Dealer probability table

Me being interested in the "why" behind everything, my question is.. how do you calculate, for instance, P(17|2) for the dealer, assuming 6 deck S17? I tried Bayes, but it doesnt really help me.

Could anyone shed some light on this?

I'd think you'd need to create a tree of all the possible hole cards and hit cards, along with their probabilities. Then add up all the branches of the tree that lead to a 17. I'd think that a spreadsheet would be especially useful for doing this.

Meh, that is a whole lotta work. Guess I'll have to do that then.

Quote: PapaChubby

I'd think you'd need to create a tree of all the possible hole cards and hit cards, along with their probabilities. Then add up all the branches of the tree that lead to a 17. I'd think that a spreadsheet would be especially useful for doing this.

Yep. If you can live with an infinite deck assumption it can be done in Excel pretty easily.

And if I wanted to do it for a 6-deck? Would simulation be the best option?

Quote: Janner

And if I wanted to do it for a 6-deck? Would simulation be the best option?

It is an option, but I don't think it is required because of the 6-deck restriction. Let's say you're building the tree, and you're already on a branch which includes a two and jack for a dealer total of 12. You're building the branch which adds another two to the hand to make 14. For infinite decks, the probability assigned to this branch is 1/13. For six decks, the probability is 23/310. It'll take a little extra effort to build the tree for six decks vs. infinite decks, but its not prohibitive.