chgobjpro: Automatic Win Option

[chgobjpro]

If a player is holding a two-card 20 (10/10 or A/9) and the dealer is showing a 10-value up-card (no blackjack), exercising Automatic Win means electing not to play out the hand in return for keeping the original bet and being paid half its value in winnings.

A recent surge in acceptance has seen the option picked up in the Chicago area.

Casino owners are attracted to Automatic Win because players stand to win about 55 percent of the time when they're holding a 20 against the dealer's 10. Getting players to accept the half-bet win is in favor of the house.

Is there a TRUE Count (6D,S17) where the automatic win option is the right play?

[Dog Hand]

chgobjpro,

I found a website about the Casino Surrender option: see link below. If you're dealt a two-card 20 vs. a dealer's X, she first checks for BJ like usual: if she has it, you lose. If not, you have the option to "force" the dealer to "surrender" and pay you half your bet. For example, if your wager is $100, you tell the dealer to pay you $50 (half you bet), then she collects your cards.

According to the "Tips and Stats for Experienced Blackjack Players Only!" page on the Casino Surrender website:

When you are playing Blackjack and the count +4 or greater, you should ALWAYS take the Casino Surrender option because it actually reduces the house edge!

Note that they do NOT claim that the option becomes +EV at +4. This made me wonder how high the HiLo TC has to be to make this option worthwhile. I ran a series of CVData sims for a 6D, S17, DAS game with 4/6 pen. The sim had two players: one who plays all, and one who wongs in when the count reaches a specified level. The table below shows the results of these sims.

The first column shows the minimum TC that the HiLo counter plays (the "any" row means he plays all). Columns 2 (AX vs. X) and 4 (XX vs. X) are output from CVData showing the EV (in percent) for these hands before the dealer checks for BJ. Column 3 shows the fractional probability that the dealer's X has an A in the hole. I calculated this probabilty as follows:

BJ Prob = 1 - (AX vs. X)/150%

Finally, Column 5 (XX vs. X No BJ) shows the player's EV (in percent) for playing (not "Casino Surrendering") X,X vs. X when the dealer does NOT have a BJ. I calculated this as follows:

(XX vs. X No BJ) = 100%*[(XX vs. X)/100% + (BJ Prob)]/[1-(BJ Prob)]

Of course, the EV for taking Casino Surrender is +50%. According to these results, the option becomes +EV for the player when his minimum TC is somewhere between +8 and +10. Note, though, that the "TC" used here is the TC at the start of the round, rather than the actual TC once you and the dealer have received your cards, because that's the way CVData sorts the data. Since we already know you have X,X and the dealer has X, the TC is (almost certainly, and definitely if you're playing one hand heads up) lower once this situation arises compared to the beginning of the round. For our hypothetical situation, if on average the discard rack has two decks, then the TC NOW is about 3/(6-2) = 0.75 lower than at the start of the round.

One other flaw in this methodology is this: for a min TC played of +10 the EV for playing (not surrendering) is given in the table as 49.38%. However, what this means is that the EV for not surrendering is 49.38% considering ALL TC of +10 and higher. In other words, the EV at EXACTLY +10 might be 50.50%, but at higher TC's the EV is below 50% such that the weighted average becomes the reported 49.38%.

If I could get CVData to report the Hand results only for a specified TC, I could refine these results. I might be able to do this... I'll have to think about it a while.

min TC	AX vs. X	BJ Prob	XX vs. X	XX vs. X No BJ
any	138.28	0.078133	42.35	54.41495516
+4	137.30	0.084667	39.84	52.77494538
+6	137.00	0.086667	38.77	51.93795620
+8	136.32	0.091200	37.24	51.01232394
+10	136.21	0.091933	35.65	49.38330519
+12	133.64	0.109067	32.93	49.20308291

Hope this helps!

Dog Hand

Casino Surrender website

[kc]

> chgobjpro,

> I found a website about the Casino Surrender option:
> see link below. If you're dealt a two-card 20 vs. a
> dealer's X, she first checks for BJ like usual: if she
> has it, you lose. If not, you have the option to
> "force" the dealer to "surrender"
> and pay you half your bet. For example, if your wager
> is $100, you tell the dealer to pay you $50 (half you
> bet), then she collects your cards.

> According to the "Tips and Stats for Experienced
> Blackjack Players Only!" page on the Casino
> Surrender website:

> When you are playing Blackjack and the count +4 or
> greater, you should ALWAYS take the Casino Surrender
> option because it actually reduces the house edge!
> Note that they do NOT claim that the option becomes
> +EV at +4. This made me wonder how high the HiLo TC
> has to be to make this option worthwhile. I ran a
> series of CVData sims for a 6D, S17, DAS game with 4/6
> pen. The sim had two players: one who plays all, and
> one who wongs in when the count reaches a specified
> level. The table below shows the results of these
> sims.

> The first column shows the minimum TC that the HiLo
> counter plays (the "any" row means he plays
> all). Columns 2 (AX vs. X) and 4 (XX vs. X) are output
> from CVData showing the EV (in percent) for these
> hands before the dealer checks for BJ . Column 3
> shows the fractional probability that the dealer's X
> has an A in the hole. I calculated this probabilty as
> follows:

> BJ Prob = 1 - (AX vs. X)/150%

> Finally, Column 5 (XX vs. X No BJ) shows the player's
> EV (in percent) for playing (not "Casino
> Surrendering") X,X vs. X when the dealer does NOT
> have a BJ. I calculated this as follows:

> (XX vs. X No BJ) = 100%*[(XX vs. X)/100% + (BJ
> Prob)]/[1-(BJ Prob)]

> Of course, the EV for taking Casino Surrender is +50%.
> According to these results, the option becomes +EV for
> the player when his minimum TC is somewhere between +8
> and +10. Note, though, that the "TC" used
> here is the TC at the start of the round , rather
> than the actual TC once you and the dealer have
> received your cards, because that's the way CVData
> sorts the data. Since we already know you have X,X and
> the dealer has X, the TC is (almost certainly, and
> definitely if you're playing one hand heads up) lower
> once this situation arises compared to the beginning
> of the round. For our hypothetical situation, if on
> average the discard rack has two decks, then the TC
> NOW is about 3/(6-2) = 0.75 lower than at the start of
> the round.

> One other flaw in this methodology is this: for a min
> TC played of +10 the EV for playing (not surrendering)
> is given in the table as 49.38%. However, what this
> means is that the EV for not surrendering is 49.38%
> considering ALL TC of +10 and higher. In other words,
> the EV at EXACTLY +10 might be 50.50%, but at higher
> TC's the EV is below 50% such that the weighted
> average becomes the reported 49.38%.

> If I could get CVData to report the Hand results only
> for a specified TC, I could refine these results. I
> might be able to do this... I'll have to think about
> it a while.

> min TC AX vs. X BJ Prob XX vs. X
> XX vs. X No BJ any 138.28 0.078133
> 42.35 54.41495516 +4 137.30
> 0.084667 39.84 52.77494538 +6
> 137.00 0.086667 38.77 51.93795620
> +8 136.32 0.091200 37.24 51.01232394
> +10 136.21 0.091933 35.65
> 49.38330519 +12 133.64 0.109067
> 32.93 49.20308291 Hope this helps!

> Dog Hand

I don't know if this will do any good as a point of reference but I used my program that computes shoe comp for a given HiLo or KO running count based on a weighted average of all possible subsets to get a comp for a HiLo running count of +30 with 156 cards left dealt from a 6 deck shoe given 3 tens have been removed initially to allow for X-X vs X. Comp I get is 2-6 .05739, 7-9 .07792, T .38096, A .09831. Multiplying each of these by 156, you get an approximate shoe comp of 2-6 8.95 ea, 7-9 12.16 ea, T 59.43, A 15.33. Using a shoe comp of 2-6 9 ea, 7-9 12 ea, T 60, A 15, I computed EV for X-X v X using my CA and happen to get exactly 50.00% for standing. If I use 59 T and 16 A I get an EV of 50.31% for standing. Either comp would be a HiLo TC of +10 at the time a decision needs to be made.
An observation: if the shoe consisted of a very large percentage of tens, the option to take a sure 50% profit becomes more attractive. In the exteme case where shoe is all tens you get a sure 50% profit versus surely breaking even.

kc

[Dog Hand]

kc,

Nice to see that two different methods give very similar results!

I also realized that as the TC increases, the advantage of this option shifts from the house to the player... apparently at a TC of about +10.

For this particular option, keeping an "Insurance" count would provide a more-accurate result than does HiLo, since the main advantage to this option is getting the half-bet when your 20 will push the dealer's two-card 20.

Dog Hand

[Don Schlesinger]

Nice intellectual exercise, guys. Congrats.

But, you understand, of course, that obtaining an edge at TC = +10 or higher on a shoe game is virtually worthless.

I admire the math, but the conclusion is that we may as well forget about this as a way of making money.

Don

[Dog Hand]

Don,

I had to run a 5-billion hand sim to get a grand total of 60,000 hands where the player had X,X or A,9 vs. the dealer's 10 with an initial TC of +10 or more. Let's see... you'd get to face this hand once every 800+ hours!

Dog Hand

[PrizeCar]

> Don,

> I had to run a 5-billion hand sim to get a grand total
> of 60,000 hands where the player had X,X or A,9 vs.
> the dealer's 10 with an initial TC of +10 or more.
> Let's see... you'd get to face this hand once every
> 800+ hours!

> Dog Hand

Hey Don and DogHand,

I just want you guys to know, I know of a casino in the Midwest that offers automatic win with a double decker, 50% pen, reno rules. Not that it matters much. You'll still probably only utilize it once every few hundred hands, but definitely more frequently than a shoe.

Prize

[PrizeCar]

Don and Doghand,

I ran a sim using a double decker, and it's still not much better than once every 800 hours, as you mentioned. I guess you're right, we should forget about it! Oh, also, Don, I'm enjoying your book very much. Just got it in the mail 3 days ago, BJ attack, 3rd ed soft cover. About half-way though!

Cheers,

Prize

[Don Schlesinger]

> I ran a sim using a double decker, and it's still not
> much better than once every 800 hours, as you
> mentioned. I guess you're right, we should forget
> about it!

Yup. Afraid so.

> Oh, also, Don, I'm enjoying your book very
> much. Just got it in the mail 3 days ago, BJ attack,
> 3rd ed soft cover. About half-way though!

Glad you're enjoying. Take your time. Lots to assimilate.

Don