Jumboshrimps
Joined: Jan 11, 2010
• Posts: 75
March 4th, 2010 at 3:29:38 PM permalink
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?
wildqat
Joined: Nov 11, 2009
• Posts: 157
March 4th, 2010 at 4:01:28 PM permalink
Whoops. Never mind.
Wizard
Joined: Oct 14, 2009
• Posts: 25135
March 4th, 2010 at 4:15:23 PM permalink
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.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
boymimbo
Joined: Nov 12, 2009
• Posts: 5994
March 4th, 2010 at 4:18:21 PM permalink
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
----- You want the truth! You can't handle the truth!
Jumboshrimps
Joined: Jan 11, 2010
• Posts: 75
March 4th, 2010 at 5:16:25 PM permalink
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
teddys
Joined: Nov 14, 2009
• Posts: 5522
March 4th, 2010 at 5:23:04 PM permalink
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.
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
Jumboshrimps
Joined: Jan 11, 2010
• Posts: 75
March 4th, 2010 at 5:32:56 PM permalink
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?
ZPP
Joined: Feb 7, 2010
• Posts: 31
March 4th, 2010 at 6:09:11 PM permalink
No, to be completely unambiguous, the table shows the expected return for an initial bet of one unit.
Jumboshrimps
Joined: Jan 11, 2010
• Posts: 75
March 4th, 2010 at 6:33:36 PM permalink
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?
boymimbo
Joined: Nov 12, 2009
• Posts: 5994
March 4th, 2010 at 8:03:32 PM permalink
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.
----- You want the truth! You can't handle the truth!