Also, I think Sam's "sure-thing" bet gets him $30, not $31? Your point still holds—$30 is more than $23.50 by a good bit—but it's not quite as stark as $31 vs. $7.50.
In your improved bet, Sam pays ($1) and ($1) to the two bettors and ($65) to Asher. The losing bettor will lose $97 in total ($98 paid to the winner offset by Sam's $1) and so Asher pays Sam $97. $97 - $65 -$1 - $1 = $30, not $31. I'm sure I've made a dumb mistake but that's how it looks to me.
> Doing so would bring his net losses for the day from $99 to $65,
> violating the proposition that the max intern loss is $99
Could Sam and Asher reasonably have disagreed about the terms of the contract?
This post reads the contract as self-referential, i.e. the maximum intern losses must be computed in a way that includes the contract payout. But one could imagine reading the contract otherwise, i.e. that it should pay out the maximum amount lost by any intern *prior* to the contract paying out.
Maybe the first reading is obviously the correct one for some reason.
> The EV of Sam’s trade is thus (0.5 × $97) – (0.5 × $82) = $7.5.
Expanding on this, if Sam loses the coin flip, his accounting is as follows:
($65) to Asher for the contract
($1) to the other intern for the coin-flip bet
($98) loss to the other intern on the coin-flip bet
$82 paid by Asher to make Sam's loss the greatest intern loss, i.e. $82
Grand total: Sam loses ($82)
But if Sam wins the coin flip his accounting is as follows:
($65) to Asher for the contract
($1) to the other intern for the coin-flip bet
$98 win from the other intern on the coin-flip bet
$97 paid by Asher because the intern who lost the coin flip lost $97
Grand total: Sam wins $129
So why isn't Sam's EV (½ 𐄂 $129) - (½ 𐄂 $82) = $23.50?
Also, I think Sam's "sure-thing" bet gets him $30, not $31? Your point still holds—$30 is more than $23.50 by a good bit—but it's not quite as stark as $31 vs. $7.50.
In your improved bet, Sam pays ($1) and ($1) to the two bettors and ($65) to Asher. The losing bettor will lose $97 in total ($98 paid to the winner offset by Sam's $1) and so Asher pays Sam $97. $97 - $65 -$1 - $1 = $30, not $31. I'm sure I've made a dumb mistake but that's how it looks to me.
> Doing so would bring his net losses for the day from $99 to $65,
> violating the proposition that the max intern loss is $99
Could Sam and Asher reasonably have disagreed about the terms of the contract?
This post reads the contract as self-referential, i.e. the maximum intern losses must be computed in a way that includes the contract payout. But one could imagine reading the contract otherwise, i.e. that it should pay out the maximum amount lost by any intern *prior* to the contract paying out.
Maybe the first reading is obviously the correct one for some reason.
> The EV of Sam’s trade is thus (0.5 × $97) – (0.5 × $82) = $7.5.
Expanding on this, if Sam loses the coin flip, his accounting is as follows:
($65) to Asher for the contract
($1) to the other intern for the coin-flip bet
($98) loss to the other intern on the coin-flip bet
$82 paid by Asher to make Sam's loss the greatest intern loss, i.e. $82
Grand total: Sam loses ($82)
But if Sam wins the coin flip his accounting is as follows:
($65) to Asher for the contract
($1) to the other intern for the coin-flip bet
$98 win from the other intern on the coin-flip bet
$97 paid by Asher because the intern who lost the coin flip lost $97
Grand total: Sam wins $129
So why isn't Sam's EV (½ 𐄂 $129) - (½ 𐄂 $82) = $23.50?
"Doing so would bring his net losses for the day from $99 to $65, violating the proposition that the max intern loss is $99"
???
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