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Last updated: December 17, 2024
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Quantum Blackjack
🔑 Analysis
Introduction
Quantum Blackjack is a live dealer blackjack variant by Playtech.
The game is dealt to a single player hand, which🔑 an unlimited number of players may bet
on. If players don't all take the same action, then only those cards🔑 pertinent to each
players hand will be shown. The twist is the game will randomly deal 1 to 3 cards🔑 from
a separate deck. A multiplier is associated with each card. If the player gets a card
to match a🔑 multiplier card, then he gets that multiplier if he wins. The take-back is
if the dealer busts with three cards,🔑 all hands left standing push.
Rules
The game
follows conventional blackjack rules, which I assume the reader is familiar with,
unless otherwise🔑 stated below. An unlimited number of players may play on one single
player hand. Each player may control is own🔑 fate. If some players stand, any further
cards dealt to other players will not be shown to those players who🔑 stood. Eight decks
are used. Dealer stands on soft 17. The dealer take a hole card and peeks at it🔑 for
blackjack. In addition, one to three cards will be dealt from a separate single deck.
These will be displayed🔑 on the screen. I will call these the Multiplier Cards. Each
Multiplier Card shall have a multiplier associated with it,🔑 from 3x to 10x. I do not
know the probability distribution of each multiplier. If at any point a card🔑 is dealt
to the player that matches one of the Multiplier Cards, then any player will shall get
that multiplier.🔑 If the player earns more than one multiplier, the players actual
multiplier will be the product of all earned multipliers.🔑 For example, if the player
gets a 3x and a 5x multiplier, then his overall multiplier will be 15x. Wins🔑 with a
multiplier are expressed on a "for one" basis. For example, if the player betR$100 and
won with a🔑 3x multiplier, his actual winnings would beR$200, plus the return of
hisR$100 wager. The same Multiplier Card may not 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 overall multiplier would still be
only🔑 10x. I assume the following other rules, but am not sure: no surrender, player may
double on any two cards,🔑 player may double after a split, player may split once only
(no re-splitting). At Playtech, the 21+3 and Perfect Pairs🔑 side bets are offered.
Multipliers do not apply to side bets. The side bet pay tables are below.
Strategy
It
isn't often🔑 that I say this, but working out a basic strategy for this game would be
very difficult. It would be🔑 easy to say that the player is strongly incentivized to get
as many cards on the table as he can,🔑 without taking ridiculous risks. In other words,
the player should hit and split more, double and stand less. I'm afraid🔑 I can't be more
specific than that.
Analysis
All I can say about the main game is Playtech claims the
return is🔑 99.47%. I am quite sure that is based on optimal player strategy, whatever
that is.
I can offer the following table🔑 that shows the probability of the dealer
busting with three cards by dealer up card.
Dealer Bust with Three Cards Up
Card🔑 Bust
with 3 Cards
Probability Ace 0.00% 2 9.46% 3 14.23% 4 19.58% 5 25.54% 6 31.92% 7 17.69%
8 17.64%🔑 9 17.79% 10 17.77% Average 17.30%
I can at least say that the 21+3 side bet
follows the 5-10-30-40-100 pay table.🔑 The following return table shows a house edge of
3.70%.
21+3 — 8 Decks Event Pays Combinations Probability Return Suited three🔑 of a kind
100 2,912 0.000244 0.024446 Straight flush 40 24,576 0.002063 0.082524 Three of a kind
30 61,568 0.005169🔑 0.155055 Straight 10 368,640 0.030947 0.309465 Flush 5 700,928
0.058841 0.294207 Loser -1 10,753,536 0.902736 -0.902736 Total 11,912,160 1.000000
-0.037039
The🔑 Perfect Pairs side bet follows the 6-12-25 pay table. The table below
shows a house edge of 4.10%.
Perfect Pairs —🔑 8 decks Hand Pays Combinations Probability
Return Perfect pair 25 1456 0.016867 0.421687 Colored pair 12 1664 0.019277 0.231325
Red/black🔑 pair 6 3328 0.038554 0.231325 Non-pair -1 79872 0.925301 -0.925301 Total
86320 1 -0.040964
More Analysis
As long as a wrote a🔑 custom program for this game, here
are the probabilities of various dealer outcomes by up card. This assumes the dealer
🔑 always plays out his hand.
Dealer Events — Stand on Soft 17 — 8 decks Event Ace 2 3 4 5
🔑 6 7 8 9 10 Average Dealer blackjack 0.308434 0.000000 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 0.000000 0.077108 0.047451 Total🔑 of 17 0.130210 0.139694
0.134482 0.130539 0.121946 0.165640 0.369048 0.128846 0.120241 0.111791 0.145215 Total
of 18 0.130813 0.134518 0.130524 0.124534🔑 0.122390 0.106208 0.137898 0.359800 0.118011
0.111608 0.139318 Total of 19 0.130643 0.129929 0.125313 0.121300 0.117607 0.106390
0.078478 0.128684 0.351581 0.111814🔑 0.133629 Total of 20 0.130879 0.124021 0.120695
0.116451 0.112134 0.101592 0.078668 0.069263 0.120275 0.340560 0.179709 Total of 21
0.053595 0.118308🔑 0.114871 0.111707 0.108021 0.097247 0.073878 0.069452 0.060864
0.034738 0.072838 Bust with 3 cards 0.000000 0.094616 0.142297 0.195751 0.255352
0.319236 0.176940🔑 0.176393 0.177871 0.177685 0.173015 Bust with 4 cards 0.077930
0.186456 0.177740 0.161866 0.136237 0.086546 0.073111 0.059515 0.045791 0.031980
0.087163 Bust🔑 with 5 cards 0.032068 0.062196 0.047464 0.033718 0.023657 0.015599
0.011055 0.007532 0.005068 0.002614 0.019139 Bust with 6 cards 0.004990 0.009388
🔑 0.006106 0.003847 0.002499 0.001462 0.000885 0.000498 0.000298 0.000101 0.002337 Bust
with 7 cards 0.000415 0.000826 0.000484 0.000275 0.000151 0.000077 0.000039🔑 0.000016
0.000009 0.000001 0.000177 Bust with 8 cards 0.000022 0.000046 0.000024 0.000011
0.000005 0.000002 0.000001 0.000000 0.000000 0.000000 0.000009 Bust🔑 with 9 cards
0.000001 0.000002 0.000001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000000
External Links
SportingBet rules — This is the🔑 best explanation of
the rules I can find.
Live Casino Comparer video — In this video, the Comparer explains
Quantum Blackjack🔑 as he plays. It should be noted he claims if the player gets a
multiplier he still gets it on🔑 a push. This contradicts the SportingBet
rules.
Discussion about Quantum Blackjack in my forum at Wizard of Vegas.
Written by:
Michael Shackleford
