Need math/odds help: Dealer's top card known

Here's the situation: The game is double-deck blackjack. Dealer hits soft 17, player can split aces but only gets one card, player can otherwise split up to four times, can double on any two cards, player loses original bet against dealer blackjack, no surrender, and blackjack pays 3-2. Played optimally, what impact does knowing the next card off the top of the deck have on the player's odds? Specifically, I'm looking for value to associate with this. For example, the odds calulator shows the house advantage without this knowledge as 0.37988%. What does that change to with the player knowing the next card off the top of the deck before their action?

First post, welcome.

I see that you like to live... dangerously...

http://www.youtube.com/watch?v=HkzMA1jrm00

Crunching the numbers on this would be so difficult because the complexity goes tot he point where you have to rate the percentage win rate of every possible 2cards vs 1dealer card situation, multiplied by the ten possible next card values. I would guess that the edge is somewhere above 3%, and therefore significant. To me it's worth noting that any situation in which you know the next card clearly represents illegal activity where you may be found guilty of a crime where you may be fined or have to do time.

Thanks for the concern -- rest assured I am not using this information for that sort of activity. The question arose regarding this type of activity and I was simply (or not so simply) looking to get a number set to the advantage. I think the best way to solve this is to run a significant amount of simulations of a program that will deal out the game and play the player's hand with the best strategy. My best guess was a bit higher than 3% but I don't know.

try dealing it out yourself, flatbetting, and peeking yourself at the next card. 3% was conservative, it might be something like 10%- but yeah, I don't now either, not too interested in these sorts of questions.

deleted

Quote: mprimm

Here's the situation: The game is double-deck blackjack. Dealer hits soft 17, player can split aces but only gets one card, player can otherwise split up to four times, can double on any two cards, player loses original bet against dealer blackjack, no surrender, and blackjack pays 3-2. Played optimally, what impact does knowing the next card off the top of the deck have on the player's odds? Specifically, I'm looking for value to associate with this. For example, the odds calulator shows the house advantage without this knowledge as 0.37988%. What does that change to with the player knowing the next card off the top of the deck before their action?

The answer will depend on whether you only know the first hit card, or whether you essentially have one-card clairvoyance and always know the next card each time. That is, you can't see two cards into the future, but if you take the first hit then you know the card after and can make another decision.

Quote: Ibeatyouraces

Strategy is fairly easy. If the card makes you bust, stand. If it gives you 19-21, double. If your hand is a pair this could get tricky but anything else just hit.

I'm not sure that's true. The optimal strategy will be to maximize conditional EV of the wager, and that might mean something like doubling on an 8 with a 7 coming next if the dealer has a 6.

Also, the analysis totally changes if you're at 3rd base and the dealer will take the top card if you don't.

deleted

Thanks for all the help and replies. Assume you're playing heads-up against the dealer so you won't have to figure out anyone else's hands/strategies. Also, assume you have one-card clairvoyance. You always know the next card off the top of the deck but not any deeper. Once you take the top card, you then can know the next.

Quote: mprimm

Thanks for all the help and replies. Assume you're playing heads-up against the dealer so you won't have to figure out anyone else's hands/strategies. Also, assume you have one-card clairvoyance. You always know the next card off the top of the deck but not any deeper. Once you take the top card, you then can know the next.

Then the strategy needs to incorporate where the next card should go (to you or to the dealer) to maximize your EV vs. the dealer. Example: if you had a 2,3 but knew a 10 was coming vs. a dealer 6, you might give the dealer the 10 and bank on the bust. That's a +EV play: dealer stands and wins with 5 ranks and busts with 8.