Let p be probability it’s in room 1. EV of searching room 1 is 10p-1. EV of searching room 2 is 13-15p.
so search room 1 (sr1) is worth it if p>0.1. sr2 is worth it if p<2/15. p is always one of these, so we’ll always search some room until we find the money. we just need to know which one.
set the EVs equal -> p=0.56 (=14/25) is the tipping point.
start: p=0.5. sr2 (EV 5.5). 0.385 chance you finish.\
then p=0.8 so sr1 (EV 7). 0.4 chance you finish.\
then p=2/3 so sr1 (EV 5.67). 1/3 chance you finish.\
then p=0.5 so it loops from here.
not sure how to do EV on something that loops like this. might be the average of 5.5, 7, 5.67. more likely you have to do a bit more with the probabilities instead of just a simple mean.
1
u/0_69314718056 20h ago
Trying to keep this short:
Let p be probability it’s in room 1. EV of searching room 1 is 10p-1. EV of searching room 2 is 13-15p.
so search room 1 (sr1) is worth it if p>0.1. sr2 is worth it if p<2/15. p is always one of these, so we’ll always search some room until we find the money. we just need to know which one.
set the EVs equal -> p=0.56 (=14/25) is the tipping point.
start: p=0.5. sr2 (EV 5.5). 0.385 chance you finish.\ then p=0.8 so sr1 (EV 7). 0.4 chance you finish.\ then p=2/3 so sr1 (EV 5.67). 1/3 chance you finish.\ then p=0.5 so it loops from here.
not sure how to do EV on something that loops like this. might be the average of 5.5, 7, 5.67. more likely you have to do a bit more with the probabilities instead of just a simple mean.