Quantum Blackjack

I just put up an first draft of a page on Quantum Blackjack. If my understanding of the rules is correct, this would be one of the most difficult games to analyze I've ever seen. Briefly, the game affords the player to win multipliers if he matches any of one to three random cards from a separate deck. This is paid for by a rule where if the dealer busts with 3 cards, standing bets automatically push. Please click the link for more details.

The question for the poll is would you play Quantum Blackjack?

I think the point below on your site is wrong
"11. The same Multiplier Card can be used more than once. For example, if a Multiplier Card was the 7 of diamonds with a 10x multiplier and the player had three 7 of diamonds in his hand and won, then his win would be 1000 for 1. "

Reason, on the "Sporting Bet rules" page it says (see below):

"Rules
Multiplier cards
... Note that if you have two (2) or more identical cards in your hand that match the suit and value of one multiplier card, you are awarded the corresponding multiplier ONLY ONCE..."

Note: The game is "so new", that they may have changed/tweaked the rule(s) in the week or so that it has been available ?

Hope this helps, as I understand the WoO page is a "first draft" at the moment.

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Also, I voted "maybe" when asked if I would play the game.
It looks fun, but I only like to play BJ If I know the basic strategy, and you said the BS is very complex.

One other thing I really like about it is: "If you Double and your winning hand contains a multiplier cards, your whole bet is multiplied..." (if it means what I think it means, then If your first two cards have at least one "multiplier card" and you double it, then the whole bet is multiplied in those situations too ?)

There is at least one thing to dislike about it too: see the "push on three card dealer bust" rule that you mention (but this is the main (or only?) thing they decided to "take away" to pay for the "benefit(s)").

The game would probably be a better one for the "counter" than regular BJ, if they knew the correct strategy, but I think it is ALWAYS dealt out of a machine "that is shuffled every round?" (at this point in time, at least)

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Update (about 310 am):

Just out of curiosity, what are some hands*** that you would hit (instead of double) if this was a "standard BJ game" that had the "3 card dealer bust is a push" rule?
***: I can already guess that you probably wouldn't double much against a dealer 8 to 10, so I am more interested in the 2 to 6 dealer up card scenarios.

Quote: ksdjdj

I think the point below on your site is wrong
"11. The same Multiplier Card can be used more than once. For example, if a Multiplier Card was the 7 of diamonds with a 10x multiplier and the player had three 7 of diamonds in his hand and won, then his win would be 1000 for 1. "

You're right, thanks for bringing that to my attention. I am trying to take a side between the SportingBet rules and those by the Casino Comparer, going with SportingBet. I agree there was probably a rule change somewhere.


Direct: https://www.youtube.com/watch?v=OTrbQuE08ck

Quote:

Just out of curiosity, what are some hands*** that you would hit (instead of double) if this was a "standard BJ game" that had the "3 card dealer bust is a push" rule?
***: I can already guess that you probably wouldn't double much against a dealer 8 to 10, so I am more interested in the 2 to 6 dealer up card scenarios.

I would have to list this as one of the most difficult games to analyze I've ever seen. Up there with Lunar Poker and Klondike Solitaire. Personally, I would have to go by educated guesses, like hit 12 vs 4 or 6, 13 vs 2. If I could actually play the game I might be able to feel out strategy better.

I think there’s a typo in step 8

Should the word “will” be “win”?

Hmmm.

Let's say I have a 13 vs 2, and the three cards that are multipliers are Qs (3X), Td (5X) and 8h (3X). I may want to hit the 13 because there's a 1/52 chance that I'll get the 8h which will give me a 21 -a probable win - and the multiplier will double my win. But that's only amounts to less than a 2% improvement in EV. How does that compensate me for pushing on Dealer Bust with 3 cards?

I imagine that almost 12% of the time one of the multiplier cards will be in the first two 2 player cards. That might be exciting.

This game is such a radical departure from any existing game, it may be hard for players to learn and accept it.

Quote: michael99000

I think there’s a typo in step 8

Should the word “will” be “win”?

Thanks.

Quote: gordonm888

Hmmm.

Let's say I have a 13 vs 2, and the three cards that are multipliers are Qs (3X), Td (5X) and 8h (3X). I may want to hit the 13 because there's a 1/52 chance that I'll get the 8h which will give me a 21 -a probable win - and the multiplier will double my win. But that's only amounts to less than a 2% improvement in EV. How does that compensate me for pushing on Dealer Bust with 3 cards?

I imagine that almost 12% of the time one of the multiplier cards will be in the first two 2 player cards. That might be exciting.

This game is such a radical departure from any existing game, it may be hard for players to learn and accept it.

Good point about considering the specific Multiplier cards. Yet another reason the analysis would be complicated and any strategy very difficult to quantify. All due points for creativity to Playtech, but I think it's too far out in left field to make it.

It sounds an interesting idea to take something (Bust with 3-cards) and make some hands (with multipliers) exciting. However before one could even begin to analyse the game one needs to know the exact rules and probabilities of the bonus cards.

I haven't read the rules so my guess would be the bonus pack of cards (one deck) has multiplier values on every card and randomly (is it Pr=1/3) one, two or three of these are chosen. If any (one or more) of your cards match a bonus card then you receive that card's bonus. If more than one bonus card is matched then all bonus cards take effect. Where a hand has been split each hand can be considered for any bonus and is evaluated independently. When a hand is doubled the rules are slightly ambigous, I think the bonus only applies to the "initial" "main" bet. When the hand is a Blackjack any bonus applied to the total return of 2.5 units.

Each bonus card has (i) a Suit (ii) a Rank and (iii) a multipier (x3, x5, x10). Where only one bonus is payable the return, including initial wager(s), is multiplied; for example "x3" actually means the same as pay out double (i.e. 3-1=2 ). Where several bonuses are payable the return of all the bonus multipliers are multipled together and then applied as above (i.e. "x3" "x5 actually means pay out 14x (i.e. 3x5-1 = 14). (For some technical reason the rules say the initial bet is taken and the enhanced payout made.) It is possible to have the same multiplier on all three bonus cards, so possible to have a payout of 999 to 1 for a regular hand or 99 to 1 for a Blackjack.

Of course if the details are that the multipliers are assigned randomly to the bonus pack, then the mathematics starts to be really complicated!

I think that even though working out the "overall strategy" for this game is complex, you could treat it as two games and start with a "basic strategy " for the "main game"***.

***: I am treating the "main game basic strategy" as "how you should play the game, if you DID NOT have the bonus(es) to worry about" (see example of "player 10 vs dealer 6" below).

Example: for this version of BJ, you would NOT double a 10 vs a 6, because I think it worth about -$6.33 if you double, where as hitting is worth about -$3.17, for a $100 initial bet.

I won't work out the whole "main game basic strategy", there are at least two reasons why I don't want to do it (see below).
1. I am using "infinite deck" for the "player total", to work out the above "$ EVs" (so my figure will be out slightly).
2. It takes me about 15+ minutes to analyze each "two card player total, and dealer up card" (since I don't have a "specialized program/spreadsheet", I have to do each hand from "scratch").

After the "main game strategy" is complete, you can possibly start on the "way more" complex "bonus card strategy"

Do you think it is worth working out the strategy this way (or similar) for this game?

Does Playtech still use "Playtech Peek", where both split bets are lost against a dealer BJ?

The reason why I ask is, it doesn't tell me in the game rules on the "sporting bet" site what happens with splits against an A or 10 (as far as I can see).

If they still use the "Playtech Peek", then you shouldn't:
1. split 8's vs a dealer 10 or A
2. split A's vs a dealer A.

Note: this is only correct if you have zero bonus cards in your hand (I haven't checked what you should do if you had at least one bonus card).

What are those two side bets?

21+3 and Perfect Pairs, are the ones in the video, and the WoO link below:

https://wizardofodds.com/games/quantum-blackjack/ >>>then go to "Rule 13"

Well, that's disappointingly mundane. You'd think they'd come up with another way to use/exploit those bonus cards.

I like it.
Mainly because I think a simple game with a clear basic strategy that one would execute gets boring. Even though I love blackjack, I've always hoped for a more skill-based version.
Now Im not saying that this is it, but wouldn't it be great if there was a version simple to understand, but with a basic strategy so complex that almost nobody can play it perfectly. Then the casino can offer and advertise a card game with a small positive EV if played perfectly, but so few people would be able to do that that it would still be profitable to casinos... maybe I'm just dreaming...

Quote: ksdjdj

I think that even though working out the "overall strategy" for this game is complex, you could treat it as two games and start with a "basic strategy " for the "main game"***.

***: I am treating the "main game basic strategy" as "how you should play the game, if you DID NOT have the bonus(es) to worry about" (see example of "player 10 vs dealer 6" below).

Example: for this version of BJ, you would NOT double a 10 vs a 6, because I think it worth about -$6.33 if you double, where as hitting is worth about -$3.17, for a $100 initial bet.

I won't work out the whole "main game basic strategy", there are at least two reasons why I don't want to do it (see below).
1. I am using "infinite deck" for the "player total", to work out the above "$ EVs" (so my figure will be out slightly).
2. It takes me about 15+ minutes to analyze each "two card player total, and dealer up card" (since I don't have a "specialized program/spreadsheet", I have to do each hand from "scratch").

After the "main game strategy" is complete, you can possibly start on the "way more" complex "bonus card strategy"

Do you think it is worth working out the strategy this way (or similar) for this game?

Yes, I think the first step is to work out the basic strategy for the game decisions in the absence of multipliers -taking into account the "Dealer 3-card Busts are a Push" rule. I suspect you will almost always hit and rarely stand, double or split.

The screenshot indicates that you can see the multiplier cards before you make your playing decisions. So there would be a different strategy table for each of thousands of combinations of multiplier cards.

An obvious human-feasible advantage play would be to count the multipliers in the multiplier deck and raise your bet when the average multiplier remaining in it is very high, but I only see one shoe. Are they generating the multipliers electronically?

I have worked out a preliminary strategy for playing hard 12-20 for Quantum Blackjack. This strategy does consider any multiplier cards that you have in your hand but ignores the possibility of getting a multiplier card when drawing to your hand.



Explanation: Given the above table, if you have 15 vs a dealer 6, you should stand except if the cards that are currently in your hand have a multiplier value of 3 or higher in which case you should hit.

Because I have not factored in the possibility of drawing a card that is a multiplier, the above strategy table should be regarded as a starting point in which outstanding multiplier cards might influence you to Hit some hands that are shown as marginal Stand hands. However, I should point out that outstanding multiplier cards have no influence on your decision if their rank is high enough to cause you to bust. Ex: you have 17 vs 10, with no multiplier cards in your hand and all the multiplier cards for this hand have ranks in the range of 5-T: in this case, the possibility of drawing multiplier cards cannot help your hand (they will make you bust) and the correct move will be to Stand. I get Stand EV = -0.5098 and Hit EV = -0.5433 for this situation.

Note that I show that you should hit a H17 vs 8. I calculate this as Hit EV=-0.560353846 and Stand EV= -0.5612 - a very close decision indeed! Because I use some infinite deck approximations in my calculation, I consider that my calculation is not precise enough to give a reliable strategy for this particular situation. However, I do note that if any of the defined multiplier cards for the hand are an Ace, 2, 3 or 4, then the possibility of drawing one of those cards will certainly make it optimal to hit the H17 vs 8.

My next step will be to add the effect of drawing a card that is a multiplier card and that also does not bust your hand. I am afraid this is likely to get very complicated. For example, with H17 vs T an Ace that has a multiplier of 3X may not be sufficient to make you hit whereas a 4 with a multiplier of 3X may indeed be enough to make hitting be the optimal move. It may be hard to simplify define the strategy in some (Many?) cases.

I just learned of this game about a week ago and became intrigued because of the complexity of the math, and wondered if there was a possibility to find a strategy with positive EV.

Starting with the Wizard's infinite deck spreadsheet/workbook (I love this workbook btw thanks for sharing) i added the category of "bust with 3 cards" to the dealer sheet and inserted the probabilities that the Wizard posted about this game. First step, ignoring multiplier cards, I found a basic strategy which gives a house edge of about 15% and the hitting and standing agrees with the table posted by gordonm888.

The next phase was to suppose there is exactly one multiplier card. For each possible rank of the multiplier card, I added sheets for hitting expectations, hit-stand, doubling, splitting, ev, er. I found strategy charts for each possible scenario, having a single multiplier card. With a single 3x multiplier card, house edge is approximately 13%, except if it is Ace it is about 11%. With a 5x multiplier card, i found house edge as about 10%, except for ace it was about 5%. And with a 10x multiplier card, i found about 0% house edge, 10% player advantage with an 10x Ace multiplier card. The workbook has about 270 sheets, so there is quite possibly some errors. Using copy, paste and Find-Replace, it was not an unrealistic task.

Before I go any further and go to the next level (2 multiplier cards), I'm wondering if this game is still around. I'm thinking it might fail if there are not enough players. Optimal strategy is very hard to determine, and without optimal strategy the house edge is too high.

Also, I watched the 17 minute video by Live Casino Comparer and wrote down the occurrences of the multiplier cards: There were 15 hands, 9 of which had a single multiplier card, while 3 hands had two multiplier cards and 3 hands had three multiplier cards. Also, out of a total of 24 multiplier cards during these 15 hands, 17 of them were 3x, while 4 were 5x and 3 were 10x. This is too small a sample to make conclusions, but it looks like maybe the 3x, 5x and 10x do not occur with equal probabilities, and that one multiplier card, two multiplier cards, and three multiplier cards do not occur with equal probabilities.

Has anyone played this game? Lately? I'm debating whether to pursue this further.

Asking again, has anyone played quantum blackjack and kept a record of the frequencies for number of multiplier cards and for magnitude of the multipliers?

KevinR above has made a start, does anyone else have more observations to add to this? You may PM me if you are reluctant to post.

Quote: gordonm888

Asking again, has anyone played quantum blackjack and kept a record of the frequencies for number of multiplier cards and for magnitude of the multipliers?

I have not. Haven't even thought about it for a year.

This seems a bit complicated for the typical tourists

I would play it if they had the blond with the low cut dress hahaha. That was so long ago, she has probably hit menopause by now.

There are some fascinating strategy issues on some rare situations involving pairs in this game.

Lets say the multiplier card is 2d and 3X,

You are dealt 2d-2d vs 10. I think you split it, to get the 3X multiplier on both hands.

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Alternatively, the multiplier cards are 8s and 8d, both at 3X.

You are dealt 8s-8d vs 9. I think you do not split this, i.e., I think its better to play 16v9 at 9x than play 2 split 8s each at 3X.

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There are numerous variations on this that no one has yet looked at. Ex: there may be times when you don't split AA pair when the Aces are different suits and both are (high) multipliers.

It's been a long time since I put this calculation on pause (about 9 months) and looking at my infinite-deck spreadsheets, I realize it might take a few hours to get re-acquainted with the flow of these sheets, so I am not super confident in what I'm seeing.

I did do the cases of two 3X multipliers, two 5X multipliers, and two 10X multipliers. Being unemployed and locked down with covid regulations, I was bored and had time on my hands.

My sheet says if we are holding a pair containing two 3X multipliers, we hit 2-2 vs. 10 and double on 8-8 vs 9. In fact we never split when holding two 3X multipliers and we double a lot. I think this sheet assumes that if we double in this scenario, we will be paid 18 times our original wager if we beat the dealer.

The first scenario you mentioned with one 3X multiplier card and we are holding two copies of it, I realize now this may be different than the case in my 3X-3X sheet, where there are two multipliers and we are holding two of them. If we get paid only 3 times our original wager holding a perfect pair of the 3X multiplier, perhaps you are right about 2-2 vs. 10. I think my sheet for one 3X multiplier has not considered this case (yet).

I am trying to learn how to paste a jpg image of the chart here in this post, unsuccessfully.

I haven't looked at this in any detail but can imagine if you have a multiplier there will be many occasions when you double on your initial two cards providing it doesn't sacrifice too much from not being able to re-hit. The main problem is that you don't win anything if the dealer busts with three cards, so stiff hands aren't as valuable as in regular BJ. However vs a 2 apart from 2 T T all other busts will have >3 cards, so might even double things like 32 with a reasonable multiplier! Where you were only going to take one more card it would be reasonable to double with a nice multiplier.