How to Calculate Basic Strategy?

I would like to learn how to calculate basic strategy for Blackjack and/or Spanish 21. How would I do it?

Personally I use infinite deck analysis - but if I was paid to do it I would construct a database of all possible dealer Blackjack hands and their totals and compare the options against that database at each stage.

As a simple example consider your options on a 16 vs 10 (UK). If you stand you only win when the dealer busts (21%), if you hit you have 1/13 chance of winning with a 21 (91%), 1/13 chance of winning with a 20 (72%) etc. As this is bigger (21.24%) than standing (21.21%), then you hit. Similarly calculate for all the other options you can have. This is also why when some 5s have gone, your chances of a 21 are less, so you stand on 16 vs 10. (btw I use chances of winning, others use expected values - it's just the way I started doing it before I got to know the game.)

With non-infinite deck you cannot use "1/13" but have to use the ratios depending on the cards actually gone, which obviously depends on the number of decks and which cards make up your 16 (or other totals being checked out).

Quote: unnaturalusr

I would like to learn how to calculate basic strategy for Blackjack and/or Spanish 21. How would I do it?

The Wizard has made his spreadsheet to calculate best play for infinite decks available to the public.

The only differences between infinite and four decks is to hit soft 13 vs. 5, and soft 15 vs 4 only when the dealer stands on soft 17.

To do the calculation for a specified number of decks you must write a computer program. I suggest you try and understand the spreadsheet first, since the infinite deck problem is easier to calculate.

I have asked before, but I am still wondering. Can you buy an infinite deck from Bicycle cards ?

I originally thought "Yes" - as you only need less than 30 sets of A thru 2. Whenever a card is needed pick one of the unused sets and deal out one of the cards. When the hand is over, reset all the sets. Unless there are plenty of splits, you shouldn't need that many sets.

Then someone says quite nicely, but surely you could get an infinite number of splits!

Then you wonder if you finish with one of the hands before moving onto the next - at this stage you can remember the total achieved (say using 3 cards) and start again.

What this has to do with Wiggins winning the Tour De France beats me!

The first thing you need to do is, determine the probabilities of the dealer getting 17, 18, 19, 20, 21, and busting for each combination of (a) dealer's up card, (b) number of decks, and (c) whether the dealer hits or stands on soft 17. If you want, you can assume "infinite decks" (i.e. at any time, the next card has an equal chance of being Ace, 2, 3, ..., Queen, or King); there are very few situations where the number of decks affects basic strategy.

Once you have that, "work backwards", starting with "hard 21" - obviously, a hit puts you over, so determine the result (probability of winning minus probability of losing) if you stand (which is the sum of the probabilities of the dealer having 17, 18, 19, 20, or busting). Yes, you do have to calculate them separately for each possible dealer's up card.
Next, 20 - the result of a hit is (the probability of drawing an Ace x the result for 21) + (the probability of drawing a 2 or higher x -1, since you bust); compare this to the result of a stand, and whichever is better is what you do. (You need to know the result of 21, which is why you work backwards.)
Next, 19, then 18, and so on down to 4, since there is no such thing as a "hard 3" or a "hard 2" (the only 3 is A-2, which is soft 13; the only two is A-A, which is soft 12.)

You should be able to work out how to calculate soft numbers, doubling, and splitting on your own at this point.

Quote: ThatDonGuy

The first thing you need to do is, determine the probabilities of the dealer getting 17, 18, 19, 20, 21, and busting for each combination of (a) dealer's up card, (b) number of decks, and (c) whether the dealer hits or stands on soft 17. If you want, you can assume "infinite decks" (i.e. at any time, the next card has an equal chance of being Ace, 2, 3, ..., Queen, or King); there are very few situations where the number of decks affects basic strategy.

Once you have that, "work backwards", starting with "hard 21" - obviously, a hit puts you over, so determine the result (probability of winning minus probability of losing) if you stand (which is the sum of the probabilities of the dealer having 17, 18, 19, 20, or busting). Yes, you do have to calculate them separately for each possible dealer's up card.
Next, 20 - the result of a hit is (the probability of drawing an Ace x the result for 21) + (the probability of drawing a 2 or higher x -1, since you bust); compare this to the result of a stand, and whichever is better is what you do. (You need to know the result of 21, which is why you work backwards.)
Next, 19, then 18, and so on down to 4, since there is no such thing as a "hard 3" or a "hard 2" (the only 3 is A-2, which is soft 13; the only two is A-A, which is soft 12.)

You should be able to work out how to calculate soft numbers, doubling, and splitting on your own at this point.

I'll try this and see how far I get.

The Wizard's spreadsheet looks interesting, too.

Thank you all for your help.