Blackjack Early Payout
admin 3/24/2022
- How To Win Blackjack Strategy
- Blackjack Early Payout Meaning
- Blackjack Chart Printable
- What Is Blackjack Early Payout
Casinos have tinkered with the basic format of blackjack on a number of occasions, but these changes have never been as successful as the introduction of early payout. Early payout can now be found at many casinos, but they realized that live casino games could service more than one player per seat.
At first, this sounds like some kind of scheme to squeeze every penny possible out of their blackjack tables, but they managed to put the players’ interests first. Like the name suggests, live blackjack with early payout gives you a chance to get paid without seeing your hand to completion. Here is how it works.
What Is Live Blackjack With Early Payout? Owner: MonaDvd226. Description: Some of the online horse betting sites are not reliable on the cyberspace. You must be weary of this in earlier place. A click of one button may possibly be given a thousand options to gamble using the net. You cannot be contingent on everything being a matter of. The Wizard tests the values of the early surrender offers. Blackjack Early Payout was developed by the people at Visionary iGaming for their Live Blackjack games and you’ll only find it available at casinos using their live casino software. It’s essentially a different version of Blackjack Surrender, where you’re able to cash.
How To Win Blackjack Strategy
- Live Blackjack with Early Payout can be a very profitable blackjack variant to those who know how to play it efficiently. As the name suggests, this unique and exciting game allows players to take early payouts and save their initial bet. The hands are played by the live dealer who uses the optimal blackjack strategy for calculating the best move.
- In reality, early payout blackjack is probably good for everyone involved. It works out for casinos because they can take care of lots of players at a single table, all at the same time. Early payout takes care of the biggest logistical problem facing casinos that offer live blackjack, which is the fact that they are basically opening a real casino to an infinite number of players.
Gameplay
The game starts like normal with the dealers giving two cards to each seat, and then two to themselves. The difference, though, is that each seat can host multiple players. To account for the fact that not everyone will agree with how to play any given hand, the casino takes the reigns.
You are offered to play according to basic strategy, which is known to be the most viable way unless you are a math wizard and can track the deck and count cards.
Initially, the game was created so that everything would be out of your control: hitting, standing, splitting, doubling down, everything. Everyone was playing basic strategy and playing it right from a statistics point of view. Some players didn’t like this, so a new interface was recently introduced at Celtic Casino. Players are now offered to choose between sound basic strategy and a play of their own choice.
Basic strategy decision will be coloured in green, thus inviting You to make the call while other decisions will be coloured in silver. You are always free to do whatever you want and other players can never affect the outcome of your play directly.
There really isn’t a rational reason to go off the suggested course of utilizing basic strategy, but we do see many players often following their gut feeling. The latest addition suits all players and you are not forced into doing anything, which should be considered a positive thing for sure.
Taking The Early Payout
The size of your early payout depends on a lot of things. For example, how much money have you already wagered on your hand? What cards do you have and what is the dealer’s card that you can see? If the hand is too close to call, or if you have a clear disadvantage, the early payout will be smaller than your original wager.
The casino expects to win, so there is no way that they are going to take a loss by paying you to take the easy out. But if you are in a strong position, the early payout can actually be worth more than your starting bet. The decision is always up to you and you will have to weigh the risk vs. reward for each situation. We can think of a couple of scenarios where players might be interested in taking the early payout.
The first thing coming to mind is a situation where You made a wager that is causing some discomfort due to stakes involved being a bit too high. Don’t worry, we have all been there. The dealer might also have a high card, such as an 8, 9 or even a ten. You have 18 – 20 and would rather lock up a sizable win than risk having losing a significant portion of your bankroll.
Is Early Payout Blackjack a Good Thing?
Some players believe that early payout takes the fun out of live online blackjack since they no longer have to make the basic decisions of the game. So does early payout ruin blackjack? Maybe, but then you could say that using optimum strategy, in general, takes the guesswork out of things. In reality, early payout blackjack is probably good for everyone involved.
It works out for casinos because they can take care of lots of players at a single table, all at the same time. Early payout takes care of the biggest logistical problem facing casinos that offer live blackjack, which is the fact that they are basically opening a real casino to an infinite number of players. Taking care of everyone can quickly become unmanageable.
At the same time, early payout blackjack should be great for players. Since the house is ensuring that your hand is played according to perfect blackjack strategy, the house edge is totally minimized without any effort on your part. Also, if things are not quite going your way, you at least have the option of taking an easy out without losing everything.
It is especially useful in a situation where you are playing at high stakes tables and you are looking to play for a long time, as it gives you that get out clause if you had made a hasty wager. If you have a couple G’s on the table, a poor hand and the options for Early Payout, you will be thanking your lucky stars that you chose to play this game.
Although there is a couple negatives that we have pointed out below, we would certainly deem Early Payout games as a good thing to play.
Negatives of Early Payout
Although Early Payout, sounds good in theory, as it allows you take your money and run if things aren’t going your way. However, of course, this can have an adverse effect if you call it wrong.
The key thing about early payout is not to panic, as although you might not look in a good stead at certain parts of the game, there is always to the possibility of the dealer going bust at any money. Depending on whether the dealer hits or stands at 17, should also alter your decision.
Again, as mentioned, some may argue that it also takes the fun out of the game a bit. This is due to the option dramatically lowers the risk and as such, the thrills too. Therefore, you like the high intensity of blackjack, these may be a bit lax for you.
However, regardless of any of these comments, if you like to play it safe, then you won’t find any negatives to Early Payout.
Playing On Mobile
As is the case with most games in the modern age, the early payout game variation is available for mobile play at most casinos.
However, this is not to say that is the only place and you can be assured that at any casino that offers Early Payout Blackjack and a mobile version will let you amalgamate the two services.
Whatever device you use should not affect your service either, as most casinos support all formats of phone software. This means whether you are using, IOS or Android, a phone or tablet, you should be able to access the game as and when you want, wherever you are!
US Friendly Casinos Offering It
Blackjack Early Payout Meaning
The situation with live dealer casinos in the US means that you only have a few legitimate brands to choose from in legal gambling states like New Jersey.
Our recommendation for US players interested in playing this game would be to research what casinos are available in their state and check if online casino will be allowed in 2020 onwards. Online casinos such as 888 and bet365 operate in New Jersey and have been around since the early days of online gambling and offer various ways to gamble for players worldwide. Although the design of their website can look a bit simple and old, be assured that gameplay and the services offered are to highest standards.
Unfortunately, due to the regulations in the United States, it limits the game selection and so niche options like Early Payout, fall by the wayside. However, you can find a selection of the best US Casinos, so feel free to browse them to find one that suits your needs.
Early Payout vs. Regular Game Types
Everyone is in a different spot, so You’ll have to make a choice on Your own, but there’s merit for both, avoiding early payout Blackjack and choosing to play it. What we don’t really like is the low stream and playing interface quality.
In terms of the gameplay, it is definitely an interesting twist on the original and provides you the opportunity to save some money in tight situations. It may not have as many twists and turns as games such as Blackjack Switch or Surrender, but is simple and effective.
However, it definitely surpasses the option of the option of insurance that most tables offer, which has been overwhelmingly voted down in terms of the service it provides by countless blackjack players. Making it the best option for players who are hoping not to lose too much too soon when playing at a blackjack table. Playing high stakes with Early Payout is where the game really shines, as if you are on the verge of losing big bucks, early payout prevents this.
Although it doesn’t surpass the thrill and excitement as other variations offered online, as well as in real-life casinos, it allows the option for players to take more control over the gameplay. They no longer have to go head to head with the dealer, wagering big amounts, only to lose it all with a bit of bad luck.
Overall
With Blackjack Early Payout, you really can’t go wrong with the option it allows you to utilize. Essentially, you stand to minimize losses to the highest extent you can, and at the same time, the worse case is that you lose some of the suspense of the classic game.
Although this is a game more for the reserved then the risk-taker, it is still an alternative that is well worth a try, especially if you are running a bit low on account funds and want to take it a bit easy.
Regardless of your reasons, we would recommend this variation to anyone who wants to give something new a try.
ksdjdj
There is a blackjack game out there with the following rulesAfter 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%
-------------------------------------------------------
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.
Blackjack Chart Printable
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')?
| DP | 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
Mission146
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.
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.
ksdjdj
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.
Mission146
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.
Vultures can't be choosers.
ksdjdj
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).
------------------------------
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:
What Is Blackjack Early Payout
P12-16 vs D14 = 1.10P17 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
Last edited by: ksdjdj on Jan 21, 2019
Mission146
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.
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.
ksdjdj
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').
---------------------
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.
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').
---------------------
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.
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)')
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.
Mission146The 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.
Thanks for this post from:
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.
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.
ksdjdj
Thanks Mission146Update:
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.
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