Detecting an Unfair Die with Bayes’ Theorem | The Chemical Statistician

Detecting an Unfair Die with Bayes’ Theorem | The Chemical Statistician:

"An occasionally dishonest casino uses 2 types of dice.  Of its dice, 97% are fair but 3% are unfair, and a “five” comes up 35% of the time for these unfair dice.  If you pick a die randomly and roll it, how many “fives”  in a row would you need to see before it was most likely that you had picked an unfair die?”"

This is the same problem of identifying the correct regime that should use a Hidden Markov Model to detect which is the most likely.  This is the same problem that will seek to identify the state of the Minsky cycle by looking at the returns that are recorded in the carry trade.