Greets all,
Thanks to everyone for their input so far. :) I'd really like to avoid getting too bogged down in discussing whether I can calculate these odds or not (I've provided brief responses to Meerclar and Nick below, however, if you'd like to discuss probability matters related to this further, perhaps we can start another thread or do it via private message). What I think is truly interesting here is the challenge of programming something to calculate these addition combinations (I can't solve it in a parsimonious matter). So, for now, I'm hoping we can put aside a discussion whether our grasps of odds calculations are correct and discuss how this particular problem of getting the combinations can be solved. That's what I'm truly interested in.
Meerclar,
Thanks for the input on calculating odds.
Quote: You've already given a scanario thats almost impossible to calculate accurate odds on unless you have some way of knowing what the dealers face down card is because your counts will always be wrong for that card otherwise.
Actually, you can calculate the odds for this using conditional probability. ;) If you're unconvinced, I can provide an example, but that'll take a lot of writing and I'd like to save that time if you're willing to trust me on this.
Quote: Even if you do know, knowing the odds the dealer can beat your hand doesn't really help very much I'm afraid because you can only calculate the % chance of the dealer drawing a better hand based on the cards they currently have - once you're done hitting you can't update the odds again until the dealer is played out and by then it's too late.
Again, I very strongly believe that what I need re: calculatin odds can be achieved and I'd be willing to discuss this in another thread or privately).
Nick,
The problem with what you propose is I don't know if I need a 4 to "win." I think what you're getting at is, if I had 17 (thus needing a 4 to get to 21), I could calculating the odds of me getting a 4, 3, 2 or ace v.s. the odds of me getting something bigger than that (and busting).
However, there's more to it than that. Sometimes the odds of me hitting and busting are large, but the odds of the dealer beating my hand (by flipping her hole card and hitting as needed)without busting if I stand is even greater. In a situation such as this, it's a better bet to hit than stand.
However, to calculate those odds, I need to know all the combinations of cards she could attain to beat my hand if I stand. |