That depends on how much money your bet affects each time. If the first wake up only affects 1 penny and the second wake up affects 1 dollar, betting something much closer to 1⁄2 becomes optimal.
If a non-negligible amount of money is at stake only for Tuesday bets, then it’s obvious that you should bet on Tails, since Tuesday bets exist only when the coin lands Tails.
One can come up with a variety of betting scenarios, but for all the ones I’ve seen, you get the correct decision regarding what odds offered would give good bets only if you think the probability of Heads is 1⁄3. You do have to be sure you’re doing the decision theory correctly, though, accounting for the mechanism of the bets.
You don’t know that it is Tuesday though (and therefore don’t know how much money is affected by decision, unless the consequences for Monday and Tuesday are the same).
What you do on Mondays doesn’t matter (let’s simply life by assuming nothing is at stake on Monday, rather than a negligible amount). So you can assume it’s Tuesday for decision making purposes.
That depends on how much money your bet affects each time. If the first wake up only affects 1 penny and the second wake up affects 1 dollar, betting something much closer to 1⁄2 becomes optimal.
If a non-negligible amount of money is at stake only for Tuesday bets, then it’s obvious that you should bet on Tails, since Tuesday bets exist only when the coin lands Tails.
One can come up with a variety of betting scenarios, but for all the ones I’ve seen, you get the correct decision regarding what odds offered would give good bets only if you think the probability of Heads is 1⁄3. You do have to be sure you’re doing the decision theory correctly, though, accounting for the mechanism of the bets.
You don’t know that it is Tuesday though (and therefore don’t know how much money is affected by decision, unless the consequences for Monday and Tuesday are the same).
What you do on Mondays doesn’t matter (let’s simply life by assuming nothing is at stake on Monday, rather than a negligible amount). So you can assume it’s Tuesday for decision making purposes.