Doubling down on Blackjack in 6:5

I was playing 6:5 at a strip casino a while back and had consumed just enough free booze that I doubled-down every time I got a blackjack against a deal 2-6. fortunately, I won evey time. But, I wonder how bad my decision was. Anybody done the math? How about if blackjack paid even money? Would it make sense then?

Whoops. Never mind.

Quote: Jumboshrimps

I was playing 6:5 at a strip casino a while back and had consumed just enough free booze that I doubled-down every time I got a blackjack against a deal 2-6. fortunately, I won evey time. But, I wonder how bad my decision was. Anybody done the math? How about if blackjack paid even money? Would it make sense then?

My blackjack appendix 9 is useful to answer questions like this. For example, assuming six decks, and the dealer hits a soft 17, the expected value of doubling on a blackjack against a dealer 5 is 0.622136, and against a 6 is 0.667063. Both are much less than 1.2. Even if a blackjack only pays even money, as is unfortunately sometimes the case now, you should stand on the blackjack. The only game where you should not stand on a blackjack is in Triple Up 21, where you should triple on a blackjack against a dealer 6.

You read the chart wrong. The expected return by doubling table shows the expected value based on ONE unit bet. NEVER Double a Blackjack.

You can verify this by looking at the chart for doubling an 11 versus a six versus hitting. The expected value of doubling is exactly double that of hitting.

The expected value on blackjack is 1.2 on a 6-5 game.

The expected value of doubling and hitting A-10 is as follows:

Dealer	2	3	4	5	6	7	8	9	10	A
Double	.4706	.5178	.566	.6147	.6674	.4629	.3507	.2278	.1797	.109
Hit	.2384	.2603	.283	.3073	.3337	.2921	.23	.1583	.1195	.143

Quote: Wizard

Quote: Jumboshrimps

I was playing 6:5 at a strip casino a while back and had consumed just enough free booze that I doubled-down every time I got a blackjack against a deal 2-6. fortunately, I won evey time. But, I wonder how bad my decision was. Anybody done the math? How about if blackjack paid even money? Would it make sense then?

My blackjack appendix 9 is useful to answer questions like this. For example, assuming six decks, and the dealer hits a soft 17, the expected value of doubling on a blackjack against a dealer 5 is 0.622136, and against a 6 is 0.667063. Both are much less than 1.2. Even if a blackjack only pays even money, as is unfortunately sometimes the case now, you should stand on the blackjack. The only game where you should not stand on a blackjack is in Triple Up 21, where you should triple on a blackjack against a dealer 6.

I can't believe I'm going to belabor this, now that the Wizard has spoken, but I simply must. What's wrong with the following analysis?

Expected return on $5 bet resulting in a natural = 5 * 1.2 = $6

Expected return on $5 bet doubled on 11 = 10 * 0.667063 = $6.67063

Quote: Jumboshrimps

Expected return on $5 bet resulting in a natural = 5 * 1.2 = $6

Expected return on $5 bet doubled on 11 = 5 * 0.667063 = $3.33

Corrected.

The table shows the expected return for one unit , not two.

Quote: teddys

Quote: Jumboshrimps

Expected return on $5 bet resulting in a natural = 5 * 1.2 = $6

Expected return on $5 bet doubled on 11 = 5 * 0.667063 = $3.33

Corrected.

The table shows the expected return for one unit , not two.

Okay. So I can expect to win $3.33 on my initial $5 unit. And another $3.33 on the other $5 unit. Right?

No, to be completely unambiguous, the table shows the expected return for an initial bet of one unit.

I truly appreciate all of your attempts to help me understand, but I'm not there yet.

I understand that the chart reflects the expected return on a single unit. So, when I am dealt any eleven against a dealer 6, and opt to double down, the expected return on that initial unit is .667063.

OR, are you all trying to tell me that the expected return on that initial unit is half that?

Take a look at the chart above. And let's simplify things and say that you are betting $10 and the dealer shows a 6.

Taking the blackjack wins $12.
Whether you decide to hit or double 21 you would always take one card on a six.


Hitting blackjack wins, on average, $3.337.
Doubling blackjack wins, on average, double: $6.674
You don't win $13.34 (.6674 x 20).

Here is the table that makes up the result of hitting blackjack. It is off a little bit because I am using the Wizard's appendix 2 which takes the dealer probability for 8 decks S17.

Your hand	Dealer	17	18	19	20	21	Bust	Total
Hand	Probability	.16564	.10621	.10639	.10159	.09725	.42292	1
12-16	5/13	Lose	Lose	Lose	Lose	Lose	Win	-.05929
17	1/13	Push	Lose	Lose	Lose	Lose	Win	.00088
18	1/13	Win	Push	Lose	Lose	Lose	Win	.02180
19	1/13	Win	Win	Push	Lose	Lose	Win	.03815
20	1/13	Win	Win	Win	Push	Lose	Win	.05415
21	4/13	Win	Win	Win	Win	Push	Win	.27778
Total	1	.02548	.00000	-.01637	-.03126	-.06732	.42292	.3335

The expected value for hitting is 1/2 as much as doubling.

When you hit or double 11 you have a better chance of getting 12-16 than you do 21. The dealer only busts 42% of the time. On the other 58% of the time, the dealer has a chance of beating or pushing you.

Quote: boymimbo

You read the chart wrong.

Actually, I had a massive brain fart and figured the EV of a BJ to be 1 less than it should have been. My bad.

Quote: boymimbo

Take a look at the chart above. And let's simplify things and say that you are betting $10 and the dealer shows a 6.

Taking the blackjack wins $12.
Whether you decide to hit or double 21 you would always take one card on a six.


Hitting blackjack wins, on average, $3.337.
Doubling blackjack wins, on average, double: $6.674
You don't win $13.34 (.6674 x 20).

Here is the table that makes up the result of hitting blackjack. It is off a little bit because I am using the Wizard's appendix 2 which takes the dealer probability for 8 decks S17.

Your hand	Dealer	17	18	19	20	21	Bust	Total
Hand	Probability	.16564	.10621	.10639	.10159	.09725	.42292	1
12-16	5/13	Lose	Lose	Lose	Lose	Lose	Win	-.05929
17	1/13	Push	Lose	Lose	Lose	Lose	Win	.00088
18	1/13	Win	Push	Lose	Lose	Lose	Win	.02180
19	1/13	Win	Win	Push	Lose	Lose	Win	.03815
20	1/13	Win	Win	Win	Push	Lose	Win	.05415
21	4/13	Win	Win	Win	Win	Push	Win	.27778
Total	1	.02548	.00000	-.01637	-.03126	-.06732	.42292	.3335

The expected value for hitting is 1/2 as much as doubling.

When you hit or double 11 you have a better chance of getting 12-16 than you do 21. The dealer only busts 42% of the time. On the other 58% of the time, the dealer has a chance of beating or pushing you.

Outstanding! I get it now. A bird in hand is better than a drunken bird at Bill's Gambling Hall & Saloon doubling down on blackjack.

Quick question, kinda off topic:

What is the advantage of doubling down in blackjack? Is it because you win more double downs than you lose, thus gaining an advantage? What has been said here seems to me that you lose more often than you win DDs.

You don't lose more double downs (if only done when the strategy is correct), or else it wouldn't be beneficial to ever double down. It's just that in the case of a blackjack, you've already won 1.5 units, so it's not beneficial to risk a 150% win to get a 200% win. If you bet 10 bucks, you are throwing away 15 (plus risking your now safe original ten) to have a shot at winning only 20 (while risking an additional 10). Should be pretty easy to see why it's a bad call.

If you have 11 and the dealer is showing a 6, you will win more than 50% of the time by drawing only one card, which means it's a good time to risk an additional wager to take advantage of that.

Quote: teddys

Quick question, kinda off topic:

What is the advantage of doubling down in blackjack? Is it because you win more double downs than you lose, thus gaining an advantage? What has been said here seems to me that you lose more often than you win DDs.

Any positive number in appendix 9 (or the table applicable to the game you're playing) indicates that, on average, you are more likely to win money than to lose by taking that action.

In more accessible terms, doubling-down is a good move in certain situations because, when you are holding better cards than the other guy, you want to bet as much as possible.