Blackjack - General Questions

Are there any casinos in Vegas besides Mandalay Bay where the dealer stands on a soft 17? I ran a shoe of Spanish 21 at MGM. I don't see any advantage with the tens missing. Especially on double downs.

Jim from North Olmsted, Ohio, USA

As far as I know, the vast majority of shoe games in Vegas stand on soft 17. Usually the dealer will hit a soft 17 in single-deck games and double deck can go either way. I try to explain why card counting words in my page on card counting.

How does the house have the advantage in Blackjack?

Rob

The dealer has the advantage because the player has to go first. If both of you bust it isn't a tie, but YOU lose.

What is the minimum blackjack bet at most online casinos? Are there a time limits in which to make your decisions at the blackjack tables? If so, what are they?

Reg A. from Vancouver, British Columbia

The minimum varies from place to place. At Unified Gaming casinos it is $1, Microgaming is $2, Starnet and Cryptologic are $5. If you are playing by yourself, then you can take a long time. I've had phone calls in middle of a hand, came back 15 minutes later and resumed the hand without having been logged out. You will get logged out for inactivity eventually but it takes quite a while. However, if you are playing at a group table there is a time limit per decision of about 30 seconds. At the Sands of the Caribbean you can see your clock ticking down.

As a first time gambler in Vegas, I've been told to play craps and Caribbean Stud. How much money should I prepare to take to a sitting of each to try to stay in the game long enough to see results?

Vinnie from Tulsa

If you play long enough, the only results you will see is that you will lose all your money. Don't bring to the table more money than you care to lose in that sitting.

Second, Caribbean Stud Poker has a house edge of 5.22%, so if you're trying to stay in the game as long as possible, I would avoid that one. The best table games are craps and blackjack, when played properly.

Why are basic strategy blackjack charts setup with the apparent theory that the dealer has a "10" card in the hole. When in reality I believe that the odds are 9-4 against a "10" card being anywhere. Am I missing something? Your website is very interesting. Thanks a lot.

Eddie from New Orleans, Louisiana

Assuming that the dealer has a 10 in the hole is just a memory device, it has nothing to do with the way the basic strategy was constructed. I can't stand in when I hear one player telling another, "You always assume the dealer has a ten in the hole." If this were true the player should hit a 19 against a 10, certainly that is an unreasonable play.

Across the various blackjack strategies you provide on your site, does the standard deviation change much? I would guess that when DAS is allowed, one's results are more variable, but how much? Is there a good reference book that provides variance figures for various basic blackjack strategies?

Nathan from University, Mississippi

Good question. Unfortunately I don't have exact standard deviation figures according to specific sets of rules. The 1.15 figure on my site is based on liberal Vegas Strip rules. I agree that the double after split rule increases the standard deviation. Surrender would decrease it. Sorry I am not of more help than that.

Is there any mathematical proof you can provide that will prove a player sitting at "third base" on the blackjack table can’t change the outcome of the game by making bad decisions based on "basic strategy" I have had many people argue that poor decisions at third base, or anyplace on the table for that matter, cost them money. I would love to see the actual numbers on this if it is possible. Great site by the way. I love gambling, and your site is one of the best I have seen on the web. Actually has real proven info.

Mike Castelluccio from Lafayette, U.S.

Thanks for your kind words. Unfortunately I do not have any such proof at hand. If I did set about proving it myself I would use a computer simulation. However skeptics would probably claim something ridiculous, like that bad players disrupt the karma of the game, which can’t be replicated in a computer.

Can it actually be true that what I experience has a statistical base? It seems to me that it takes a lot longer to win X number of chips that to lose the same amount (I only play blackjack). For example, if I start with 300 chips, it might take hours to double my money (my goal), yet I can lost that number in what seems like almost no time at all. Can this really be true? Also, do you have a rule of thumb about when to leave the table when you are winning?

Chris from Gaithersburg, Maryland

What you have experienced is likely the result of some very bad losing streaks. It may also be the result of progressive betting or mistakes in strategy. The basic strategy flat bettor should have a roughly symmetrical expectation in terms of steep ups and downs, slightly favoring steep downs due to the house edge and a 48% chance of a losing hand compared to 43% chance of winning. If I'm playing for fun then I leave the table when I'm not having fun any longer.

Which is a better game for the player Spanish 21 or just regular blackjack in Atlantic City.

Michael from Philadelphia, USA

Spanish 21! Under Atlantic City rules blackjack has a house edge of 0.43% and Spanish 21 of .40%.

Do you mean to tell me that man has designed a way to put three million transistors on a single chip (microprocessor) the size of a finger nail, and we don't have a way to beat a 50/50 even money game bet. I find that to be unbelievable, besides I found that computer simulations are definitely not the same as live world action. Also why don't casinos introduce video blackjack to thwart the card counters and get rid of dealers?

Mark from Chicago, USA

I have said numerous times that there is no long-term way to beat a game with a house edge. If there were a true 50/50 game with no house edge it would be impossible to guarantee beating or losing to it under real world conditions. The results always approach the house edge in the long-term. It is not just computer simulations that back this up but the fundamental laws of probability.

About video blackjack, that may be the way of the future. I have seen fully electronic tables with video display at the World Gaming Expo. I have also seen tables that with cameras can track every bet and every play each player makes. This enables the house to accurately comp players and alert them to card counters. These tables look and feel like any other blackjack table, so you card counters may be out of business if these tables are successful.

Where is the best place to play Blackjack in Atlantic City and why?

Mike and Taffy M. from Philadelphia, Pennsylvania

The Claridge is the best. As far as I know, they are the only Atlantic City casino to offer late surrender, which lowers the house edge from 0.43% to 0.36%.

I know that you have the casino advantage for blackjack listed on your web site in the case that a person plays the basic strategy, but I was wondering what the casino advantage was on average against a typical beginner. Also, can you formulate what the best advantage a casino could have over the worst of players, assuming that they would never hit anything higher than a hard sixteen? Thank You Kindly.

John from Storrs, Connecticut

According to Extra Stuff by Peter Griffin the cost due to player mistakes of the average player is 1.41%. This is above whatever the house edge is assuming proper basic strategy. It also varies by place, Atlantic City players are better than Las Vegas players, for example. Your other question about bad strategies was such a good one I added information to my blackjack section about it. See my remarks on bad strategies.

First of all, I think your web site is great and want to thank you for all this great, solid information. My question is this: blackjack tables have a maximum bet limit that more than increases when you move up from the five dollar table to the ten etc. I suppose this is to discourage larger stakes gamblers from playing at lower stakes tables but how do they calculate these limits? I notice that they are different at different casinos. Also, on your chart of the house edge, it would be great to see a comparison of house edge for a blackjack player using Basic Strategy vs. one who is counting cards. Thanks again for the great work.

Michael from Santa Cruz, USA

You're welcome! Casinos generally try to keep the maximum bet about 200 to 500 times the minimum bet. Why? If a casino is comfortable with a $10,000 bet on a $100 table, why not take it on a $5 table? The answer seems to be that casinos like to corral their big bettors into certain areas. Such high-limit areas tend to have the best staff and surveillance. Limiting the ratio of maximum to minimum bet is also a defense against cheating and advantage play.

The advantage of card counting depends on how good and aggressive the card counter is. Other than my introduction to card counting, I leave that topic to other gambling writers.

In the game of blackjack, can you tell me if people entering and leaving the game changes your odds of winning or losing? It seems to have an effect when I am playing.

Jerry from Shreveport, USA

No, other players entering and leaving will have no long term effect on your odds. This may seem to be true but I suspect you are more likely to remember when entrances and departures hurt you than the times they helped you. In the long run the cards are the cards and all other factors cancel each other out.

I enjoy both Caribbean Stud and Blackjack. The element of risk for Stud is 2.56% and Blackjack is 0.38% or a ratio of 6.7. Assume I play $15 Blackjack and $5 ante Stud i.e., $15 at risk when I bet. Since the number of hands dealt per hour is many more for Blackjack versus Stud, does that mean that I will lose the same amount of my bankroll if the ratio of hands dealt per hour is 6.7?

John from Monsey, USA

No. If you’re interested in comparing expected loses it would be better to use the house edge. My section on the house edge shows the blackjack house edge to be 0.43% (Atlantic City rules) and that of Caribbean Stud Poker to be 5.22%. The expected loss for 1 hand of Caribbean Stud Poker at a $5 ante is $5 * 5.22% = 26.10 cents. The expected loss for 6.7 hands of blackjack at $15 per initial bet is 6.7 * $15 * 0.43% = 43.22 cents. So given these two options you will lose less in Caribbean Stud Poker. The ratio of the house edge of Caribbean Stud Poker to blackjack is about 12. So the expected loss of a $1 initial Caribbean Stud Poker bet is about the same as a $12 initial blackjack bet.

My question is about table maximum bets in BJ. Say the posted limit is $200. I bet $200 and I get dealt 8-3. Can I double down, or have I already reached the limit? Or suppose I’m betting $200 and get dealt a pair of aces. Can I split them, turning one hand into two hands?

Jack from Boston, USA

Yes, you could double or split in those situations. The maximum applies to the initial bet. If the limit were $200 you could also play multiple hands of $200.

My friend and I have a side bet going on. I said to him that I think that blackjack has the best odds in a casino, he said to me that he thinks poker has the best odds. In a casino, what game do you have the best odds in winning, blackjack or poker?

Jeff from Chicago, IL

Although they are hard to compare I say blackjack is the better bet. It is easy to be a good blackjack player by learning the basic strategy. It is difficult to be a good poker player. Casino poker rooms are often full of very good players just waiting for an inexperienced player to fleece. However some people may be naturally gifted at poker, so take my answer with a grain of salt.

In Blackjack, what is the difference between early surrender and late surrender?

Dan from Brooklyn, USA

In early surrender you can surrender before the dealer checks for blackjack. With late surrender you only have the option after the dealer checks for blackjack. Early surrender is much better because you can still save half your bet when the dealer does have blackjack. As far as I know no casino on the land or Internet currently offers early surrender.

Dear Wizard, Just a quick question, why does the house edge change for an insurance bet in blackjack depending on the number of decks used?

Rick

Because we already know an ace has been removed for the shoe. That leaves the rest of the shoe slightly ten heavy. A greater the ratio of tens in the shoe the more likely the insurance bet is to win. The fewer the decks the greater this effect is. Insuring a 20 (except A/9) increases the house edge on the insurance bet because there are two less tens in the shoe.

In response your last column from a player who was concerned about the dealer calling "table max" when he went from $15 to $300. It should be added to your answer that this is most likely the internal procedure of the casino as most do this when any maximum bet is placed in order to draw the supervisor’s attention. Most players tend to believe the actions of a casino are directed against them when the usual reason is simply the staff are following company procedures.

anonymous

Thanks for this good point. I stand corrected.

Love your site! I enjoy casino gambling but generally can only afford a small bankroll (less than $100 per session). What game would you recommend to maximize the life of my bankroll and chances for a winning session?

anonymous

Thanks. Considering both odds of winning and bankroll preservation I think the choice comes down to blackjack (which favors winning) and pai gow poker (which favors bankroll preservation). If you can find a $5 table in either game I would go with blackjack. If the minimums are $10 then I would go with pai gow poker.

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?

anonymous

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.

I realize that decisions per hour in games like blackjack and craps can depend heavily on factors like the number of other players at the table, the hand shuffle vs. machine shuffle, shooter and dealer speed. Still, I was curious if you could give me a rough approximation of how many decisions per hour an individual can expect at a mostly-full craps table and a blackjack table with both a hand shuffle and machine shuffle. This would help me estimate my expected loss per hour and weigh it against the comps I am being offered.

anonymous

The following tables show the number of hands/tosses per hour in blackjack, craps, and roulette. The source of the tables is Casino Operations Management by Jim Kilby.

Hands per Hour in Blackjack

Players Hands per hour
1 209
2 139
3 105
4 84
5 70
6 60
7 52

Rolls per Hour in Craps

Players Rolls per hour
1 249
3 216
5 144
7 135
9 123
11 102

In craps 29.6% of total rolls are come out rolls, on average.

Spins per Hour in Roulette

Players Spins per hour
1 112
2 76
3 60
4 55
5 48
6 35

How long would it take me to lose $10,000 with $5 flat bets playing 6-deck Vegas strip blackjack?

Rachel from La Paz

The expected loss per hand would be $5*0.0062 = 3.1 cents, assuming you play proper basic strategy, and that the dealer hits a soft 17, which is usually the case in $5 games. Assuming you lost exactly that amount per hand it would take 322,580 hands. However the actual number would be a little less because of bankroll volatility and you can’t play after you go broke. To make an educated guess I would say about 300,000 hands. At 60 hands per hour this would be 5000 hours, or two and a half years of full-time play.

Great site keep up the excellent work. I am looking for a game/games that are suitable to get up one unit. i.e. If i bet 10 dollars I would like my original 10 back plus the 10 I bet. I belives the craps pass line would be the best bet to do this. I dont mind going down a little money if I have to, but I would expect to get positive at least the amount of my original bet sometime before the end of the shoe or game. Is craps the answer...or is there a card game that may be better? Thanks for your time and effort.

Mike from Westfield, MA

Thanks. If your goal is to win just one unit I agree craps is the best place to start. The don’t pass is slightly better than the pass. However if you lose your first bet I would switch to blackjack. Only when exactly where you started would I go back to craps. This is because you won’t need to double or split to win just one unit, and a hit/stand only blackjack game has a house edge of about 2.5%.

I’m very glad to see that you are back changing the world 1 mathematically challenged emailer at a time. I have a combination of a dear abby and an odds question. Here goes: A coworker of mine has gone his entire gambling life getting angry at the 3rd base player in blackjack whenever that player doesn’t follow basic strategy. He insists that that "bad" player is hurting his odds. I am 100% certain that it doesn’t change your odds at all. I have tried to explain to him that the reason he thinks it hurts him is because the times that it has in fact hurt him stand out in his mind, and he probably doesn’t even pay attention to the times that it helped him. I told him that mathematically, his odds are the exact same whether he plays at a table of people who never hit, a table of people who never stay, or a table of people playing perfect basic strategy. He doesn’t buy it. But, how can I possibly convince him that he’s wrong? Should I even continue to try? If he admits that he’s wrong, he has to admit that he has wrongly berated countless people at blackjack tables when those people were not hurting anyone else but themselves (and in some cases, if they were counting cards and adjusting their strategy accordingly, they weren’t even hurting themselves). Don’t you think casinos would be better places if people really understood that what I do with my blackjack hand doesn’t change your odds in the long run?

Aaron from Detroit, MI

Your coworker sounds hopeless. As I have said before, the more ridiculous a notion is the more tenaciously it tends to be held. I’d give up on him and let him believe in his delusion. Personally I don’t give unsolicited gambling advice because it is seldom well taken.

I had a blackjack and the dealer paid me. Then at the end of the deal he turned his cards over and he discovered he had a blackjack. He forgot to check his hand before paying me. The supervisors wanted me to return the winnings. I refused. Seems I remember these scenario from a book on blackjack. Was I correct?

Woloshen from Montreal

I say you should have returned the winnings. I have never seen this addressed in any book. However, is a book really required? That is what you have a conscience for. You were asked to make things right, it is the right thing to do so.

Love your site! I just ran across your detailed list of Las Vegas Blackjack tables and their edges, so I was wondering: Suppose that there two BJ tables, one with an edge of 0.2% with a table minimum of $10 and 0.4% with a table minimum of $5. Both tables have the same $0.02 loss per hand. Is there any advantage to choose one table over the other?

Milton from Santa Fe

Thanks. To answer this question you first have to ask yourself why you are gambling in the first place. If you are trying to lose as little as possible then you shouldn’t play at all. However, if you are playing for the fun of gambling then I would choose the $10 game with the 0.2% edge. The expected loss will be the same but you’ll get more of a fix with the larger wagers.

My friends and I are planning a weekend trip to Las Vegas. As a college student, I’ve decided the most I can afford to lose (the best way to set a limit when gambling I think) is $500. I was curious what games you thought I should play? What stakes? You could call me slightly risk-seeking, because I’d love to return to Durham with a big stack and I’m mentally ready to lose it all. Thanks so much, your web site is fantastic.

Ben from Durham

Thanks for the kind words. The three games where you can get the house edge under 0.5% are blackjack, craps, and video poker. Of the three I would recommend blackjack. I would start betting $10 a hand. By playing conservatively at the beginning you won’t go bust too soon and have to beg your friends for a loan. Let’s say you want to double your bankroll or go bust trying, then press your bets as you get close to the end of your trip. Be sure to memorize the basic strategy before you play and don’t accept anything more than a 0.4% house edge.

How much would it increase the house edge if the player took insurance every time in blackjack?

RJM

The dealer will have an ace up 1/13 of the time. The house edge on insurance is 7.395% in a six-deck game, on average. However, this is applied to half a bet size. So the expected loss of always taking insurance is (1/13) × 7.395% × 0.5 = -0.00284. So the house edge would go up by 0.284%.

For recreational blackjack players, who use basic strategy, and don’t count, does the house advantage increase as the penetration increases? I believe it does because the deeper you get into the shoe, the greater the absolute value of the count will tend to get, which should trigger count-based strategy changes. Since the non-counter wouldn’t know when and how to make such changes, he would be making more mistakes as the count gets further away from zero. Thus, wouldn’t a non-counter be better off at a table with shallow penetration?

Jon from Doylestown, PA

In a non-cut-card game, the house advantage is always the same for the non-counter. Clumps of high or low cards are just as likely to appear at the beginning of the shoe, as the middle, as the end. Just because the count is zero at the top of the shoe doesn’t mean you’ll have an exact balance of high and low cards. You seem to be suggesting that the cards are more clumpy at the end of the deck. However, if that were true, then the odds would change if the dealer dealt the cards in reverse order. Surely that is a ridiculous notion.

Let’s say the basic strategy player has 16 against a 10 late in the shoe, and hits. If the count were high, standing would be the right play, resulting in what would look like an error to a counter who was watching. However, if the count were negative then hitting would be all the better. In the end, it averages out, for the basic strategy player.

For reasons I explain in my blackjack appendix 10, the basic strategy player should prefer a game with a continuous shuffler, if his goal is to minimize the house edge. Aside from that, the house edge is not affected by penetration. I should add that with a shallower penetration there will be more time spent shuffling, and thus a lower expected loss on an hourly basis.

What do you think about the future of blackjack?

pacomartin

Let's look at the data first. The following table shows the number of tables by game and year for Clark County from the Nevada Gaming Control Quarterly Statistical Reports. All years are based on the fourth quarter except 2009, which is based on the third quarter, because at the time of this writing, the fourth quarter was not yet available. Sports, racing, bingo, and keno are not included.

Total Table Games 1990-1999

Game 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
21 2132 2094 1954 2132 2140 2134 2345 2383 2404 2664
Roulette 197 202 203 232 252 258 287 303 311 354
Craps 290 284 272 286 303 308 325 334 344 372
Other games 3 5 8 28 95 15 25 51 56 71
Baccarat 54 57 49 51 64 70 72 81 83 103
Pai gow poker 73 98 99 107 101 95 109 120 139 170
Three card poker 0 0 0 0 0 0 0 0 0 0
Mini baccarat 26 33 39 40 43 51 73 77 85 94
Let it ride 0 0 0 0 23 148 144 110 108 118
Pai gow 26 22 19 19 2 23 22 36 42 33
Wheel of fortune 47 44 42 39 48 46 37 34 34 36
Caribbean Stud 0 2 13 95 127 120 109 100 95 94
Chuck a luck 1 0 0 0 1 1 1 3 2 2
Sic bo 3 3 2 2 2 2 2 3 3 3
Crapless Craps 3 3 1 1 6 4 2 1 0 0
Double Middles 3 3 3 2 0 0 0 0 0 0
Nines up 2 1 0 0 0 0 0 0 0 0
Over & under 7 1 1 1 1 0 0 0 0 0 0
Over & under 13 3 11 12 3 0 0 0 0 0 0
Red Dog 13 14 17 10 0 0 0 0 0 0
P&M Pokertable 2 0 0 0 0 0 0 0 0 0
Super pan nine 4 1 0 0 0 0 1 0 0 0
Total 2883 2878 2734 3048 3207 3275 3554 3636 3706 4114

Total Table Games 2000-2009

Game 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
21 2659 2605 2546 2561 2508 2662 2589 2528 2537 2448
Roulette 359 362 352 360 360 392 394 393 405 407
Craps 372 370 352 352 338 364 351 340 334 336
Other games 101 143 52 68 81 121 196 283 243 226
Baccarat 106 98 93 109 115 133 175 176 233 218
Pai gow poker 179 198 207 217 211 192 192 175 194 216
Three card poker 0 3 105 135 160 182 185 191 208 197
Mini baccarat 110 118 126 115 124 147 148 130 143 140
Let it ride 129 132 121 112 105 109 97 94 98 97
Race book 81 83 80 78 83 86 84 81 82 67
Pai gow 43 41 40 43 49 73 76 82 80 58
Wheel of fortune 41 42 41 40 40 37 37 33 37 40
Caribbean Stud 88 80 75 69 56 45 30 23 22 17
Chuck a luck 2 1 2 2 3 1 1 1 1 1
Sic bo 3 6 6 4 2 1 2 1 1 1
Crapless Craps 0 1 2 0 2 0 0 0 0 0
Double Middles 0 0 0 0 0 0 0 0 0 0
Nines up 0 0 0 0 0 0 0 0 0 0
Over & under 7 0 0 0 0 0 0 0 0 0 0
Over & under 13 0 0 0 0 0 0 0 0 0 0
Red Dog 0 0 0 0 0 0 0 0 0 0
P&M Pokertable 0 0 0 0 0 0 0 0 0 0
Super pan nine 0 0 0 0 0 0 0 0 0 0
Total 4192 4200 4120 4187 4154 4459 4473 4450 4536 4402

The next table shows the percentage of the total table game market for each game for 1990 and 2009. Note how 21 is the biggest loser, going from 74.0% to 55.6%.

Market Share Comparison

Game 1990 2009
21 74.0% 55.6%
Roulette 6.8% 9.2%
Craps 10.1% 7.6%
Other games 0.1% 5.1%
Baccarat 1.9% 5.0%
Pai gow poker 2.5% 4.9%
Three card poker 0.0% 4.5%
Mini baccarat 0.9% 3.2%
Let it ride 0.0% 2.2%
Pai gow 0.9% 1.3%
Wheel of fortune 1.6% 0.9%
Caribbean Stud 0.0% 0.4%
Chuck a luck 0.0% 0.0%
Sic bo 0.1% 0.0%
Crapless Craps 0.1% 0.0%
Double Middles 0.1% 0.0%
Nines up 0.1% 0.0%
Over & under 7 0.0% 0.0%
Over & under 13 0.1% 0.0%
Red Dog 0.5% 0.0%
P&M Pokertable 0.1% 0.0%
Super pan nine 0.1% 0.0%

This begs the question of why blackjack is losing market share. Here are what I think are the main reasons:

  1. Popularity of poker-based games is causing some players to switch.
  2. Casinos don’t comp blackjack play as well as other games.
  3. The rules are getting worse. I’m not suggesting most players know this, but over time, players can feel rule changes, like the dealer’s hitting a soft 17, in their wallet.
  4. All casino games have a natural lifespan, and blackjack is getting more grey.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

Some Playtech blackjack games have a ten-card Charlie rule. What is the value of that?

anonymous

For the benefit of other readers, a "ten-card Charlie" rule means that if the player gets to ten cards, without busting, then it is an automatic winner.

According to my simulation, the probability of the player getting to at least ten cards is 1 in 60 million. So, it lowers the house edge by about 0.0000017%.

At the Spielbank Bad Homburg casino, near Frankfurt Germany, they have a special card in their blackjack game. This card is an ace and replaces one of the regular aces in a six-deck shoe. The card features the image of the casino founder Francois Blanc. If the player gets a blackjack including this card it pays 3 to 1 instead of the usual 3 to 2. It is also an automatic winner for the player, but an ordinary blackjack for the dealer. Six decks are used. How does this rule affect the house edge?

anonymous

I show the combined value of these rules is worth 0.31%.

The blackjack rules they follow, which seem to be standard at all Speilbank casinos, are:

  • Six decks.
  • Dealer stands on soft 17.
  • No dealer hole card.
  • Double on 9 to 11 only.
  • Double after split allowed.
  • Re-split any pair, including aces, up to four hands.
  • No surrender.
  • Continuous shuffler.


Using my blackjack house edge calculator, I get a house edge before the Francois Blanc card of 0.55%. The Francois Blanc card rule lowers the house to 0.24%!

According to the Spielbank Bad Homburg rule book, the Francois Blanc is exclusive to their casino.

For how to play under these rules, please visit my European basic strategy.

What is the house edge on this awful set of blackjack rules, known as "Party Blackjack" at the Adelaide casino:

  • Six decks
  • Dealer hits a soft 17
  • No dealer hole card. Player loses total amount bet if dealer gets a blackjack.
  • Double on 9 to 11 only.
  • Double after split allowed.
  • Player may re-split to three hands, except no re-splitting aces.
  • Blackjack pays 6 to 5.
  • Push on dealer 22.


Michael P. from Australia

Oy! Those rules are so bad that the hair on the back of my neck stood up reading them.

Using my blackjack house edge calculator, I get a house edge of 2.22% before considering the no hole card and push 22 rules. I'm assuming a continuous shuffler is used and the player can re-split to four hands. The no hole card rule costs the player another 0.11%. However, the most offensive rule is the push 22, which costs the player 6.91%. The bottom line is a house edge of 9.24%! That is simply an abomination to the game.

I invite my readers to let me know if there is a worse set of blackjack rules out there somewhere.

Harrah's in Philadelphia is paying the following bonuses in blackjack:

Harrah's Philadelphia Promotion

Hand Pays
Triple sevens $500
Five-card 21 $250
Black ace and black jack $150
Red ace and black jack $100
Suited blackjack $50

To get the bonuses a minimum bet of $25 is required. Six decks are used. Can you tell me the value of this promotion?

gamerfreak

Nice promotion! The following table shows the probability of each event. The probability for the five-card 21 should be considered a bit rough.

Harrah's Philadelphia Promotion Analysis

Hand Pays Probability Return
Triple sevens $500 0.000384552 $0.19
Five-card 21 $250 0.00453345 $1.13
Black ace and black jack $150 0.002968093 $0.45
Red ace and black jack $100 0.002968093 $0.30
Suited blackjack $50 0.011872372 $0.59
Total $- 0.011872372 $2.66

The bottom right cell shows the bonuses are worth $2.66 per hand played.

The blackjack rules are pretty liberal there, with a house edge of only 0.35%. On the minimum required bet of $25, the expected loss per hand is $0.08. So, the promotion is worth $2.57 per hand played.

Unfortunately, the promotion has ended as of this publication date.

This question was raised and discussed in my forum at Wizard of Vegas.

I know of a blackjack machine where, through a bug, the player can get back a losing insurance bet. The rules are eight decks, blackjack pays 3 to 2, dealer hits a soft 17, double after split allowed, no surrender, and no re-splitting. What is the house edge of this game if I get back every losing insurance bet?

Blony1789

This bug is equivalent to getting an extra unit every time the dealer has a blackjack with an ace up. That will happen 2.37% of the time. The house edge would be 0.72% without this bug. With it, the player advantage is 2.37% - 0.72% = 1.66%.

For further discussion on this question, please see my forum at Wizard of Vegas.

There is a blackjack game called Hot Action Blackjack being played at the California Grand Casino in San Francisco. The rules of the game are as follows:

  • Six decks in a continuous shuffler with an additional 18 jokers with a face value of 2.
  • Dealer hits soft 17.
  • Double on any first 2 cards.
  • Re-split up to four hands.
  • No drawing to or re-splitting aces.
  • No surrender.
  • Blackjack pays 6 to 5.
  • If the player's first two cards are jokers, then he gets a 4 to 1 bonus.
  • If the player's first two cards are suited aces, then he gets a 5 to 1 bonus.
  • Player must pay a 5% commission to play.

What is the basic strategy and house edge?

JPClav

First, here is my basic strategy under these rules:

All things considered, I show a house edge of 6.01% (ouch!) based on the initial wager. In other words, if the player bet $100, not counting the $5 commission, then he could expect to lose $6.01. It goes to show why I would stay away from player-banked games in California, unless you're the one banking.

This question is raised and discussed in my forum at Wizard of Vegas.

I saw the following rules on a bar-top blackjack machine at Binion's in Las Vegas: Single deck, dealer stands on soft 17, blackjack pays even money, both player and dealer must stand on six cards, and no doubling or splitting. What is the house edge on this awful set of rules?

Charles from Winnipeg

Ouch! According to Norm Wattenberger, creator of Casino Vérité blackjack software, the house edge under these rules is 4.30%. This does not factor in the rule about standing on six cards, which I figure cuts roughly equally both ways. Unfortunately, bar-tops elsewhere have this same set of terrible rules.

This question is asked and discussed in my forum at Wizard of Vegas.

I found a blackjack machine with a player advantage of 0.1%. As a group, we've played flat bet 2,015,000 hands and am down 1,475 units. I don't specify the exact rules, lest I give the play away, so please take the 0.1% player advantage on faith. What are the odds of running as bad as we are, assuming the game is fair?

anonymous

Based on that advantage and hands played, the expected win is 2015 units. Assuming a standard deviation of 1.1 per hand, a standard deviation on the entire play is 1,561. The difference between your actual win and expected win is 3,490. That is 3,490/1,561 = 2.24 standard deviations. The probability of results that bad or worse is 1.27%.

I found a blackjack machine with a player advantage of 0.1%. As a group, we've played flat bet 2,015,000 hands and am down 1,475 units. I don't specify the exact rules, lest I give the play away, so please take the 0.1% player advantage on faith. What are the odds of running as bad as we are, assuming the game is fair?

anonymous

Based on that advantage and hands played, the expected win is 2015 units. Assuming a standard deviation of 1.1 per hand, a standard devation on the entire play is 1,561. The difference between your actual win and expected win is 3,490. That is 3,490/1,561 = 2.24 standard deviations. The probability of results that bad or worse is 1.27%.

Hello Wizard. In 100,000 hands of blackjack, how many losing streaks can I expect to see of 10 hands or more?

Michael

First we have to find the probability of a win for any given hand, which will depend on the rules, which weren't stated in your original question. In my page on variance in blackjack, I give the probability of a net win, push, and loss under "liberal Strip rules," which are: six decks, blackjack pays 3 to 2, dealer stands on soft 17, double after split allowed, surrender allowed, re-splitting aces allowed. Under those rules, here are the requisite probabilities:

  • Win: 42.43%
  • Push: 8.48%
  • Loss: 49.09%

Your question also didn't state how to treat pushes. I'll assume that a push counts as a hand played, but does not advance nor reset a series of losses. Taking out the pushes, the probability of a win and loss, given a resolved bet, are:

  • Win: 46.36%
  • Loss: 53.64%

That said, a very good approximation for questions like this is:

n × l × wm

Where:
n = number of hands played
l = probability of a loss
w = probability of a win
m = minimum number of hands in a losing streak

In this case, the expected number of losses is 100000 × 46.36% × 63.64%10 = 91.4. In other words, there will be a losing streak of at least 10 hands every 1,094 hands, on average. A random simulation backs this up.

At this point, I'm sure my perfectionist readers are preparing to Email me with intellectual whipping on Markov chains. I'd like to emphasize that my formula is an ESTIMATE and in fact quite a good one.

Hello. I have a coupon that allows me to push a hand of 22. I can hold onto the coupon until my first 22. It doesn't apply to doubles or splits. What is the value of this?

MrGoldenSun

A quick answer is the value of the maximum you're allowed to bet. Just wait for a 22 and then play it, resulting in walking away from the table with an extra unit.

A more rigorous answer should look at the cost of waiting for that 22. This is something I don't know exactly, but can estimate.

The cost to the player of the dealer-push-22 rule is 6.91%. However, the dealer will get to 22 more than that, because the player won't care if he busted first. Depending on the rules, the player will bust about 15.7% of the time. If we assume this is uncorrelated with the dealer's probability of busting (which it's not), then the probability of a dealer bust is 6.91%/(1.0-0.157) = 8.2%.

I know this is rough, but let's assume the player's 22 probability is the same. I know the dealer will bust more than the player, but this coupon also doesn't count after a split, so let's just say those factors offset. So, if the player gets a 22 8.2% of hands, then he will get a 22 once every 1/0.082 = 12.2 hands on average.

Let's say the house edge in the base game is 0.75%. The cost of playing 12.2 hands at that house edge is 12.2*0.0075 = 0.0915. So, subtract that from the one unit value and you get a value of the coupon of 1.0 - 0.0915 about 91% of face value.

This question is raised and discussed in my forum at Wizard of Vegas.

I'm thinking of creating a side bet for "push 22" blackjack variants that would pay 11 to 1 if the dealer busted with 22. What would be the odds?

Jay from Henderson

I'm thinking of creating a side bet for "push 22" blackjack variants that would win if the dealer busted with 22. What odds should it pay and what would be the house edge?

Assuming the dealer always drew out his hand (even if every player already busted), then I show a probability of busting on 22 of 7.88% if the dealer stands on soft 17 and 8.00% if he hits a soft 17.

Assuming the dealer hits a soft 17, at a win of 11 to 1, the house edge would be 4.04%. At 10 to 1, it jumps to 12.04%.

I should warn you and advise players that this would be countable (shut up Wiz!).

I found a blackjack game that pays 6 to 5 if the player a blackjack after splitting tens or aces? Re-splitting aces is not allowed. A dealer blackjack still beats any hand except pushes against a natural player blackjack. If the dealer draws to 21 points, a player ace and ten after splitting wins.

Scrooge

Let's ignore splitting tens, because even with this rule, the player should still stand on 20 against anything.

Assuming six decks, the probability of a pair of aces is combin(24,2)/combin(312,2) = 276/48,516 = 0.5689%.

The expected number of the two aces that will develop into a blackjack is 2*(16*6)/(312-2) = 0.619355.

The probabilitiy the dealer does not have a blackjack is 1 - (16*6)*(4*6-2)/combin(52*6-2,2) = 95.590354%.

The probability of the dealer drawing to 21 points is 7.7981%. The math on that is too complicated to explain.

The probability the rule is helpful is 0.5689% * 95.590354% * (1-7.7981%) = 0.3368044%.

The benefit per incident = Pr(dealer does not get to 21 points) * (0.2) + Pr(dealer does get to 21 points) * 1.2 = (1-0.122077839) * 0.2 + 0.122077839 * 1.2 = 0.3220778.

The overall benefit of the rule is the product of how often the situation occurs and the benefit when it does = 0.003368044 * 0.322077839 = 0.11%.

The Morongo casino in southern California is running a promotion where they pay a bonus of $16 if the dealer is dealt a hard 16. What is the value of this?

morongo

calwatch

This is a good one for the player! Their web site doesn’t elaborate on the details so I’m going to assume it is for the initial two cards only. I see my from an old Current Blackjack Newsletter from October 2018, most tables have the following rules:

  • Dealer hits soft 17
  • Six decks
  • Blackjack pays 3 to 2
  • Double after split allowed
  • Re-splitting aces allowed

My blackjack house edge calculator says these rules have a house edge of 0.55% with a continuous shuffler and 0.57% with a cut card.

Regardless of the rules, the probability of a hard 16 in the first two cards is 6.51%. Getting $16 with a 6.51% chance is worth $1.04 per hand. I’m going to assume a minimum bet of $25 because most casinos are raising their minimums in this era of the coronavirus. Not counting the bonus, the expected loss per hand is $0.14 at a $25 bet. That makes the expected win per hand $1.04 - $0.14 = $0.90. Relative to the bet amount, that is a player advantage of 3.59%!

If we assume a good case scenario of playing three hands of $25 at 80 rounds per hour, that would be an expected hourly win of $216!

This question is asked and discussed in my forum at Wizard of Vegas.

In 12 hours of blackjack play, what is the probability of seeing 60 or more wins in a row?

anonymous

According to my variance in blackjack page, based on liberal Strip rules, the following are the probabilities of a net win, push, or loss:

  • Win — 42.43%
  • Push — 8.48%
  • Loss — 49.09%

Let's ignore the ties, giving us a probability of winning, given the hand resolved in a net win or loss, of 46.36%.

Let's use 100 hands per hour as a playing speed.

We can approximate the probability of seeing at least one streak of at least 60 hands in a row as:

100×12×0.463660 = 1 in 89,412,355,233,588,500.

As a basis of comparison, if you purchased on Powerball and one Megamillions ticket, the probability of winning both would be 1 in 88,412,922,115,818,300.

So it would be a little more likely to win both lotteries than to see 60 wins in a row in 12 hours of play.

In the movie License to Kill, James Bond plays three rounds of blackjack, playing five hands at a time. I notice he never once hit to any of them. What are the odds of that?

You may find a clip of the scene on YouTube.

anonymous

The game does see a suspiciously high number of large cards, doesn't it. Here are the cards I could make out. Note that in some cases, the cards could not be seen clearly.

License to Kill -- Ranks Observed

Rank Observed
2 0
3 0
4 0
5 2
6 2
7 1
8 4
9 4
10 8
J 3
Q 6
K 4
A 1
Total 35

You are indeed right, Bond does not hit any of his 15 initial hands. He splits eights once, but doesn't hit after splitting either. Here is a count of his initial action on all 15 hands:

  • Double — 1
  • Split — 1
  • Stand — 13

Here are the basic strategy probabilities of each initial action, assuming six decks, double after split allowed, dealer peeks at the hole card, and dealer stands on soft 17.

Blackjack -- First Action Probabilities

Action Probability
Stand 43.46%
Hit 39.78%
Double 9.53%
Split 2.48%
Blackjack 4.75%
Total 100.00%

If surrender were allowed, that probability would be 4.14%, coming out of the probability of standing.

It should be noted that Bond once stood on 16 vs. 10. The basic strategy play is to hit that, but it's very marginal. Given the flood of tens that came out that hand, Bond may have known the count was high, which would trigger a basic strategy exception, standing in that situation.

The probability of not hitting any one hand is 60.22%. The probability of not hitting 15 out of 15, assuming each hand is independent, is 0.60216215 = 0.000496253 = apx. 1 in 2015.

At the Golden Lion casino in Panama City the dealer offers insurance with a 10-point card up. They pay the same 2 to 1, if the dealer gets a blackjack, as with an ace showing. They use six decks. What is the house edge when the dealer has a 10 up?

PG

Ouch! I saw this same awful and ignorant rule at the MGM in Macau.

The probability the hole card is an ace with a 10 up is (6*4)/(6*52-1) = 7.717%. The expected return is 0.077170×2 + 0.922830×-1 = -0.768489. In other words, the house edge is 76.85%.

I see somebody on your forum is claiming to have witnessed 60 consecutive winning hands in a row in blackjack. How many hands would one need to play, on average, to witness that? Also, how does it compare with the event mentioned in Ask the Wizard column 363 of somebody allegedly witnessing 18 totals of 11 in a row in craps?

anonymous

To answer your question, we must first assume some rules for the blackjack game. I will use what I call the "liberal strip rules," which are as follows:

  • Six decks
  • Dealer stands on soft 17
  • Double after split allowed
  • Re-splitting aces allowed
  • Surrender allowed

Under these rules, assuming perfect basic strategy, here are the probabilities of a net win/loss:

  • Net win: 42.43%
  • Net push: 8.48%
  • Net loss: 49.09%

I questioned the witness to this event and he said the 60 hands does not include pushes. In other words, 60 resolved hands. I am also going to assume that if the player splits it still counts as one hand only and there was a net win among all the hands the player split to.

As explained in the question on the 18 consecutive totals of 11, the formula for the expected waiting time is:

Expected waiting time = [(1/p)^(n+1) - 1] / [(1/p) - 1] - 1, where:
n = number of consecutive wins
p = probability of win

In this case, the probability of a net win per hand, given a hand resolved is 42.43%/ (43.43% + 49.09%) = 46.36%. To be more specific, 0.46359564.

Using the formula above, the expected waiting time to observe this event is (1/0.46359564)^61 - 1]/[(1/0.46359564) - 1] - 1 = 200,941,772,393,648,000,000 hands.

By comparison, the waiting time to observe 18 totals of 11 in a row in craps is 41,660,902,667,961,000,000,000 rolls, which is 207 times more. So, the 18 yo's still holds the record as the tallest tale told at the Wizard of Vegas forum, as far as I know.

What is the value of a free ace coupon in 6-5 blackjack?

anonymous

In my value of a free ace page I state it's value is 50.1844% of the bet amount in 3-2 blackjack.

In six-deck blackjack, the probability of getting a winning blackjack, given an ace as the first card, is 29.3139%. When that happens, you win 0.3 less units in 6-5 blackjack than 3-2.

So the value of a free ace in 6-5 six-deck blackjack is 50.1844% × 29.3139 × 0.3 = 41.3902% of the initial bet.

Your basic strategy for six decks and dealer stands on a soft 17 stays to hit a 11 vs. ace. Would would be the right play if the player were limited to just one card if he chooses to hit?

Don

My blackjack hand calculator shows that with six decks and dealer stands on soft 17, player 6+5 vs. dealer ace, the following expected values of each play:

  • Hit = +0.147596
  • Double = +0.129710
  • Stand = -0.661883

Hitting, being limited to one card, would be like doubling, but without doubling the bet. The expected value would thus be half that of doubling, or +0.129710/2 = +0.064855. That is less than the expected value of doubling of +0.129710. Therefore, if you're limited to one card after hitting, then you should double.