A semi-technical question about prediction markets and private info

There ex­ists a 6-sided die that is weighted such that one of the 6 num­bers has a 50% chance to come up and all the other num­bers have a 1 in 10 chance. No­body knows for cer­tain which num­ber the die is bi­ased in fa­vor of, but some peo­ple have had a chance to roll the die and see the re­sult.

You get a chance to roll the die ex­actly once, with no­body else watch­ing. It comes up 6. Run­ning a quick Bayes’s The­o­rem calcu­la­tion, you now think there’s a 50% chance that the die is bi­ased in fa­vor of 6 and a 10% chance for the num­bers 1 through 5.

You then dis­cover that there’s a pre­dic­tion mar­ket about the die. The pre­dic­tion mar­ket says there’s a 50% chance that “3” is the num­ber the die is bi­ased in fa­vor of, and each other num­ber is given 10% prob­a­bil­ity.

How do you up­date based on what you’ve learned? Do you make any bets?

I think I know the an­swer for this toy prob­lem, but I’m not sure if I’m right or how it gen­er­al­izes to real life...