Maximum number of cards in a hand
- Thread starter BJFan
- Start date
Reasonably, as the player, you could draw a,2,a,a,a,a,a,4,a,a,a,a,any. If it was negative by this point (which it should be) you could hit hard 17 vs. A, and end up with 13-14 cards.
If you hit aces instead of split, it would be one more. If you hit a soft nineteen or above, it could be more.
For the dealer, hitting soft seventeen, it's possible to end up with a,a,a,a,a,a,a,5,a,a,a,a,any for a total of 13 cards.
Obviously, you COULD draw all the aces in a shoe and have 21.
If you hit aces instead of split, it would be one more. If you hit a soft nineteen or above, it could be more.
For the dealer, hitting soft seventeen, it's possible to end up with a,a,a,a,a,a,a,5,a,a,a,a,any for a total of 13 cards.
Obviously, you COULD draw all the aces in a shoe and have 21.
Thanks for the replies, but there's a catch: it depends on the number of decks!
And also, applying common sense and provided that the player uses BS, the answer would be 17 in case #decks>5 (if #decks=4 the player can't reach 17 due to previous ace splittings, if max splits=4 and ace resplitting is permited).
Any other answers?
And also, applying common sense and provided that the player uses BS, the answer would be 17 in case #decks>5 (if #decks=4 the player can't reach 17 due to previous ace splittings, if max splits=4 and ace resplitting is permited).
Any other answers?
Not true. You asked what is the most possible (can have). The most cards a hand "can have" is in the situation of 8-deck with 22 of the aces available. If you now want to rephrase the question to the most cards a hand can have in singe deck, we can go from there. But as stated, everyone responded appropriately. Ace splitting, BTW, has nothing whatsoever to do with the solution to your query. Also, BS was not a requirement of the original question. Don't ask if you don't want to get the right answer. And if you already knew the answer, or thought you did, why did you ask it in the first place? :whip: 
:grin: :whip: :whip:
:grin: :whip: :whip:Sorry Aslan, I didn't mean to upset you. Take into account that English is not my mother tongue. The purpose of the question was figuring out the maximum dimension of an array of cards as I'm building a blackjack simulator. I'm using 11 as the maximum number of cards for 6 decks and it works after billions of rounds.
Thanks.
Thanks.
A good part of what I said was tongue in cheek, and I certainly do not have any hard feelings toward you. Next time, perhaps, tell us why you need the information and everyone will want to pitch in and help you. I think billions of rounds will probably do, but if you want the correct answer, ask Qfit. I personally have never seen more than 7, but I know that is far too low. There is likely a mathematical way to determine the odds of a hand that exceeds 11-- what are you going to do if that happens to occur? If it's not a commercial program, I guess it really doesn't matter, but since it is a simulator you're building, you will be running billions routinely.
The maximum number of cards that a basic strategy player can have in his hand is 14, and there's only ONE way to do it, and only if he's planning on hitting soft 18: His first eight cards must be an ace, followed by a four; and then the next five cards have to be aces.
The chance of this happening (six deck game) is ((1/13) * (23/311) * (22/310) * (21/309) * (20/308) * (19/307) * (18/306) * (17/305) * (24/304) * (16/303) * (15/302) * (14/301) * (13/300) * (12/299)) = 5.5547899468003904893691065475784e-19.
If I'm reading this number correctly, that works out to be about one in 1.9 sextillion.
The chance of this happening (six deck game) is ((1/13) * (23/311) * (22/310) * (21/309) * (20/308) * (19/307) * (18/306) * (17/305) * (24/304) * (16/303) * (15/302) * (14/301) * (13/300) * (12/299)) = 5.5547899468003904893691065475784e-19.
If I'm reading this number correctly, that works out to be about one in 1.9 sextillion.
