"Casino Surrender" rule in Spanish 21.

FLASH1296

Well-Known Member
#1
I have a question for all of our bright math boys.

There is a rare rule called "Casino Surrender" where the casino surrenders to YOU;
that is, they give you a chance to collect a 1/2 win without playing out the hand IF your hand is a two card 20.

It is simple enough to see how to play this in Blackjack, but how does one take advantage of this rule in Spanish 21,
where the dealer bust % is lower than it is in BJ AND the player's two card 20 is worth more than in blackjack ?
 

1357111317

Well-Known Member
#2
My guess is that the count would need to be absurdly high to take this. I think I read somewhere that in BJ you need a +5 HiLo count to take it and with the 4 missing 10s per deck I'm sure you would have a tough time finding a count high enough to use it in SP21.
 

Brock Windsor

Well-Known Member
#3
Early Casino Surrender?

Can you surrender for a half win before the house checks for BJ? I think this rule would be of no use to the counter and would get frequently used by civilians (much like 'even money' does). Of course it could lend itself very beneficial by forcing surrender if you had a way of determining that the dealer had a hand of 21,20,11,10 or soft hand of AA-A6.
BW
 

FLASH1296

Well-Known Member
#4
I (badly) NEED feedback


If you check in the extensive (invaluable) tables in Blackjack Attack, 3rd ed. you will see the equity that a player's 20 has against the various dealer's up card.
Some of the results are (surprisingly) counter-intuitive (to me); but I do not YET have tables for Span21, although I am working on it with a computer programmer/player.

Searching the approx. equities for how a 20 fares against all the dealer's upcards, I find that we need to look at the Best and Worst case scenarios.

Thus, extrapolating to the logical extremes, at the margins we find that, [using an 8 deck S17 game], the BEST and WORST situations are:
vs. the dealer's EIGHT and ACE respectively.

if the equity of a hand is -.50 or worse (larger negative number) then LATE SURRENDER is a good idea.
IN THIS CASE, we need to search for an equity that exceeds a 50% LOSS.
Naturally, in this case all equities are positive with a holding of 20, so the above does not apply.
if the equity of a hand is +.75 or better (larger positive number) then the mean result is a profit of a HALF a BET, so CASINO SURRENDER is a good idea.
IN THIS CASE, we need to search for an equity that exceeds a 50% PROFIT in order to NOT take the HALF WIN being proffered.
It should be obvious to the reader that if the net profit is less than 50% of the bet then acepting the automatic 1/2 win is a fine idea.

I note that Ploppies are absolutely certain to either never take Casino Surrender or badly misuse it.

Equity and profit (in % of bet) for all hands when holding a two card TWENTY at a zero True Count:

2 = .64 - 36 = + 28%
3 = .65 - 35 = + 30%
4 = .66 - 34 = + 32%
5 = .67 - 33 = + 34%
6 = .70 - 30 = + 40%
7 = .77 - 23 = + 54%
8 = .79 - 21 = + 58%
9 = .76 - 24 = + 52%
X = .56 - 44 = +12%
A = .60 - 40 = +20%


Our 20 is worth the MOST against an EIGHT = .79 meaning that the equity is .79 - .21 = .58 gives a massive 58% equity.
Our 20 is worth the LEAST against a TEN = .56 meaning that the equity is .56 - .44 = a modest 12% equity.

SO ... if this Casino Surrender was applied to ordinary BJ,
Basic Strategy would be to take the 1/2 WIN with a 20 against
ALL cards EXCEPT the the dealer's SEVEN, EIGHT or NINE.

Remember, in Span21, the % of Tens is 3/12 [8.33% x 3] = 25% while in BJ the % of Tens is 4/13 [7.77 x 4] = 31%
Showing a non-Face card, In Spanish 21, the dealer hits to 20 and 21 more often than in BJ - that should be obvious.
Also, In Span21, the dealer's overall bust rate does NOT drop as the True Count climbs.

I note that converting a "push" into a 1/2 win is a BIG DEAL, as it is a "swing" of 1/2 of a wager.

The above "1/2" was corrected from my erroneous "1/4" following the helpful posting by DownUnderWonder.

I think that this is more complex than it appears and as I do not have sufficient data for Spanish21 to delve into this problem, I am frustrated.

This still looks wrong to me and I have been puzzling over what I have presented here for the last hour.

ALL feedback will be very much appreciated
 

1357111317

Well-Known Member
#5
The EV for TTvT is 55%. This is basically regardless of the rules and for 4-6 decks. For the Casino surrender to be a good idea the EV would have to be less than 50%. I am not sure where you get your figures.
 
#6
FLASH1296 said:

If you check in the extensive (invaluable) tables in Blackjack Attack, 3rd ed. you will see the equity that a player's 20 has against the various dealer's up card.
Some of the results are (surprisingly) counter-intuitive (to me); but I do not YET have tables for Span21, although I am working on it with a computer programmer/player.

Searching the approx. equities for how a 20 fares against all the dealer's upcards, I find that we need to look at the Best and Worst case scenarios.

Thus, extrapolating to the logical extremes, at the margins we find that, [using an 8 deck S17 game], the BEST and WORST situations are:
vs. the dealer's EIGHT and ACE respectively.

if the equity of a hand is -.50 or worse (larger negative number) then LATE SURRENDER is a good idea.
IN THIS CASE, we need to search for an equity that exceeds a 50% LOSS.
Naturally, in this case all equities are positive with a holding of 20, so the above does not apply.
if the equity of a hand is +.75 or better (larger positive number) then the mean result is a profit of a HALF a BET, so CASINO SURRENDER is a good idea.
IN THIS CASE, we need to search for an equity that exceeds a 50% PROFIT in order to NOT take the HALF WIN being proffered.
It should be obvious to the reader that if the net profit is less than 50% of the bet then acepting the automatic 1/2 win is a fine idea.

I note that Ploppies are absolutely certain to either never take Casino Surrender or badly misuse it.

Equity and profit (in % of bet) for all hands when holding a two card TWENTY at a zero True Count:

2 = .64 - 36 = + 28%
3 = .65 - 35 = + 30%
4 = .66 - 34 = + 32%
5 = .67 - 33 = + 34%
6 = .70 - 30 = + 40%
7 = .77 - 23 = + 54%
8 = .79 - 21 = + 58%
9 = .76 - 24 = + 52%
X = .56 - 44 = +12%
A = .60 - 40 = +20%


Our 20 is worth the MOST against an EIGHT = .79 meaning that the equity is .79 - .21 = .58 gives a massive 58% equity.
Our 20 is worth the LEAST against a TEN = .56 meaning that the equity is .56 - .44 = a modest 12% equity.

SO ... if this Casino Surrender was applied to ordinary BJ,
Basic Strategy would be to take the 1/2 WIN with a 20 against
ALL cards EXCEPT the the dealer's SEVEN, EIGHT or NINE.

Remember, in Span21, the % of Tens is 3/12 [8.33% x 3] = 25% while in BJ the % of Tens is 4/13 [7.77 x 4] = 31%
Showing a non-Face card, In Spanish 21, the dealer hits to 20 and 21 more often than in BJ - that should be obvious.
Also, In Span21, the dealer's overall bust rate does NOT drop as the True Count climbs.

I note that converting a "push" into a 1/2 win is a BIG DEAL, as it is a "swing" of 3/4 of a wager.

I think that this is more complex than it appears and as I do not have sufficient data for Spanish21 to delve into this problem, I am frustrated.

This still looks wrong to me and I have been puzzling over what I have presented here for the last hour.

ALL feedback will be very much appreciated
Excuse my cluelessness. What is equity? What are the two numbers used in the calculation? Why does the equity need to be +.75 rather than +.5 to result in an expected profit of half a bet? How is turning a push into half a win a swing of 3/4 of a wager and not of 1/2 of a wager?

If you like Flash, I could do a combinatorial analysis for SP21 for 8 full decks, which would give you some base numbers to work with but wouldn't help you find the pivots. Let me know.
 

FLASH1296

Well-Known Member
#7

"Excuse my cluelessness. What is equity? What are the two numbers used in the calculation? Why does the equity need to be +.75 rather than +.5 to result in an expected profit of half a bet?"

"Equity" is the present value of a hand, based upon what will, on average, occur.
I may be presenting this quite wrong, but I shall continue.
If the equity of the play is .75 then that means that you will win 75% of the time and lose 25% of the time.
75% - 25% = 50%. -- averaging out to be a profit of exactly 1/2 of a bet.
The same as the "Automatic Half Win" that I am referring to as "Casino Surrender".

The 1st column that I presented is obviously the dealers Up-Card
The 2nd column is taken from Don Schlesinger's tables, which I believe to be the decimal equivalent of the winning chances of the hand.
The 3rd column is 100% - the 2nd column figures, which equates to the losing chances.
The 4th column is the difference between the 2nd and 3rd columns, which equates to the profit forecast in terms of % of the bet.
Hence, if that figure exceeds 50% you can earn more than 50% (a half bet) by standing on the hand. i.e A dealer's 7's, 8's, and 9's.

A "swing" in gambling parlance is the difference between the two possible results.
A 1/2 win and a loss in this case. Rather than winning a half bet [+0.5] you lose a full bet [-1.0]
The difference between the two possible events under consideration is from +.5 to -1.0 That equates to 1.5 bets.

I thank you for your offer to do a C.A. on this for me.

I will p.m. you immediately.
 
#8
FLASH1296 said:

A "swing" in gambling parlance is the difference between the two possible results.
A 1/2 win and a loss in this case. Rather than winning a half bet [+0.5] you lose a full bet [-1.0]
The difference between the two possible events under consideration is from +.5 to -1.0 That equates to 1.5 bets.

I thank you for your offer to do a C.A. on this for me.

I will p.m. you immediately.

I understand the term swing. What I am confused about is how going from a push to half a win is a swing of 3/4. A push is +0 and half a win is +1/2, so isnt that a swing of 1/2 not 3/4?
 
#10
I think you have made an error in your calculations for chance of losing the hand flash, you are not taking pushes into account. This may throw off the numbers.

If you are favourite to win 50% of the time for a particular hand, it does not follow that you will lose 50% of the time. Ill illustrate this with two extreme examples to demonstrate the concept.

If you have a bet that is 60% chance to win, 40% chance to lose then your EV for that situation is 20% (0.6 x 1 + 0.4 x (-1) = 0.2). If you are 60% chance to win and 40% chance to push your EV is 60% (0.6 x 1 + 0.4 x 0). In the first situation you should take casino surrender but in the second you shouldn't.

I don't know how big the effect will be in the scenario but in theory the difference is important and it will change the numbers for sure.
 

FLASH1296

Well-Known Member
#11
Boy, am I getting old and absent-minded !

I somehow forgot completely about pushes.

Will someone please check the tables in
BlackJack Attack, 3rd ed. and explain the data to me.

 

FLASH1296

Well-Known Member
#12
Oh no !!


I finally checked the legend in C.B.J.N.

It states:

"Casino surrender. Player with a two-card twenty can accept a half win against a 10, if the dealer does not
have a natural."

I sincerely apologize to all of the good people who have put up with me.

I really need a vacation !


IT WOULD MAKE ME HAPPY IF THIS ENTIRE THREAD WAS DELETED.
 
#13
Since I have done a combinatorial analysis I thought I may as well share the results, even though I am sure the conclusions are intuitive for most of you.

I first did a calculation for Spanish 21 as if it was the first hand in a shoe.
This ignored hands where the dealer had an A in the hole because the option is not available in this instance.

To take this option your EV should be below 0.5

for 10,10 vs 10 your EV is 0.597
for A,9 vs 10 your EV is 0.593

I then did the calculation with 2 decks, to see how much the effect changed during the shoe for the same true count.

for 10,10 vs 10 your EV is 0.609
for A,9 vs 10 your EV is 0.593

So, this option gets even worse for you as the shoe progresses for 10,10 vs 10.

So, I wondered if there would be a count where the option would become a good one. I worked out the EORs for each card type for this situation. They are as follows (rounded to 3 dp).

A: -0.001
2: -0.003
3: -0.004
4: -0.003
5: +0.001
6: +0.001
7: -0.006
8: -0.007
9: -0.009
10: +0.010

As you can see, in respect to using an unblanced hi-lo count, this poses all sorts of problems. First, the 3 cards that have the most effect in reducing the EV in this situation (making it more likely to take the bet) just happen to be the 3 cards that hi-lo counts as 0. Secondly, if you look at the +1 cards (2 through 6) you can see that 3 of them have a - effect and 2 have a + effect, making it rather useless as a way to judge this bet. There were also interesting effects of multiple card removal, for instance removing a 5 and a 6 from each deck, although individually improving the EV, left the EV the same.

There is no real point using a hi-lo count where this option becomes +EV. If we remove all 32 of the 7s, 8s and 9s (the cards with the biggest effect) from an 8 deck shoe your EV becomes 0.491, making the option a 0.009 EV favourite. So, if you use a rediculous side count and wait for an impossible situation, you may get to make 90c in EV on a $100 bet.

I did a similar analysis for regular BJ with similar reaults, although the EV for 10,10 vs 10 off the top of an 8 deck shoe is lower at 0.558 due to the increased chance of pushes with the extra 10s in the deck.

All together, this is all pretty obvious intuitively, but was good practice for my blackjack math so I enjoyed it anyway. If there are any massochists who would like to see the spreadsheet just let me know too.
 

Kasi

Well-Known Member
#14
DownUnderWonder said:
To take this option your EV should be below 0.5
Maybe it's late and maybe I didn't read this thread very carefully but are we talking about surrender?

To take surrender shouldn't your EV be below-0.5, not +0.5?

Is Flash suggesting surrendering a 2-card twenty vs a dealer 10?

I must be missing something.

Apologies lol.
 

k_c

Well-Known Member
#15
Kasi said:
Maybe it's late and maybe I didn't read this thread very carefully but are we talking about surrender?

To take surrender shouldn't your EV be below-0.5, not +0.5?

Is Flash suggesting surrendering a 2-card twenty vs a dealer 10?

I must be missing something.

Apologies lol.
They're taking about locking in a 50% win on a pat 20 rather than playing out the hand and risking a push or a loss.
 
#16
Kasi said:
Maybe it's late and maybe I didn't read this thread very carefully but are we talking about surrender?

To take surrender shouldn't your EV be below-0.5, not +0.5?

Is Flash suggesting surrendering a 2-card twenty vs a dealer 10?

I must be missing something.

Apologies lol.
We are talking about casino surrender, where you automatically win half your bet before the dealer draws a hand, so it is +0.5. Yes, flash is talking about a 2 card 20 vs a dealer 10.
 
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