Hitting hands out of order: an advantage?

A player brought up a question that I thought was interesting. I'll throw it to you knowledgeable folks.

If a player was playing more than one hand, and he was able to choose what order he acted on them, would that affect his odds in any way?

For the sake of this discussion, let's disregard the idea of next-card information. Does being allowed to play your hands out of order naturally provide any advantage or disadvantage to the player?

While anything the player is allowed to do can be used to our advantage, I believe that in this case, next card information would be needed for any play I can think of.

Otherwise, unseen cards are unseen cards.

The player would not get an advantage nor a disadvantage by playing his hands out of order.

The only situation that I can think of (because I saw someone else do it), is when a player puts the last of his money down on two hands. The second hand was a blackjack. The first hand (I don't remember what it was) was a hand worth doubling down on. Because he had no more money, he asked the dealer if he could get paid on his blackjack so he could use the winnings to double down on his first hand. The floor person said it was OK, dealer paid off the BJ, and allowed the player to double-down his original hand.


Now, there is a slight tiny possibility where a player might gain an advantage (or rather, decrease his disadvantage), although I'm not sure about it...but intuitively it seems like it might make sense. Let's say a player has a 16 on his first hand and 8 on his second hand, where dealer is showing a ten up. (PS: The player is a card-counter.) At this point in time, the count indicates that standing on 16 and hitting 16 is worth the exact same (EV-wise). He could hit his second hand (with an 8 starting total). As cards are dealt to his second hand (the 8), he gains further information about the count (and an ever-so-slightly more precise ratio of cards remaining). Using this information, he could figure out whether hitting the 16 or standing on the 16 is a better play, then act on the 16-hand AFTER the 8-hand has completed.



But overall, if you're strictly a basic strategy player and don't use any information (count, next-card, or *basic multi-card-hand "configurations"(?)), then playing hands out of order is not going to change a thing.


*ie: You're supposed to HIT 2-card 16's verse 10, but stand on multi-card 16's verse 10. There's another weird one (I think for single deck, perhaps?), where you should HIT a 12v4 if it consists of a 10 (ie: 10-2)...but should stand on the 12v4 if it doesn't (ie: 7-5, 8-4, or 9-3). Although I'm not 100% on the 12v4 rule.

PS: ** The mult-card thing isn't what I would call "basic strategy", but a slightly better basic strategy.

My gut instinct tells me there's a tiny, tiny, tiny advantage to playing them in any order of your choosing. How small? Small enough to essentially not matter... but from the technicality of it, if you're playing a single deck game and you know the TC is +5, then there are 5 extra big cards in the remaining deck. Say on your first hand you have 10-4, and on your second hand you have 6-5, to a dealer 9. One would intuitively think it's better to draw with the TC +5 on the 6-5 first, because if you remove one of the extra 10's you know is in there on the first hand, that *slightly hurts the other hands double down.

Now surely the "but you don't know the next card, what if it's small and helps the double down hand" argument is valid... However I submit that the odds of removing the big card are higher than the odds of removing another small card, simply because we know there are 5 extra big cards remaining in the deck. So I do believe it would be 'technically' better to play the 6-5 hand first.

Do note, I'm still also saying this is so minuscule that I'm not sure what kind of impact (if any) it would even have on the game. Just my gut feeling / educated guess.

The counter should chose to play whichever hand is likely to require more cards first, giving as much information for playing decisions to the other hand as he can. E.G. he has 8-8 (splitting hand) and T-6 against a T. Play 8-8 first. Or, if he has 2-3 and T-2 vs. 4. Play 2-3 first. Etc. Using this strategy, the counter can gain a little bit of EV.

True counts don't change (on average) as cards are dealt. That's called the "True Count Theorem."

http://web.archive.org/web/20060825034348/http://www.bjmath.com:80/bjmath/counting/tcproof.htm

I think I've got it. There is definitely a difference if one of the hands is a double (or Split). In an extreme case where you have say 11 and 16 against a known dealer 20, and there is only a 2 and a 10 left, your EV playing the 11 first is -1, while you EV playing the 16 first is -0.5, because if you pull the 2 you can confidently double the 11 and get to 21.

If there is no opportunity to double or split the difference is much smaller, but it's there. Don't we encourage counters to sit at 3rd base so they have maximum count info for their playing decisions? So I think you put the most borderline case last (e.g. 16 vs 10), and collect count info.