Quote:
Originally Posted by Zorkman
I offer to bet $200 as follows:
I pay you $200 by September 17, 2017 if you do all of the following and promptly provide proof at each step of the way:
--Register for the SAT by July 28, 2017.
--Take the August 26, 2017 SAT.
--Receive on or about September 15, 2017 a score of 800 on the math section of that SAT.
You pay me $200 by September 17, 2017 if you fail to complete timely the above set of tasks.
Settlement via Paypal.
I have never welched on a bet.
This offer expires 48 hours from the timestamp on this post or when I revoke it, whichever happens first.
I will decline this.
I'm not too sure what my probability of scoring an 800 would be if I did this, although I'm fairly confident 25% < probability < 75%. Every question would be a question I should get correct, but there is always the possibility of making dumb mistakes, and there are a lot of questions (FWIW I got 780 on the quantitative section of the SAT when I took it in HS).
However, even if we assume the very high end of that range I think this bet is -EV for me because:
1. We have to discount the fact that any procedural error, or something that comes up on August 26, or any other failure to take the test seems to throw the contest to you. I will estimate this probability at 5%.
2. I would be out the test fee of $45, plus transportation to the test center, so we will say $55 total.
3. I would need to study a little as I believe there is geometry on the test and I forget a lot of it, and I would probably want to brush up on a couple other things if there is any way of getting the probability up to 75%. We'll say this takes 4 hours.
4. I need to spend ~5 hours taking the test (and travelling to it, etc.)
Basically my EV here is (assuming high end of 800 probability range)
= $200*(.75)*(.95) - $200*(1-.75*.95) - $55 - x + (.75)*(.95)*y1 + (1-.75*.95)*y2
= $30 - x + .7125*y1 + .2875*y2
where x = the value of 9 hours of my time
y1 = the utility I get from the satisfaction of knowing I win
y2 = the utility I lose from the embarrassment of knowing I lost
I'm not exactly sure how to value my time, but I've come up with a heuristic and I'll say that 9 hours of it on a day off is worth $200.
So we are at
EV = -$170 + .7125*y1 + .2875*y2
If EV is to be > 0, then .7125*y1 + .2875*y2 > 170.
Unfortunately I do not derive that much pleasure from winning this bet so that inequality is unlikely to hold.
Thanks for reading.
Last edited by TiltedDonkey; 06-23-2017 at 11:55 AM.
Reason: I highly doubt EV(writing this post) > 0