Which of these wagers would you be most comfortable making?
I have 3 sets of dice giving different odds. Let’s say once a week for the rest of the year a portion of your paycheck will be taken out and granted to a forest elf named Griffy. Which set of dice do you wish Griffy to roll? (all profits return to you)
A. Risk $10 – with a 31% chance of making a profit of $20
B. Risk $20 – with a 47% chance of making a profit of $20
C. Risk $40 – with a 63% chance of making a profit of $20
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16 Answers
I’ll take C, thank you very much.
C. That is rather a silly question.
Are you studying risk assessment, by any chance?
Mathematical analysis time!
Option A-
69% lose $10
31% gain $20
Expected profit-
0.69*(-10) + 0.31*(20) = -$0.70
Option B-
53% lose $20
47% gain $20
Expected profit-
0.53*(-20) + 0.47*(20) = -$1.20
Option C-
37% lose $40
63% gain $20
Expected profit-
0.37*(-40) + 0.63*(20) = -$2.20
I would choose option A.
This explains why I stay away from forest elves.
I know that I go big or go home…..
Once again, I’m glad to be a sailor.
A. I’m not one much for gambling and $40 is a lot of money to me at this point in my life.
C.
I’m a risk taker, and if you’re going to risk, risk big I say!
Hmmm. i used math too but got a different answer. Why?
Normalize them all to a 10 bet and multiply the odds of winning x the payoff.
A 31% x 20 = 6.20
B 47% x 10 = 4.70
C 63% x 5 = 3.15
Now subtract the losing side.
A 69 % x 10 = 6.90
B 53% x 10 = 5.30
C 37% x10 = 3.70
A= 6.20–6.90 = -0.70
B=4.70–530= -0.80
C = 3.15 -3.70=.-0.55
C is best.
All best are negative.
As Joshua said “What a strange game. The only winning move is not to play.”
I know why we got different answers. You calculated which choice is fairest (smallest house edge). I calculated which was the best in terms of total losses with the given bet size. Even though C may have the smallest house edge, you lose more money in the end because you are forced to bet more.
@PhiNotPi Yep. I agree with your analysis. My method showed which bet was the best rate of return. But that was not the question. The OP wants to know which of the 3 bets to pick. Your answer is correct.
If I had $40 to bet, would go with four $10 wagers over one $40 wager.
But given my past history with elves, I would whack Griffy over the head with a cold iron mace and take his or her dice.
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