This is not code golf. I'm looking at an interesting problem and hoping to solicit comments and suggestions from my peers. This question is not about card counting (exclusively), rather, it is about determining the best table to engage based on observation. Assume if you will some kind of brain implant that makes worst case time / space complexity (on any given architecture) portable to the human mind. Yes, this is quite subjective. Assume a French deck without the use of wild cards.
I recently visited a casino and saw more bystanders than players per table, and wondered what selection process turned bystanders into betting players, given that most bystanders had funds to play (chips in hand).
You enter a casino. You see n tables playing a variant of Blackjack, with y of them playing Pontoon. Each table plays with an indeterminate amount of card decks, in an effort to obfuscate the house advantage.
Each table has a varying minimum bet. You have Z currency on your person. You want to find the table where:
- The least amount of card decks are in use
- The minimum bet is higher than a table using more decks, but you want to maximize the amount of games you can play with Z.
- Net losses, per player are lowest (I realize that this is, in most answers, considered to be incidental noise, but it could illustrate a broken shuffler)
You can magically observe every table. You have X rounds to sample, in order to base your decision. For this purpose, every player takes no more than 30 seconds to play.
What algorithm(s) would you use to solve this problem, and what is their worst case complexity? Do you:
- Play Pontoon or Blackjack ?
- What table do you select ?
- How many rounds do you need to observe (what is the value of X), given that the casino can use no more than 8 decks of cards for either game? Each table has between 2 and 6 players.
- How long did you stand around while finding a table?
I'm calling this the "standing gambler problem" for lack of a better term. Please feel free to refine it.
Where would this be useful if not in a casino?
I'm not looking for a magic gambling bullet. I just noticed a problem which became a bone that my brain simply won't stop chewing. I'm especially interested in applications way beyond visiting a casino.