: bet $1 200 times independently on red
which are correct?

The chance of coming out ahead is greater with strategy A than with strategy B
The chance of making more than $20 is greater with A than B
The chance of losing more than $20 is greater with A than B

Answer 1

There's a brief explanation here http://openstudy.com/study#/updates/5187907fe4b05c6f7f0dca71

The attachment may be a little easier to follow.

Answer 2

Ok.
I checked - Right answer is: select all three options!
v The chance of coming out ahead is greater with strategy A than with strategy B
v The chance of making more than $20 is greater with A than B
v The chance of losing more than $20 is greater with A than B

Best Regards!

Answer 3

if somebody need help for homework 6 or 7 - i am ready to help.

Answer 4

@Oles, that is correct :)

A higher variance strategy will always have more chance of winning a lot or losing a lot, I know this from playing poker. I knew B and C would be true, just from experience, but it was nice to confirm it with working it out.

I didn't realize A would be true also, but I now understand why it is - higher variance gives more chance of coming out ahead over the short term, but over a long period of time, things would even out - both strategies are equal in the long term, since they both have the same expected value of -1/19 dollars per play.

Answer 5

Many thanks for the higher variance explanation, that is what was baffling me!
MeMeMe

Answer 6

No prob. The variance is basically a measure of how spread out the results can be - the higher the variance, the larger the spread in possible outcomes.

The reason is because when you win (rarely) with the high variance strategy, you win big, but you'll frequently lose your money, and can easily deviate far from break-even in the short term.

With the low variance strategy, you are more likely to win small (frequently), and lose less often, and thus aren't as likely to deviate as far from break-even (especially over the short term).

In the long term, both strategies in the question are exactly equal, but variance has more effect in the short term.