"Early Payout" Blackjack

There is a blackjack game out there with the following rules

After each game played, a new 6 deck shoe is shuffled and dealt. Dealer stands on soft 17. Double down on any 2-card combinations, even after splits. Split pairs once. May split aces once. Blackjack pays 3/2. Insurance pays 2 to 1.

The house edge for Basic Strategy is about 0.46%

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All figures below are based on a $1.00 bet.

The game also has an "early payout" feature that you can cash out early on, for example Player hard 17 vs Dealer hard 14 = $1.19 "early payout"

Most "early payouts" are in the house's favor, but I was wondering if anyone can look at the table below and answer a few questions.


1. Are there any "early payout" values that are in the player's favor?

2.( If yes for question 1.) Are there enough in the player's favor to make it a player edge game, using correct "early payout" strategy?

3. What would the correct "early payout" strategy be for each of the values in the table below ( the options are "cash out early" or "play on")?

D\P	P12-16	P17	P18	P19	P20
D16	1.23	x	x	1.61	1.76
D15	1.17	x	1.42	1.58	1.75
D14	x	1.19	1.37	x	1.73
D13	1.03	1.13	x	1.51	x
D12	0.96	1.06	x	x	x

Note: in the table above x means hasn't occurred yet, P is player hard total and D is dealer hard total .

Also note: the game doesn't have a demo mode so I had to use real money to test it, I would have played on if it had a demo mode so that I could complete the table 'risk free'.


Also, I think the "early payout" figures so far are not worth taking for D16 (could be wrong),
taking the "early payout" option for D15 looks like the right option to me,
and D12-D14 require someone with better math skills than me to work out.


Thanks for your time

I would start with comparing each hand listed to the Blackjack hand calculator found here:

https://wizardofodds.com/games/blackjack/hand-calculator/

From the dealer 16’s (Dealer showing six on the calculator) it looks like you’re better off to take the offer in all cases. The only caveat is that the calculator doesn’t know the dealer has sixteen, you can only put in a dealer showing six.

Did you mean the dealer shows six above, or do you actually KNOW the dealer has 16? I’m willing to do the math on a few of them if you mean you actually KNOW the dealer has sixteen, though I suspect we’ll come to find that taking the offer is worse than playing it. I say that because the values are already not too far apart when all you know is the dealer has a six.

I’ll also say that the math on the pat player hands is fairly simple, all you have to do is calculate the dealer result probabilities, which isn’t terribly hard.

For example, if you have 20 against a dealer sixteen:

Dealer Draws 5-Wins (24/308)*-1= -.0779220779

Dealer Draws 4-Push (24/308)* 0 = 0

Dealer Draws A-2-3-6-7-8-9-10-Loses (260/308) = .8441558442

Therefore, the expected return is 1 -.0779220779+.8441558442= 1.766233766

Therefore, taking the $1.76 offer is ever so slightly worse overall.

And, that’s how you can calculate it for any player pat hand if you choose. In terms of non player pat hands, you just compute the best EV play, possible results, and then what the dealer could do in the event the player doesn’t bust. It’s not above my pay grade, unless I’m not getting paid! ;) I’m sure someone who can program to do this much faster than me may well take an interest.

Quote: Mission146

Did you mean the dealer shows six above, or do you actually KNOW the dealer has 16?

You KNOW the dealer has 16 by that point in the game.

Also I agree, all the dealer 16 "cash out" options look bad to me so far.

Thanks for the post.

Quote: ksdjdj

You KNOW the dealer has 16 by that point in the game.

Also I agree, all the dealer 16 "cash out" options look bad to me so far.

Thanks for the post.

No problem. I may well do a few more for you as long as I can use it for, “Ask Mission,” on LCB AND you’re willing to wait until tomorrow. I’m on my phone at the moment.

EDIT: Also, thank you for the OP. I needed some inspiration and new potential plays always interest me, though I suspect this game is not +EV overall. In fact, I wouldn’t be surprised to find the game does the same thing I did and just rounds down to the nearest penny every time, but we’ll see.

Quote: Mission146

No problem. I may well do a few more for you as long as I can use it for, “Ask Mission,” on LCB AND you’re willing to wait until tomorrow. I’m on my phone at the moment.

EDIT: Also, thank you for the OP. I needed some inspiration and new potential plays always interest me, though I suspect this game is not +EV overall. In fact, I wouldn’t be surprised to find the game does the same thing I did and just rounds down to the nearest penny every time, but we’ll see.

Thank you.

You can use it on any of your websites/forums

Below is the "fair value cash out" figures that I got so far for Dealer 15

P12-16: about 1.16 (i think it was 1.159..., but can't remember)
P18: about 1.39 (i think it was roughly in the middle of 1.39 to 1.4 )
P19: about 1.544
P20: about 1.698

Note: I was using 'infinite deck' to just get a ball-park figure, so they may be off by a small amount,

Are these close to correct?,
What did you get for the Dealer 15 "fair values"?

Also, the Dealer 12 "cash out" odds will probably be the hardest to work out (at least out of all the possible outcomes that might have a player edge).
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Update (22 January @ about 130 am EST)

I have tested the game some more, so here are some more "early payout" figures that were not in the OP, see below:

P12-16 vs D14 = 1.10
P17 vs D16 = 1.30
P18 vs D16 = 1.46
P18 vs D12 = 1.27
P19 vs D14 = 1.55
P19 vs D12 = 1.48
P20 vs D13 = 1.71
P20 vs D12 = 1.68

Good work, like I said, tomorrow shall be the day and I thank you for your permission in using it for, “Ask Mission!”

I’m probably just going to go through with your values and do all the player pat hands, since it is fairly easy. We shall see the results, but since it is so simple for a computer program to determine and just round down to the nearest penny, that is what I expect to be the case.

Honestly, I’d do it now, but the computer proper is in the bedroom and my fiancé is asleep.

Thanks Mission146,

Here is some more interesting info:


The game also pays/compensates you when you deviate from correct basic strategy, see example

example: In one game there was a hard P17 vs a D6 and I was given the choice to hit and they would pay me $0.52 (or stand and let the bet play as 'normal') so I hit and landed on 18, where I was given the option to hit again and they would pay me another $0.89, so I did and then busted

In the above example, I was paid $1.41 (profit $0.41), even though my bet lost.

According to my basic strategy analysis, and if I worked it out correctly using MGP's BJ CA, i calculated the following:

(A): Hitting a hard 17 vs a D6 and getting $0.52 was worth a net total of about 1/219 EV in my favor for that hit.
(B): Hitting a hard 18 vs a D6 and getting $0.89 was worth a net total of about 1/317 EV in my favor for that hit.

Note: in case I didn't mention it in this post, the initial bet was $1.00.


It seems that with this game you can't do too much 'damage' if you deviate from basic strategy, and if you deviate you may receive a small increase in overall EV for some hands (since they pay you for basic strategy "errors").

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Update (about 5 am EST)

Below are some more basic strategy deviations, that improve the EV in the players favor:

Note: all Player hands are 'hard hands' unless otherwise stated.

Also note: The denominator is rounded "up" to the next whole number, eg 1/304.2 would be written as "about 1/305".

(1) P13 vs D Ace: Stand on 13 and get $0.27, this improves the EV of the hand by about 1/305, compared to basic strategy
(2) P13 vs D10: Double on 13 and get $0.44, this improves the EV of the hand by about 1/3649, compared to basic strategy
(3) P17 vs D5: Double on 17 and get $1.00, this improves " " by about 1/142, " "
(4) P9 vs D Ace: Stand on 9 and get $0.60, this improves " " by about 1/265, " "
(5) P9 vs D2: Double on 9 and get $0.01, this improves " " by about 1/337, " "
(6) H20 vs D4: Double on 20 and get $2.37, this improves " " by about 1/211, " "
(7) H17 vs D7: Double on 17 and get $0.86, this improves " " by about 1/100, " "
(8) H20 vs D2: Double on 20 and get $2.35, this improves " " by about 1/229, " "
(9) H19 vs D9: Hit on 19 and get $1.00, this improves " " by about 1/550, " "
(10) H20 vs D6, Double on 20 and get $2.41, this improves " " by about 1/387, " "
(11) H19 vs D3, Double on 19 and get $1.86, this improves " ", by about 1/146, " "


Remember, the initial bet is $1.00, and any doubles will = $2.00 for the above basic strategy deviations.


Please check to see if I made any errors.
I used MGP's BJ CA and a calculator to work the overall change in EV, so any mistakes are my own.

FYI: I am now winning over $120 testing this game ($1.00 initial bets) so even if it ends up being "no good" for the AP, then at least it wasn't a complete waste of time for me.

Update:

The overall change in house edge for the best*** hand combination from the previous post so far is:

"(6) P20 vs D4..." which occurs about 1.455% of the time for an overall decrease in house edge of about 0.0069%

best***: for decreasing the house edge,"(6)" is the best so far because even though "(7)" from the previous post has the best hand improvement, "(6)" has a lot higher chance of occurring (1.455% for "(6) vs 0.352%. for "(7)")

Again thanks for the help and please correct me if any of this is wrong


Edit (about 520 pm EST)

Here are a few more basic strategy deviations, see below:

(12) P18 vs D5, Double and get $1.43, about a 1/160 improvement
(13) P7 vs D9, Double and get $0.67, about a 1/318 improvement
(14) P12 vs D9, Stand and get $0.20, about a 1/361 improvement
(15) P19 vs D8, Double and get $2.02, about a 1/222 improvement

Again, they are hard totals unless otherwise stated.

Going to take a rough guess, but I will probably have to find about 400+ basic strategy deviations before the house edge gets close to 0%, (this guess does not include the "early payout" figures/estimates from the OP).

Got to go to work now, so I am sorry that I did not double-check to see if the basic strategy deviations have been repeated in any of my posts.

Okay, we already had this one:

I’ll also say that the math on the pat player hands is fairly simple, all you have to do is calculate the dealer result probabilities, which isn’t terribly hard.

For example, if you have 20 against a dealer sixteen:

20 v. 16

Dealer Draws 5-Wins (24/308)*-1= -.0779220779

Dealer Draws 4-Push (24/308)* 0 = 0

Dealer Draws A-2-3-6-7-8-9-10-Loses (260/308) = .8441558442

Therefore, the expected return is 1 -.0779220779+.8441558442= 1.766233766

Therefore, taking the $1.76 offer is ever so slightly worse overall.

So, let's do some more player pat hands.

19 v. 16

The difference here is that the dealer has twice as many ways to win, so let's start there. I could also do the ten combination A/5 as well, but that's a pain, so I'm just going to assume 10-6.

Dealer Draws 4/5-Wins (48/308)*-1= -0.15584415584

Dealer Draws 3-Push (24/308)* 0 = 0

Dealer Draws A-2-6-7-8-9-10-Loses (236/308) = 0.76623376623

0.76623376623 - 0.15584415584 = 0.61038961039 The $1.61 is the same offer rounded down to the penny.

12-16 v. 16

Obviously, the player stands in this situation, so it's a pat hand for the player. (I'm not doing every single hand like this, so I'll assume the player has...7-8 for fifteen...the dealer can have 10-6 for 16. This is least favorable to the player as it gives the dealer the highest possible amount of winning cards and lowest possible number of losing cards.

Dealer Draws A-5-Wins (120/308)*-1= -0.38961038961

Dealer Draws 6-7-8-9-10-Loses (188/308) = 0.61038961039

0.61038961039 - 0.38961038961 = 0.22077922078

Assuming the conditions least favorable to the player, taking the $1.23 is the best deal.

The player could also have something like 5-7 while the dealer has 10-6, this takes away one winning card for the dealer and makes it a bust card:

Dealer Draws A-5-Wins (119/308)*-1= -0.38636363636

Dealer Draws 6-7-8-9-10-Loses (189/308) = 0.61363636363

0.61363636363 - 0.38636363636 = 0.22727272727

In this case, taking the $1.23 is still a good deal.

The only thing that I can think of that would make this worse for the player would be if the player's 12-16 had contained an Ace on that particular occasion. The player would definitely be better off to play it out then. If both totals are hard totals, then the player has at least one card that would otherwise bust the dealer and the dealer has two of the cards that would bust him. I would want to confirm that this was the offer on a HARD total player hand.

P20 v. D15

Okay, so you have this:

Dealer Draws 6-Wins (24/308)*-1= -.0779220779

Dealer Draws 5-Push (24/308)* 0 = 0

Dealer Draws 2-3-7-8-9-10-Loses (236/308) = 0.76623376623

But, now we have to look at Aces:

Dealer Draws Ace + 5 (24/308 * 24/307) = -0.00609162824

Dealer Draws A + 4 = 0 (Push)

Dealer Draws Ace + A-2-3-6-7-8-9-10 (24/308 * 260/307) = 0.06599263928

0.06599263928 + 0.76623376623 - 0.00609162824 - .0779220779 = 0.74821269937

The $1.75 is the slightly better offer, but again, it depends on the specific composition of player and dealer hands. For example, if the dealer's hand was 9-6, then this is a bad offer for the player.

Conclusion (For Now)

Unfortunately, some of these decisions are going to be so close that you're going to need to know the specific hand composition AND the offer to determine whether or not it's a good decision to take the offer.

Even then, because of how frequently these individual hands come up and the house edge of the base game (without offers) it seems that this game will have a negative expected value either way, so I don't know whether or not you wish to invest anymore in doing this.

If you do decide to do so and log the specific cards both player and dealer have as well as the offer, I will be happy to continue. Although, the mathematical breakdown on pat hands (as you can see) is really pretty simple. I apologize, but as you can see, the composition of the hands matters in some cases (even with six decks) so it's impossible to make a blanket statement.

Thanks Mission146

Quote: ksdjdj

Update:

The overall change in house edge for the best*** hand combination from the previous post so far is:

"(6) P20 vs D4..." which occurs about 1.455% of the time for an overall decrease in house edge of about 0.0069%

best***: for decreasing the house edge,"(6)" is the best so far because even though "(7)" from the previous post has the best hand improvement, "(6)" has a lot higher chance of occurring (1.455% for "(6) vs 0.352%. for "(7)")...

Also, I think I stuffed up the calculations for "(6) P20 vs D4..." it should have said "... occurs about 0.727xxx% of the time...", which now makes "(7)" the better overall decrease in house edge, out of those two.

Hi again,

I like to use more than one source of information (when I don't know how to work out something myself) and I am trying to work out the EV, for the hand below:

Rules: 6 decks, BJ pay 3/2, Dealer stands on all 17s, dealer peeks for BJ, split once to make two pairs, DAS.

Hand: Player 20 (T+T) vs Dealer 7
Stand EV: 0.772011
Split EV: 0.508735...*** (or is it 0.262033^^^)

***: MGP's BJ CA says it is 0.508735

^^^: Link below says it is 0.262033

https://wizardofodds.com/games/blackjack/appendix/9/6ds17r4/

The reason i would like to know this is that I am being paid by the casino $0.31 for every $1.00 in initial bet to split 10's vs 7, so I am either:
a) 4.67% better off to split (compared to basic strategy) after receiving the 31% of my initial bet for doing so.
or
b) 20% worse off to split (compared to basic strategy) after receiving the 31% of my initial bet for doing so.

Note: all the other "non-split" EV figures on the WoO site are the same or very close to what the MGP's BJ CA gives me.

Thanks

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Update (about 1240 am)

The link below gives me the same EV as MGP's BJ CA, so I may have misinterpreted the WoO website.


http://www.bjstrat.net/cgi-bin/cdca.cgi

If I recall the split figures assume you continue to split. A fairer way to get an estimate is to look at the various 10s (e.g. 28 37 64 55) and see the range of their hit returns (the 55 is 0.260394). Since each 10 is worth this, you'd guess about .52, but reduce it a bit as you already have two of the 10's in the deck, thus the .508735 you quote sounds feasible. If what you say is true you also think about splitting other pairs.

Thanks charliepatrick,

yes it is true, here are the other hands that you should deviate from basic strategy (see below):

pair of 10's vs A: Split and receive at least 54%*** of your initial bet (this is after dealer checks for BJ). This improves the EV by 4.3% x the initial bet.

***: this figure is 54.5% when your initial bet is in multiples of $2.00.

pair of 10's vs 8: Split and receive 44% of your initial bet. This improves the EV by 3.8% x the initial bet.

The biggest mistake I have found in the players' favor so far, is below:

Player 6 (2 + 4 or 3 + 3) vs Dealer 10: After dealer checks for bj, they pay you at least 105%^^^ times your initial bet if you double on a hard 6. This improves the hand by at least 32.4% x the initial bet.

^^^: this figure is 105.5% when your initial bet is in multiples of $2.00.

Note 1 : in case I haven't said it clearly before, you get to keep the "compensation" the casino pays you for basic strategy deviations, whether the hand wins, loses or draws.

Note 2: from the 20 or so best basic strategy deviations I have found so far, the game goes from a base house edge of about 0.46% to a house edge of a bit higher than 0.16%.

Hi

Sorry for the length between updates, but I now have a couple of questions and I have also done enough work on this to know that:

. The house edge for this game is ~0.46%, playing "normal" basic strategy
. The house edge can be reduced to at least*** ~ 0.046% (or ~1/2,183). when playing the "compensated" strategy.

***: I haven't seen every hand yet, but reducing the house edge by ~ 0.41% is significant.

. Another interesting point is because of the compensation received, you end up doubling a lot more when compared to playing traditional basic strategy, with this game you will double at least 36.636% of the time (when you play the correct "compo" strategy).

Q1: If i was just playing "normal" basic strategy for this game, would I be correct in saying that I would be doubling about ~9.5% of the time? (just a guess, don't know the exact figure)

Q2: Does anyone know what this would do to the variance/ standard deviation for the game? (I think it would generally increase it, but this is just a guess and i also don't have any idea of what the new figure would be)


One example of a "compensated double" that would (probably?) increase the variance, would be to "double a player BJ against a dealer 5".
With this double you are "compensated" $1.77 for every $2.00 of "initial bet".
So, you are giving up a "guaranteed" 150% profit (if you played normal basic strategy).
But you will be ~0.736%^^^ better off over the distance, every time you double that hand against a D5.

^^^: According to MGP's BJ CA, doubling a BJ against a 5, is worth ~62.236%, and being compensated $1.77 for every $2 initial bet is worth 88.5% on top of that, so the combined value of doubling on this hand is ~150.736%, less 150% for giving up BJ (pays 3/2) = a ~0.736% EV improvement on that hand.

Edit: With an initial bet of $2 and a "compo" of $1.77, the win-draw-loss amounts for this hand would be:
Win: +$5.77 (x%^*^ of the time)
Draw: +$1.77 (y%^*^ of the time)
Loss: -$2.23 (z%^*^ of the time)

^*^: feel free to post the actual figures for these "x, y and z" %'s, since I am not very good/fast at working these out.

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Hope this is interesting, and thanks for your time.