Someone offers to play rock-paper-scissors with me.
If I win I get $6. If I lose, I get $5.
Unfortunately, I’ve learned from experience that this person beats me at rock-paper-scissors 40% of the time, and I only beat them 30% of the time, so in expectation I lose $0.20 in expectation by playing.
My decision is set up as allowing 4 options: rock, paper, scissors, or “don’t play.”
This seems like a nice relatable example to me—it’s not uncommon for someone to offer to bet on a rock paper scissors game, or to offer slightly favorable odds, and it’s not uncommon for them to have a slight edge.
Are there features of the boxes case that don’t apply in this case, or is it basically equivalent?
I like the following example:
Someone offers to play rock-paper-scissors with me.
If I win I get $6. If I lose, I get $5.
Unfortunately, I’ve learned from experience that this person beats me at rock-paper-scissors 40% of the time, and I only beat them 30% of the time, so in expectation I lose $0.20 in expectation by playing.
My decision is set up as allowing 4 options: rock, paper, scissors, or “don’t play.”
This seems like a nice relatable example to me—it’s not uncommon for someone to offer to bet on a rock paper scissors game, or to offer slightly favorable odds, and it’s not uncommon for them to have a slight edge.
Are there features of the boxes case that don’t apply in this case, or is it basically equivalent?
>If I win I get $6. If I lose, I get $5.
I assume you meant to write: “If I lose, I lose $5.”
Yes, these are basically equivalent. (I even mention rock-paper-scissors bots in a footnote.)