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
In what follows, “making more than $x” means having a net gain of more than $x; “losing more than $x” means having a net gain of less than -$x.
Pick all that are correct.
1-The chance of coming out ahead is greater with strategy A than with strategy B.
2-The chance of making more than $20 is greater with strategy A than with strategy B.
3-The chance of losing more than $20 is greater with strategy A than with strategy B.
Select all options.
I checked already.
To compare the two strategies, we need to calculate the expected outcome for each of them.
For strategy A (betting on a split):
- The bet pays 17 to 1, which means that for each winning bet, you gain $17 and for each losing bet, you lose $1.
- There are 2 chances in 38 to win, so the probability of winning is 2/38 and the probability of losing is 1 - 2/38 = 36/38.
- Betting $1 for 200 times independently means you are risking a total of $200.
To calculate the expected outcome of strategy A, we can multiply the probabilities with the respective gains/losses:
Expected outcome of strategy A = (2/38 * $17) + (36/38 * -$1) = -$0.1053 per bet
For strategy B (betting on red):
- The bet pays 1 to 1, which means that for each winning bet, you gain $1 and for each losing bet, you lose $1.
- There are 18 chances in 38 to win, so the probability of winning is 18/38 and the probability of losing is 1 - 18/38 = 20/38.
- Betting $1 for 200 times independently means you are risking a total of $200.
Expected outcome of strategy B = (18/38 * $1) + (20/38 * -$1) = -$0.0053 per bet
Now let's analyze the given statements:
1- The chance of coming out ahead is greater with strategy A than with strategy B.
No, the expected outcome of strategy A is -$0.1053 per bet, which means you are likely to lose money over time. Strategy B has a smaller expected outcome of -$0.0053 per bet, indicating a slightly better chance of coming out ahead.
2- The chance of making more than $20 is greater with strategy A than with strategy B.
No, since strategy A has a negative expected outcome of -$0.1053 per bet, it is unlikely to make more than $20. Strategy B has a better chance of making more than $20 because it has a smaller negative expected outcome.
3- The chance of losing more than $20 is greater with strategy A than with strategy B.
Yes, since strategy A has a larger negative expected outcome, it is more likely to result in a net loss of more than $20 compared to strategy B.
Therefore, the correct statements are:
- The chance of losing more than $20 is greater with strategy A than with strategy B. (Statement 3)