Blackjack switch is a blackjack variant where you are dealt two hands and can choose, before being dealt any more cards, whether or not to switch the 3 and 4 cards. For example, if you were dealt A,5 and 4,10 (where the bold indicates the switchable cards), you’d want to switch to give yourself a blackjack with A,10 and a playable 9 with 4,5 (no matter what the dealer’s card was.) Obviously, the switch decision depends on your two hands and the dealer card. And the best way to make that decision is to add up the expected values of the four hands and see which is the best. So, for one rule set against, say, a dealer 6 and the previous example: A,5 .0217; 4,10 -.211; total EV of -0.1893 while A,10 1; 9, 0.1334; total EV of 1.1334. An obvious switch. However, it gets tricky when you have marginal plays and don’t have the time or the ability to do the EV calculation there at the table. For instance, say you’ve got 6,6 and 7,8 against a dealer 10. Better to switch to 13 and 14 or to hit the 12 and 15 (can’t surrender in this game.) EV calculations say it is marginally better to not switch.
Anyway, I was wondering how large a strategy card there would have to be to fit every possible decision onto the card for use in a casino. I’m thinking you’d first have to either have 10 different cards, one for each dealer card, or even better, a decahedron. (Bonus points if you shoot it at craps.) Next, there are 35 possible starting values in blackjack. So, two hands (the shoes are big enough, starting out at least) could be any of 1,225 combinations per hand, correct? Meaning that you’d have to be able to fit 1,225 decisions (in a legible manner) for each card or 12,250 total if we can put it all on a decahedron. However, that seems low, since A,5!=5,A in terms of switchability and feels like the real number should be much higher.
So, my questions. First, are my numbers right? Second, how large would the card (or decahedron) have to be to fit that many decisions? And third, what would it look like in two dimensions? I’m imagining a table kinda like:
**Dealer 2** 5|6 5|7 5|8 5|9.........6|5 6|6 5|6 X N N N............N N 5|7 N X N N............N Y 5|8 N N X N............N Y 5|9 N N N X............N Y
Where the pipe indicates the two cards. However, that would have to be gigantic and I’m not sure it could be done in two dimensions easily. How about a decahedron for each dealer card, or maybe a 100-sided solid to show everything on one object, though the only example I can think of (the zocchihedron) doesn’t fit?