 Ask the Wizard: |
Blackjack (special rules and promotions) |
Recently casinos have started an option for the player called "Automatic Win," which means if the player has 20, and the dealer has a 10 showing, the player could win half of his wager right away, without taking the chance of the dealer having a 20 or pulling a 21 somehow. The person who came up with this says that it happens more than half of the time that the player's 20 will either be a push or lose. I don't know if I can agree with his math, please let me know, thank you! P.S. Keep up the good work!
— Jason Z. from Las Vegas
That is not true about pushing or losing more than half the time. From my blackjack appendix 2 you can see that when the dealer has a 20, the possible outcomes are as follows (after the dealer peeks for blackjack, and based on six decks):
Dealer gets 17-19 or busts: 59.4%
Dealer gets 20: 36.8%
Dealer gets 21: 3.8%
So, the player will push or lose only 40.6% of the time. The value of a 20 against a dealer 10 is prob(win)-prob(loss) = 59.4% - 3.8% = 55.6%. That is more than the 50% you get by invoking the automatic half win, so you should decline the option. I address this option in my blackjack appendix 8, under the title casino surrender.
For the same reason, you should also decline “even money” when you have a blackjack against a dealer ace. In both cases two birds in the bush ARE worth more than a bird in hand. August 29, 2008
I'd like your advice on a blackjack coupon. As I understand the rules, the coupon doubles any win, up to $25, and can be presented any time. If I bet $16.50, and wait for a blackjack to use it, the coupon will double the blackjack win of $24.75. Or should I bet $25, and use it on the first win of any kind? What is the expected loss both ways? According to your Vegas blackjack survey the house edge on the Strat's 6-deck game is 0.64%. — Jim from Dallas, TX
Thank you for your support in my endeavor to seek justice against the Stratosphere.
First let's calculate the expected loss if you bet $16.50, and wait until a winning blackjack to use the coupon. The probability of a player blackjack is the number of aces × number of tens / combinations of ways to choose two cards out of the 312 in the shoe. That comes to 24×96/combin(312,2) = 0.0474895. If both of you have a blackjack, the coupon does you no good. Assuming the player has a blackjack, the probability of a dealer blackjack is 23 × 95 / combin(310,2) = 0.045621. So, the probability of the player having a winning blackjack is 0.0474895 * (1-0.045621) = 0.045323, or once in 22.06 hands. So, your way of playing 22.06 hands at $16.50 each would have an expected loss of 22.06 × $16.50 × .0064=$2.33.
Next, let's calculate the expected loss if you bet $25, and wait until the first win to use the coupon. The probability of any win is 42.42%, as found in my blackjack appendix 4. This is not exactly the applicable statistic for this situation, due to complications in splitting, but close enough. So, the expected number of hands to play to have a winning hand is 1/0.4242 = 2.36. The expected loss of betting 2.36 hands of $25 each is 2.36 × $25 × .0064=$0.38, which has a cost 84% less than waiting for a blackjack. May 13, 2008
In San Diego casinos Super Fun 21 has a $1 side bet that on the
first hand of single deck a diamond suited blackjack pays $300. What are the correct odds for getting this with 6 players and you are sitting at 1st base? — Mike L. from San Diego
There is one way to get the ace and four ways to get the 10-point card, for a total of 1*4=4 winning combinations. There are combin(52,2)=1,326 ways to choose 2 cards out of 52. So the probability of winning is 4/1326 = 0.30%. Fair odds would be 330.5 to one. The expected return is 0.0030*300 + 0.9970*-1 = -0.0920. So the house edge is 9.2%.
The reason they limit this bet to the first hand after the shuffle is a card counter could take advantage it otherwise. Without tracking the cards, you can assume the house edge is 9.2% all the time. January 2, 2008
Bally Gaming has a single-deck, multi-hand, blackjack game. The player plays seven hands against a single dealer hand. There is an interesting rule in that if the game runs out of cards, all unbusted player hands automatically win. What is the probability of running out of cards? Can have suggest any strategy changes to run out the deck? — Michael L. from West Mifflin, PA
For the benefit of other readers, the full set of rules is:
- Single deck.
-
Dealer stands on soft 17.
-
Winning blackjack pays even money.
-
Player may double any first two cards.
-
No double after split.
-
Player may resplit to four hands, including aces.
-
No draw to split aces.
-
No surrender.
-
Six-card Charlie (player unbusted six cards automatically wins).
-
Cards shuffled after every hand.
-
If game runs out of cards, all unbusted player hands automatically win.
The house edge using total-dependent basic strategy is 2.13%. I ran a 7-player simulation, using total-dependent basic strategy, and the average number of cards used per round was 21.65, with a standard deviation of 2.72. In almost 190 million rounds played, the most cards ever used was 42, which happened 7 times.
It is my educated opinion that even with computer perfect composition-dependent strategy the player would still realistically never see the last card. You could cut down the house edge much more using composition-dependent strategy, according to all the cards seen as you go along. However bucking 2.13% house edge to start with, you'll never get anywhere near break-even, regardless of how hard you try.
November 23, 2007
The Majestic Star in Gary, Indiana, offers double-deck blackjack, but you can’t split aces. How does that affect the house? The other rules are double on 10 and 11 only, no double after split, split other pairs once, and dealer stands on S17. – David T. from Chicago
Oy! Not being allowed to split aces costs the player 0.18%. Overall the house edge under these rules is 0.81%, based on total dependent basic strategy and a cut card game. September 30, 2007
I recently made a trip out to Vegas, where I came upon a game called the "World's Most Liberal Blackjack" at the Las Vegas Club. In this game you are allowed to: double down with any 2, 3 or 4 card combination, split & re-split aces as often as you choose, split & re-split any pair as often as you like, surrender your first two cards for half of your original bet and any hand with six cards automatically wins. The caveat is blackjack pays even money unless it's suited in which case it pays 2 to 1. Is this a better game than a 3 to 2 BJ with 6 decks and the dealer standing on a soft 17? Also, in this case, would it be beneficial to double down since the BJ only pays even money? – James from Chicago
The house edge of this game is 1.30% or 1.33%, as shown in my survey of Las Vegas blackjack rules, depending on whether the number of decks is five or eight. The odds are better in ANY game where blackjack pays 3 to 2. If you were to play this game, which you shouldn’t, you should still always stand on blackjack. Personally, I think the "World's Most Liberal Blackjack" claim on the marquee is false advertising. July 17, 2007
Thanks for creating a great site, with such detailed information. You stated a significant decrease in house edge for the various Charlies in blackjack, but I didn't see any suggestions on playing differently. Are there any basic strategy exceptions that are worth making to maximize profit in a large (6+ decks) shoe? I assume you would hit more if you were one card away from a Charlie against an ace, since it is so unlikely for the dealer to bust, but I would love to see specific instructions. Thanks. – Matt N. from Ann Arbor
You're welcome. For those readers who may not understand the question, a "Charlie" is a rule in which the player automatically wins if he hits to some number of cards, usually five to seven, without busting. The following table, for three or more cards, shows the basic strategy if the player is one or two cards away from such an automtic winner.
May 2, 2007
Hi Wizard. Thanks for maintaining this web site! I have a question about a blackjack rule that is applied in Dutch casinos: When being dealt a pair of sevens, a third seven will earn you 2:1 on your bet, regardless if you win the hand or not. However, this only applies when the sevens have NOT been split. I know that there are 6 dealer up cards in basic strategy that allow splitting sevens and 7 that do not, so the player should have an edge in this particular situation. But what are the odds of being dealt 3 sevens in blackjack in the first place? And if dealt 3 sevens, what are the odds they qualify for the 2:1 pay-out rule, based on a 4 to 6 decks, dealer stands on soft 17 basic strategy chart? Hope you can figure this one out for me. Keep up the good work! – Stan from The Netherlands, Europe
I show that rule is worth 0.026% to the player. Despite the incentive to hit 7,7 against a dealer 2-7, the player should still follow basic strategy and split. March 18, 2007
A local casino had a promotion on their over/under 13 side bet in blackjack. If your first two cards are suited you receive a $5 "action chip." If your first two cards and the dealer’s up card are suited you receive a $10 action chip. The action chips are good for one bet only, the player keeps any winnings but always loses the action chips. The minimum bet is $10. Six decks of cards are used. What is the house edge on the over/under 13 bet? - John from Shakopee, NM
Before considering the bonuses, the house edge is lower on the over bet at 6.55%, as I show in my blackjack appendix 8. The probability of three suited cards is 4×combin(78,3)/combin(312,3) = 4×76076/5013320 = 0.060699. The probability the player’s two cards are suited, but the dealer’s card is not, is (4×combin(78,2)×234)/(combin(312,2)×310) = 2810808/15039960 = 0.186889. Let’s assume the action chips are worth 49.5% of face value. Then the bonuses are worth 0.495×(0.060699×$10 + 0.186889×$5) = $0.76301. The expected loss on the over bet is $10×0.0655 = $0.655. So each $10 over 13 bet is worth $0.76301 - $0.655 = 10.8 cents. The overall player advantage is 1.08% on a $10 over 13 bet.
December 26, 2006
The version of " fun 21" offered on carnival cruise lines has some rules that are surprisingly favorable. They are so favorable that they appear to make up for the hit on soft 17 and then some. I can't find the catch. Any chance the edge is better then standard big casino Vegas blackjack or even slightly in players favor? Whether you answer or not, GREAT SITE and thanks much.– Eric from tallahassee
Thanks. This game is just a rip-off of Spanish 21. Note that the bottom of the card says that all queens are removed.
October 4, 2006
A local casino is offering a action chip bonus to their O/U 13 sidebet. If you bet at least $5 on your hand and a minimum of $5 on either the O/U bet, if your first two cards are suited, you win a $5 action chip. If you suited hand matches the dealers, you win $10 in action chips. The action chips can only be used for a regular BJ bet, if you win a bet using the action chip it is replaced with a casino $5 chip, if you push you can use again for another hand, it cannot be used for DD's or splits. Is this game worth playing, $5 a hand with $5 O/U bet? – Tim G from Minneapolis
Assuming six decks, the probability your cards will be suited, but not suited to the dealer’s up card is (77/311)*(234/310) = 18.69%. The probability your two cards and the dealer’s up card will be suited is (77/311)*(76/310) = 6.07%. From my blackjack appendix 4, we see the probability of a win in blackjack is 42.39% and a loss is 49.10%. The probability of a win before a loss is 42.39%/(42.39%+49.10%) = 46.33%. So an action chip is worth about 46.33% of face value. The value of this promotion is 46.33%*(18.69%*$5+6.07%*$10) = 0.7142, or about 71 cents per hand. The expected loss on a $5 blackjack bet is about 3 cents. From my blackjack appendix 8, we see the house edge on the over-13 bet is 6.55%, so the expected loss on a $5 bet would be $5*0.0655 = 0.3275. Therefore, the expected loss due to the house edge of both bets is about 36 cents, and the expected gain is 71 cents, for a net gain of 35 cents per pair of bets.
October 4, 2006
The Firelake Casino in Shawnee, Oklahoma charges a 50-cent commission on each $5 blackjack bet. The other rules are the standard, standing on all 17s. A promotion pays an extra $25 for each suited blackjack, $100 for suited 7-7-7 or 6-7-8, $125 for ace and jack of spades. – Jeff from Shawnee
Assuming six decks, the probability of a suited blackjack is 4×6×24/combin(312,2) = 1.19%. So the $25 bonus on that is worth $25×0.0119 = $0.2968 per hand. The probability of a suited 7-7-7 is 4 ×
combin(6,3)/combin(312,3) = 0.000015957. So the value of $100 on that is $0.0016. The probability of suited 6-7-8 is 4×6 3/combin(312,3) = 0.00017234. So $100 on that is worth $0.0172. The probability of a suited ace and jack of spades is 6×6/combin(312,2) = 0.0007420. So $100 extra on that is worth $0.0928 (the player is already getting $25 for the suited blackjack). Adding this all up, the bonuses are worth 11.25 cents. So this is nowhere near enough to compensate for the 50-cent commission.
September 13, 2006
In Reno there is a new type of positive EV promotion. The dealer pushes all “dealer draw to 21s”. Dealer naturals still win. (Any strategy suggestions? Table limits are $5-$25, I always play the max. The basic game is 6-Deck H17 DAS RSA to 4 hands. – Bob from Novato
Wow! According to my calculations this results in a player advantage of 6.4%. I’m assuming that the rule applies after doubling and splitting. Here is the basic strategy for that rule.
July 11, 2006
Great site! I would call it the best among all the gambling sites I have seen on the web. A question about surrender in blackjack. Some casinos (for example Foxwoods) give match play coupons for Blackjack. One good thing about the coupon is that when you surrender, you only lose half of your own money, and are allowed to keep the whole coupon. (But you lose your coupon no matter you win or lose.) I guess you want to surrender more in this situation, but was wondering what is the correct strategy? Thanks! - Austin from Cambridge, MA
Thanks. You should be doing a lot of surrendering if you can keep the match play. My blackjack appendix 9 is good for questions such as this. A match play is worth just about half of face value. So if the expected value of the hand is less than -1/3 you should surrender. Assuming the dealer hits a soft 17 here are those times.
- Player 6 vs. 10-A
- Player 12 vs. 9-A
- Player 13 vs. 8-A
- Player 14 vs. 8-A
- Player 15 vs. 7-A
- Player 16 vs. 7-A
- Player 17 vs. 8-A
- Player 8,8 vs. 9-A
The strategy is the same if the dealer stands on a soft 17, except the player will not surrender 6 against an ace.
Feb. 21, 2006
I'd like to know the house edge on blackjack after having 10% rebate on loss. When it's 8-deck and 6-deck, are the house edges different? - JJ from Seoul
It depends on your playing behavior. Your advantage can get very close to 10% if you play aggressively, always betting half your bankroll, until you multiply it many times over or go bust trying. My advice is keep your sitting short and go for a big win or lose it all, whichever comes first.
Feb. 11, 2006
I am currently playing your Ties Win BJ at Harrods. I really love it. Great game. My question is about a promo Harrods is having at the moment where if I win five hands/bets in a row I win back the lowest bet in that sequence. As I flat-bet I will win back one of my bets, effectively. Should I have chosen another game to play for this promo? Roulette is excluded but all other games at Harrods are permitted. Thanks, -Mick from Port Kembla
Thanks for playing it. Yes, Ties Win Blackjack was a good choice for this promotion. The probability of a full win is 43.314%, a half win is 8.75%, and a loss is 47.936%. So the probability of any win is 52.064%. The probability of five consecutive wins is 0.52064 5 = 3.825%. Flat betting this results in an extra 3.825% of return for the player. The house edge normally is 0.247%, so the player advantage under this promotion would be 3.5785%. However I find no mention of this promotion on the casino web site and given my usual 2-3 week delay to answer e-mail it is probably over.
Jan. 14, 2006
A popular option in Blackjack type games here in Washington State is called "Double Down Rescue." If you double down, and don't like your double down card you may surrender your double down portion, but receive your original bet back. As I understand your BJ Appendix 9, you should take this option if your double down results in a 0-16 versus a dealer 8 through Ace; since your expected loss by standing is greater than your -0.5 loss by rescuing? Fantastic site BTW. It should be required reading for any gambler. - Brain from Kennewick, WA
Thanks for the kind words. You are right, if the expected value is less than -1 then you should opt to take the double down surrender. As you said if the expected value for standing in my blackjack appendix 9 is less than -0.5 you should surrender, because you are betting two units. I would only add to your strategy that if the dealer hits a soft 17 then you should also surrender 17 against an ace.
Dec. 26, 2005
What changes should one make to blackjack basic
strategy when playing just a single hand when the objective
is to maximize the chance of winning that hand (for example
when using a match play coupon)?
It depends if the player is allowed to double
and split the match play portion of the bet. Usually the
player is not allowed to, which works against the player.
The following chart shows how to adjust your double and
splitting strategy, assuming the player may not double
the match play and if the player splits the match play
rides on the first hand played, based on infinite decks
and the dealer standing on soft 17. The hit/stand
strategy is the same. Oct. 17
30, 2004
I play occasionally with a group of players who love
poker but occasionally want to play BJ to vary the evenings
proceedings. Most of them would be beginners in terms of
strategy and probability awareness. What would be a fair set
of rules you would recommend so that BJ becomes a fair game
(or as close as possible) for both players and whoever takes
the bank?
It would depend on the specific skill factor of
the players. Without knowing that, but assuming the skill
level is equal among players, I would have the bank
option rotate from player to player.
Sept. 30, 2004
At the Privilege
Casino you can't split aces, but you can double.
How would it change the strategy assuming Cryptologic rules
6 decks and how does it increase the house edge?
Not being allowed to split aces increases the
house edge by 0.18%. You should only double against a
six, otherwise hit. Sept. 23,
2004
I received a promotion from a casino that offers to
return half my wager if the dealer gets a blackjack. How
would it affect the house edge and would there be any
strategy change to play it optimally?
That is a great offer. Assuming six decks the
dealer will have a winning blackjack with probability
2*(4/13)*(24/311)*(1-2*(95/310)*(23/309)) = 4.53%. So a
half bet every time that happens is worth 2.27%. Assuming
a house edge of 0.5% the player advantage would be 1.77%.
The strategy is the same as regular blackjack. Too bad I
missed that one. Sept. 23,
2004
I live next to a local casino that doesn't use 50-cent
chips for the Surrender Option so I get back more than half
when a place an odd-numbered bet. In particular the
surrender value of a $3 bet is $2. What is the effect of
this rule and what are the strategy changes, if any? Thanks,
Gerardo
This is a great rule! Only losing one-third of
your $3 bet by surrendering adds 2.25% to your expected
return. You didn't tell me the other rules but if we
assume a house edge of 0.5% before the surrender rule
then the player edge afterward would be 1.75%. Here are
the hands you should surrender on based on a six deck
game (hit or stand on soft 17 doesn't matter).
- Player 6 against 10.
- Player 12 or 13 against dealer 9, 10, ace.
- Player 14 or 17 against dealer 8, 9, 10, or
ace.
- Player 15 or 16 against dealer 7, 8, 9, 10, or
ace.
The only hand you would normally split that favors
surrendering is 8,8 against a 10. This advice only holds
true for a $3 bet. The value of surrendering diminishes
as the odd-numbered bet gets higher.
I noticed that all video blackjack games that I've
played in Vegas pay even money on a blackjack. Is this fair
according to the rules of blackjack? Because in a previous
question (July
4, 2004) you said, "It is a Nevada state law that
an electronic game with representations of cards or dice
must be based on fair odds. So the game should be fair with
odds the same as in a hand dealt game having the same
rules."
What I meant was that images of cards on the
screen had to be statistically fair. For example if you
took a tally of each card observed in the initial hand of
video poker or video blackjack you would see the
distribution approaching a flat line over time, much as
you would in a hand dealt game. However there is no law
that the standard rules of blackjack must be followed.
The machine can legally offer horrible rules like the
player losing on ties. The only caveat is that the
theoretical return must be at least 75%.
July 11, 2004
I have a coupon from LVA #115 Free Blackjack Insurance
up to $25.00 at Slots of Fun. What's its value?
I have that coupon too, and am running out of
time to use it. Let's assume a single deck game. The
probability the dealer has blackjack with an ace showing
is 16/51 = 31.37%. So if you bet $50 the value of this
coupon is (16/51)*$50 = $14.71. However I estimate you
will lose $1.23 due to the house edge waiting for the
opportunity to use it. So the coupon itself is worth
$14.71 - $1.23 = $13.48. Dec.
17, 2003
Here in Ontario, people have the opportunity to
"piggyback" a blackjack player instead of waiting for a spot
at a full table. When the primary player doubles or splits,
the piggybacker has the option but not the obligation to do
so. If the primary player splits and the piggybacker
doesn't, the piggybacker's original bet moves to the primary
player's first new (post-split) hand. This seems like it
would be beneficial in some cases, for example 8,8 vs 10. In
this case, E(16 vs 10) < E(8 vs 10) < 0, so the
primary player should split but the piggybacker shouldn't.
In this case, the piggybacker has turned his 16 into an 8
for free. Assuming the primary player plays perfect basic
strategy, what is the house edge for the piggybacker? If the
primary player colludes with the piggybacker to maximize
total winnings, and primary bets $5 while piggybacker bets
$100, is it possible to overcome the house edge?
I have seen this rule at the casino in Montreal
as well. Yes, this is a good opportunity for player
collusion, where the seated player bets small and makes
sacrificial plays for the big bettor in back.
Basic Blackjack by Stanford Wong goes into great
depth on this topic. There are lots of changes to the
splitting strategy, for example the seated player should
always split twos and then the back bettor should play
both hands against a 4 to 6, otherwise play only one.
Using Wong's full strategy reduces the house edge by
0.2%. Nov. 19, 2003
Your site is amazing. Here's my question. Does match
play change basic strategy at all? My non-math-based
instincts tell my that surrender becomes a bad idea, that is
if you have to surrender your coupon.
Thanks for the compliment. You are right that
you shouldn't surrender if they take the match play away.
There are some other strategy changes but I never worked
out a list. Generally the casinos don't allow doubling
the match play chip, in which case you should be less
inclined to double. 'Basic Blackjack' by Stanford Wong
indicates when to double if doubling the match play is
allowed, although I have seen this rule myself. In an
earlier column I state that the best bet to use with a
match play is the don't pass bet in craps.
Aug. 7, 2003
Hi! I have a question regarding the Microgaming no
hole card rule for single deck BJ game. I remember reading
in some forum that you concluded there is no difference to
the HA whether the hole card is dealt or not at the
beginning of the game. Is that true? I do notice that
Microgaming has a higher chance of blackjack.
Taking as an extreme example:
Dealer - Ace
Player - 2,A followed by A,A,2,2 (soft 19).
Wouldn't the dealer's chance of BJ be increased by the
fact that 4 more non-face cards were removed by the player
in a single deck? On the other hand, the player can never
remove enough face cards to significantly lower the chance
of dealer's blackjack. Please let me know what you think.
Thanks.
Although I don't remember saying that it is
true. The probability of the dealer's hole card being a
ten is the same whether it was dealt up front (as in
Microgaming casinos) or after the player's turn (as in
European casinos). In your example, yes, the dealer's
chance of getting a blackjack does go up, but it would go
up either for the next card in the deck or a hole card.
An unseen card is an unseen card, much in the same way
the effect is the same whether the dealer burns a card or
deals one less card out of the shoe. I hope this answers
your question. July 14,
2003
Since a $2.50 blackjack pays $4 (extra .25) and since
a blackjack occurs every 22 or so hands, I was wondering (at
a $1 table) if it would be possible to beat the game (albeit
very slowly) by just playing $2.50 each hand? - Rob Savickis
from Niagara Falls, New York
Actually a blackjack will occur closer to once
every 21 hands. To be more specific in a six-deck game
the probability of a blackjack is 2*(4/13)*(24/311) =
0.047489. An extra quarter this often is worth 0.25*
0.047489 = 0.011872. Divided by the $2.50 bet this adds
0.004749 to the player's expected value. Most games where
the dealer stands on a soft 17 or uses 1 or 2 decks will
have a house edge less than this. So, yes, you could gain
a small edge. Assuming six decks and dealer stands on
soft 17 the player's expected profit per hour, based on
100 hands per hour, would be 16 cents.
May 8, 2002
You go, Wiz. Our local casino hands out promotional
coupons, which act as a first-card ace in blackjack. From
your BJ appendix, most hands containing an ace have a
positive expectation, without counting the BJs you'll get
four out of every thirteen plays. Do you know the overall
expectation of having an ace as your first card? Thanks. -
Victor from Yakima, Washington
According to Stanford Wong's 'Basic Blackjack'
he says the player's edge given the first card is an ace
is 50.5% (page 124). Your question however could be
rephrased as, "what is the value of the ace, given that
the other card is not a ten." Using an infinite deck for
the sake of simplicity we can breakdown Wong's number as
follows: 0.505 = (4/13)*1.5 + (9/13)*x, where x is what
you want to know. Doing some simple algebra we get
x=28.5%. Nov. 23,
2001
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