I do wonder whether there is a strategy that would be preferable to an individual resident. Say that after you have 4 or more coins you always take 1 coin into a safe out of which you will not further bet but only buy medicine. And then on the first loss cash out. Even if we terminate at say 54, some people survive and it is not a total loss. But going full risk-neutral when we lose, we totally lose.
Stated another way. If you make full bets you obviously get faster to the condition of having saved everybody if you do. But given that you want to get to the state of having saved everyone what is the bet pattern that risks the least lives?
There’s definitely bet patterns superior to risking everything—but only if you’re allowed to play a very large number of rounds
If the pharmacist is only willing to play 10 rounds, then there’s no way to beat betting everything every round
As the number of rounds you play approaches infinity (assuming you can bet fractions of a coin), your chance of saving everyone approaches 1. But this takes a huge number of rounds. Even at 10,000 rounds, the best possible strategy only gives each person around a 1 in 20 chance of survival
I do wonder whether there is a strategy that would be preferable to an individual resident. Say that after you have 4 or more coins you always take 1 coin into a safe out of which you will not further bet but only buy medicine. And then on the first loss cash out. Even if we terminate at say 54, some people survive and it is not a total loss. But going full risk-neutral when we lose, we totally lose.
Stated another way. If you make full bets you obviously get faster to the condition of having saved everybody if you do. But given that you want to get to the state of having saved everyone what is the bet pattern that risks the least lives?
There’s definitely bet patterns superior to risking everything—but only if you’re allowed to play a very large number of rounds
If the pharmacist is only willing to play 10 rounds, then there’s no way to beat betting everything every round
As the number of rounds you play approaches infinity (assuming you can bet fractions of a coin), your chance of saving everyone approaches 1. But this takes a huge number of rounds. Even at 10,000 rounds, the best possible strategy only gives each person around a 1 in 20 chance of survival