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It would have been a better demo if reduced to more manageable numbers e.g. a deck of 2 black and 2 red cards. Turn 1 r = b so no bet Turn 2 bet 1/3 on whiche
by barbegal 2y ago
It would have been a better demo if reduced to more manageable numbers e.g. a deck of 2 black and 2 red cards.
Turn 1 r = b so no bet
Turn 2 bet 1/3 on whichever card wasn't revealed in turn 1.
Turn 3 either you were wrong on turn 2 and you now have 2/3 of your stake but you know the colour of the next two cards so you can double your stake each time to end up with 4/3 after turn 3 or you were right and you have 4/3 of your stake but have one of each red or black left so you don't bet this turn.
Turn 4 you know the colour of the final card so you double your money to 8/3 of your original stake.
And then the exercise to the reader is to prove optimality (which is fairly straightforward but I don't believe there is a short proof)
- stevage 2y agoAgreed, I could follow the general argument but not enough to be convinced about why the result is exactly the same regardless of the order of cards.
- libraryofbabel 2y agoYes. Although four cards has only one nontrivial branch, on turn 3. So, start out with the four cards example, and then show tree diagrams for the 5 and 6 cards cases (still manageable numbers) to build intuition for induction to the general case.
- deleted 2y ago[deleted]