Basic strategy "Double (Stand if not allowed)"

Basic strategy chart

So if you draw A & 7 and dealer draws 3, 4, 5 or 6 you're supposed to double down if allowed and stand if not. It seems contradictory to me. Could someone explain the mathematics behind this?

You double down if you think getting an extra card will be beneficial and you stand if not. So if it is beneficial to draw another card, but doubling down isn't allowed, shouldn't you always hit, rather than stand, then?

I'm not sure the mathematics behind it.. But I assume you are doubling down merely to increase your bet, since the dealer is likely to bust

The object of blackjack is not to get as close to 21 as possible without going over. It is to get money from the dealer. "Double if possible; else, stand" means you will lose more hands if you double than if you stand, but will win more money overall if you double.

if three or more cards equal soft 18 stand against 3 4 5 6. obviously. if a casino does not allow you to double with A7 that casino sucks. also stand A7 against 2 or 7 or 8 and hit against 9 10 or ace in most situations unless you are counting of course then vary against ace.

Soft 18 into a bust card is worth increasing your bet at the expense of the quality of your hand. If you cannot, or will not increase your bet, no need to sacrifice your 18.

Soft 17 is Double Or Hit because you have no hand quality.

Quote: Deucekies

Soft 18 into a bust card is worth increasing your bet at the expense of the quality of your hand. If you cannot, or will not increase your bet, no need to sacrifice your 18.

Soft 17 is Double Or Hit because you have no hand quality.

What's a bust card?

Quote: 1BB

What's a bust card?

lol +1... If you're in 3rd base it's quite often the card you took from the dealer, right?

To contribute: Simulations were ran with millions of hands and found that it was more advantageous (had a higher expected value) to double the hand vs. those other cards. In other simulations where you couldn't double down, it was found most advantageous (highest expected value) to stand vs. those other cards.

There are more ways to make Soft 18 than A-7. (A-A-6, A-5-2, A-3-4, A-2-2-3 ...)

Most places don't allow you to double on a three card hand. Some places don't allow you to double after you split your 7's against a 3,4,5,6 and draw an ace.

The mathematics part is simple - there are 3 ranks that improve your hand (A,2,3), 4 that keep it the same (10,J,Q,K), and 6 that worsen your hand (4,5,6,7,8,9).

3 is less than 6. You have a slim chance of improving your hand, you have a good chance of worsening your hand.

There is good value in doubling your wager if you can, but not in trying to improve your hand when you know the dealer has to draw.

The basic strategy calculation videos may be helpful if you want to see how the determination is made.



edit: 4+4 to 3+4 (like it should have been)

Quote: Caliber

Basic strategy chart

So if you draw A & 7 and dealer draws 3, 4, 5 or 6 you're supposed to double down if allowed and stand if not. It seems contradictory to me. Could someone explain the mathematics behind this?

You double down if you think getting an extra card will be beneficial and you stand if not. So if it is beneficial to draw another card, but doubling down isn't allowed, shouldn't you always hit, rather than stand, then?

When you have a soft 18, it by itself, is not a great hand, because of the pat hands 17-21 it is fairly weak. When people say the dealer is more likely to bust with an up-card of 3-6 that isn't exactly so. In fact, the likelihood of the dealer busting with a 3-6 up-card is less than 50%. But several things come into play. 1) Soft 18 is not that great a hand. 2) The dealer has a 38-43% chance of busting with a 3-6 up-card. 3) You can take an additional card without fear of busting and might even improve your hand. 4) Even if you turn an 18 into junk, it wasn't that strong to begin with, and 5) You can double your bet.

All five of these reasons, together, are why doubling is preferred. If you can't double down then that rule change alone would make standing your best option. (I would never play blackjack where DOA is not allowed.)

Trust the math!

A little side note: With a soft 17 you would always hit, even if your weren't allowed to double down. 17 is just too weak a hold.

Quote: 1BB

What's a bust card?

A 2-6. The cards where the dealer is most likely to bust. Not favored to bust, but most likely to bust.

Quote: Deucekies

A 2-6. The cards where the dealer is most likely to bust. Not favored to bust, but most likely to bust.

I should have added a smiley face when I asked, tongue in cheek, what a bust card is as I remember all the max bets I've lost against the dealer's 5 or 6.

Quote: 1BB

Quote: Deucekies

A 2-6. The cards where the dealer is most likely to bust. Not favored to bust, but most likely to bust.

I should have added a smiley face when I asked, tongue in cheek, what a bust card is as I remember all the max bets I've lost against the dealer's 5 or 6.

Aha.

Quote: Caliber

You double down if you think getting an extra card will be beneficial and you stand if not. So if it is beneficial to draw another card, but doubling down isn't allowed, shouldn't you always hit, rather than stand, then?

The difference is, the expected value of the hand when hitting or standing does not take into account the doubled bet; the expected value of the hand when doubling, does.

Here's a simplified explanation: suppose you have a hand where, if you stand, you have a 70% chance of winning and a 30% chance of losing (pretend that pushes don't happen in this example), but if you hit, you have a 65% chance of winning and a 35% chance of losing.
If you stand, the EV is 0.7 x (+1) + 0.3 x (-1) = +0.4
If you hit, the EV is 0.65 x (+1) + 0.35 x (-1) = +0.3
However, assume that, if you double, you have a 65% chance of winning and a 35% chance of losing;
the EV is 0.65 x (+1) + 0.35 x (-2) = +0.6, which is greater than the +0.4 EV for standing.

Quote: ThatDonGuy

the EV is 0.65 x (+2) + 0.35 x (-2) = +0.6, which is greater than the +0.4 EV for standing.

I think you meant this.

And as you said the value you get from doubling your wager with one extra card is greater than standing or simply hitting.