Fight the Dealer
We're going to have some fun, guys. It isn't often that I can write to tell you that what I'm about to discuss has probably never before been treated in any of the BJ literature, or on any website. It is a follow-up to the above discussion.
So, here is the premise: Consider the ten ranks from Ace to Ten. You play head-on against the dealer, and, one by one, a card of each rank is presented for you and the dealer to fight over. The winner gets to choose if he wants the card or if he wants to give it to the other person. If the player gets it, it becomes the first card of his two-card original hand. If the dealer gets it, it becomes his upcard.
The "fight" consists of flipping a coin to see if the dealer or the player gets the choice. Again, the winner gains the right to keep the card for himself or to give it to the other person.
Now, in every single case, except one, what is good for one person is bad for the other. For example, if we're fighting over the Ten, in our previous discussion, the dealer will surely want it for his upcard, and the player will want it for his first card. The question, though, is: to which person is the Ten more advantageous?
Is it positive e.v. to the player to be fighting over this card?
To answer questions such as this, we need two lists: one with the advantage to the player for starting his hand with the particular rank, and another, with the same informationfor the dealer's having the rank as his upcard. The former list has been published before, and it can be found, for example, on p. 112 (Table 30) of Wong's Basic Blackjack. But the second list is much harder to find. It can be deduced from the bottom of the chart on p. 83, in the long-out-of-print How to Play Winning Blackjack, by Julian Braun, but there is a mistake for the Ace.
I asked Norm to provide a modern-day version for the six-deck S17, DAS game, and it can be found here: http://www.qfit.com/Don895.png
Just look at the bottom "Tot" line. So, now we have all we need to answer the question of which cards the player should want to fight over, and which will actually be negative e.v. The findings are rather interesting and are certainly not what you would call instantly intuitive.
Pass on the Ten!! It has +14.3% e.v. for the player but -17.31% for him when it is the dealer's upcard. Together, that's -3% x 50% = -1.5% e.v. for the player to be "fighting" over who gets the Ten.
I'm sure it's clear to everyone that the Ace is the prize. It's worth 50.5% to the player and "only" 34.14% to the dealer. Overall, that's +8.2% for the good guys (remember, each person has 50% chance of getting the card).
So, now, what about the other eight ranks? What indeed! Which cards should the player want to fight for?? First, it is interesting to note that, of the eight ranks that are left (2-9), only TWO have positive e.v. for the player! And, in every case but one, the player would want to give the card to the dealer, and the dealer would want to give the card to the player! Can you guess what the exception is?
While the e.v. for the player for this card is negative in BOTH cases (he loses no matter who gets it), it's worse if the player gives it to the dealer than if he keeps it for himself -- even though he loses either way.
So, that's question #1. Question #2 is: of the remaining seven ranks, which are the only two that are worth it to the player to fight for?
I'll let you discuss this for a while and will be back later with the answers and all the e.v.s for every rank.
Enjoy!
Don