Blackjack - Online Blackjack

In the first 20 blackjacks the probability that you get exactly x of them is (1/2)²⁰ * combin(20,x). Let me save you the trouble. Here are the odds of exactly 0 to 3 blackjacks out of the first 20:

Pr(0) = 0.0000010
Pr(1) = 0.0000191
Pr(2) = 0.0001812
Pr(3) = 0.0010872
Pr(3 or less) = 0.0012884

So, the odds of 3 or less are 1 in 776. That is not enough to warrant an accusation of cheating. It could easily be simple bad luck.

Personally, I like to see four standard deviations south of expectations (probability of 1 in 31,574) before I get suspicious. It would take five standard deviations (probability of 1 in 3.5 million) before I made a formal accusation.

Online casinos are not the only ones to offer positive expectation games. Using basic strategy some Las Vegas casinos offer games with a negative house edge. There are video poker games all over the country with a positive expectation assuming optimal strategy. The reason the casinos can afford to do this is that the vast majority of players make errors in strategy. As someone who has played hundreds of hours of blackjack in casinos all over the U.S., I seldom see other players playing proper basic strategy. Money management has nothing to do with it.

Both games are both shuffled after every hand. Thanks to Darla with Gambler's Palace (another Unified Gaming casino) for her help on this one.

You have already pointed out some of the advantages of online blackjack, as opposed to a physical casino. Unless you are card counting, it is to your advantage that they shuffle after every hand. In the land casinos they will usually play until a specific point is reached in the deck, finish that hand, and then shuffle. This works to the player's disadvantage because more cards will be dealt when the shuffle point is reached in a deck rich in small cards than one rich in big cards. In other words, in a physical casinos the player will see slightly more small cards than large cards over the long run, which is bad for the player. However, much more important is the fact that you don't have to feel obligated to tip in an online casino. The faster play, one on one play, and the larger spreads do not help nor hurt the casual player. I attribute your better results in online casinos to any combination of luck, better rules, and not having to tip.

Bovada has lots of games you can play for fun, including blackjack. No account required, just one click and you're in. Just go to the Instant Play casino and then then click "practice" for blackjack.

I’m confident with that figure. It was determined using a random simulation program of mine. I speculate the creators of the software made a mistake and only intended to offer late surrender on tens and aces, as was the case with the preceding version. I called one online casino that uses Unified Gaming and they were not even aware the new software allowed for early surrender on aces. I give the house edge figures as a service to my visitors. (Update Jan 22, 2005: Unified Gaming changed the rules of their game years ago to remove the player advantage)

Assuming you put the greatest priority on player odds I would have to go with a Unified Gaming casino. You'll enjoy a player edge of 0.57% assuming you following the proper strategy.

Thanks for your kind words. I think that the vast majority on online casinos are fair. However I won't claim that all of them are. Check out my casino blacklist for casinos I had problems with. Assuming you aren't playing just the bad ones, I would suggest your losing is just the result of bad luck.

According to my blackjack house edge calculator, the house edge with these rules, assuming eight decks, is 0.45%. The effect of infinite decks, compared to eight, is 0.10% in the house's favor. So, the total house edge would be 0.45% + 0.10% = 0.55%.

You also seem to also imply that this casino is not dealing a fair game. Unless you provide some hard data I can't comment on that.

You can correctly use the Cryptologic basic strategy to play at a GamblingSoftware.com casino.

Most online casinos shuffle after every hand. Others shuffle at random times but do not indicate exactly when to the player. I have noticed Microgaming casinos flash the word "shuffling" about one hand in four.

However, if you track the cards between these announcements you will sometimes see the same card twice, which is impossible in a single-deck game, assuming you believe them about when they shuffle. As far as I know, they actually shuffle after every hand, but for reasons I do not understand, only indicate a shuffle occasionally. If I remember correctly, Cryptologic casinos do indeed indicate when they are shuffling their eight-deck shoe.

If you double on 11 at a Microgaming casino and the dealer gets a blackjack you will lose the total amount bet. At Unified Gaming the blackjack would be turned over immediately if the up card were a ten so there is no risk of losing to a blackjack when doubling in this situation.

All combinations of bets in roulette yield the same expected return, assuming the dreaded five-number combination is avoided. You're right that the third column has eight reds and four blacks. The probability of winning 3 units is 8/38, 1 unit is 4/38, breaking even is 10/38, and losing 2 units is 16/38. The combined expected per unit bet is return is (1/2)*(3*8 + 1*4 + 0*10 + 2*16)/38 = -2/38. Betting on black and the third column the probability of winning 3 units is 4/38, 1 unit is 8/38, breaking even is 14/38, and losing 2 units is 12/38. The expected return is (1/2)*(3*4 + 1*8 + 0*14 + 2*12)/38 = -2/38. Both combinations weight the various outcomes differently, but they average to the same number.

I know that one software company randomly picks two cards in the deck and reverses them, and repeats this numerous times. Since learning of this technique, that is also how I shuffle in my random simulation programs. As long as any method of shuffling is done enough times the deck should be properly randomized.

Manual shuffling is more vulnerable to a biased shuffle and consequently some players try to exploit this by shuffle tracking and card clumping. There are numerous ways an online casino might cheat, but a bad shuffle I don't think is one of them.

I have never played at the Vegas Palms. However, I have a lot of faith in the fairness of Microgaming and believe that it is just chance you are having streaky games. Cyberstud poker is the same thing as Caribbean Stud Poker, with a slightly more generous pay table. The expected return is 5.01%, as opposed to the usual 5.22% with Caribbean Stud. The probability of two flushes is (4*(combin(13,5)-10)/combin(52,5)) * (3*(combin(13,5)-10)/combin(47,5)) = 1 in 203,725.

Most online casinos shuffle after every hand. However, the six-deck game at Unified Gaming casinos shuffles at a random point in the deck. I have heard of other casinos that also penetrate more than one hand into a shoe, but I don't recall which ones. If the cards are shuffled after every hand there is no use in card counting, other than applying my composition dependent basic strategy exceptions.

I lost 98 units there overall. If every hand was an even money win or a loss then I would have won 170 hands and lost 268.

Thanks for the compliments. Most online casinos shuffle the cards after every hand. At single deck casinos (Boss Media version 1, Microgaming, Unified Gaming) you can use the cards already on the table to alter your play sometimes. See my blackjack appendix3A for all the details. There are some casinos that play into a shoe a little way but not far, and have restrictive betting limits. I have yet to be convinced of any worthwhile opportunity on the Internet to count cards.

In my strong opinion the variation you’re observing is the result of random variation in the cards, not where you’re playing. I suspect you are exaggerating about sometimes only winning 20 hands out of 100, that would be very unlikely. Some people believe that Microgaming has a "take down" mode in which the player will lose like crazy for a period of time. It is to be expected that in any game the player will occasionally have bad losing streaks, as well as good winning streaks. So these alleged "take down" periods I think are just normal bad luck and that all Microgaming casinos deal a fair game.

You’re right, if you used a robot player against an ordinary game you would only lose more. However some casinos do offer games with a player advantage if played properly. Unified Gaming had a blackjack game with an 0.5% player edge for several months, but no longer. Many Real Time Gaming casinos offer a joker poker game with an expected return of 100.18%. Other casinos have promotions in which the player who plays the most hands in a period of time wins a prize, in which a robot player would have a clear advantage. About your second question the bell curve is a forward looking estimate of the sum of many random variables. You can not mix together past and future events. Once an event has happened it is no longer a random variable but a cold hard outcome. If you played 1000 hands of blackjack with a return of 78% then you fell on the tail end of the bell curve during that play. Starting from hand 1001 your results could fall anywhere on a new bell curve. I hope this helps, but it really takes a course in statistics to truly understand.

I would download some Internet casino software and just play in free mode. However to learn proper basic strategy I would recommend making flash cards with every possible play. Dealing out cards at random will not test you often enough on the soft doubles and splits.

Here you go...

I’ve been questioned about this several times and continue to maintain that despite losing the total bet the option to draw to split aces overcomes the European no-peek rule, thus splitting is the better play. Based on one deck the expected value of each hand (considering the possibility of a dealer blackjack) is -0.532849 for hitting and -0.223277 for splitting. So splitting is better by about 31% of a unit. Splitting is also better for the 4-deck game, which no Microgaming player should be playing since a 1-deck game with the same rules is available.

I think the reason for this is that they don’t want a minimum bet player hogging up two spaces. This will slow down the game and possibly prevent bigger bettors from playing. Not all land casinos have this rule, I think it is more prevalent in Atlantic City, where tables are more crowded, than Las Vegas. Whether online or a land casino there is no advantage to playing more than one hand.

It is a good sign if a casino has an independent auditor to review the log files for fairness and randomness. I used to provide such a service to online casinos myself.

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.

Yes. Have a look at Beejack. Most, but not all, casinos shuffle after every hand. I don't know if it practical to actually use this product. If you try it please let me know how you do, I might like to try it myself.

Note: The link to Beejack was removed in 2014, due to a potential virus with that site. Proceed there with caution.

First, the game was Caribbean 21, not Caribbean Stud. The casino this money was won from alleges that the player used robot play, which is against their terms and conditions. If this is true (the player denies it) then it is within their rights to forfeit the winnings. Robot play is a program that can read the cards on the screen and can play against the casino by itself, by simulated mouse moves and clicks, or keyboard actions. Some casinos don’t allow it because they have some games with a theoretical return slightly over 100%. Robot play could ensure nice expected hourly profits for the person using it, but not enough to bother actually playing. A good example is Boss Media’s single deck blackjack game with a player advantage of 0.11%. Some casinos with no positive expectation game allow robot play and others do not. I do not know why those with no positive expectation games prohibit robot play. Some skeptics claim they retain the right to avoid paying big winners, simply by alleging robot play. In this situation the casino has released a taped confession in which the player offers to sell the robot. However the player says it was taken out of context. It is a long story, for more details follow this link to Casinomeister’s forum on this topic.

I could not find any hand where an extra 0.1% would cause a change in strategy. The closest case I could find, based on six decks and the dealer standing on soft 17, is A,4 against a dealer 4. In that hand doubling costs the player just under 0.3% in expected value compared to hitting. So if you can get 0.3% or more then double that hand. Other borderline hands I examined cost the player at least 1% to double or split, and I have never seen cash back that high in blackjack.

Using a random number generator _is_ the same as working like a slot machine. Online blackjack, slot machines, and video blackjack all use random number generators.

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%.

As I'm sure you know this game is offered by Lucky Chance casino. Using the appropriate basic strategy for these rules the player advantage is 7.2%! Wait it gets even better. You can bet three hands at once of $5 or more each and if you get a blackjack on all three you win a progressive jackpot that is currently at $18095. The probability of getting three blackjacks in three hands is 1 in 10552. So the progressive is worth an extra $1.71 per hand. On two days while I played they also offered 15% rebate on losses, calculated whenever you exited the game. So I simply exited after every hand, except on a push.

However I'm suspicious if the player advantage is too high. I checked Winner Online and found they allegedly used to offer a video poker game with a 120% return, although they use a normal pay table now. That is two red flags. Lucky Chance offers a 100% immediately bonus up to purchases of $500, so I put them to the test. It was my goal to either make a fortune on their Double Exposure game or prove the game was not fair. Following are my results:

• 313 of single hands: net win of 32 units.
• 1959 hands of 3 spots at once: net loss of 29 units.
• 2272 total hands: net win of 3 units.

Given a 7.2% advantage my expected win was 163.6 units. The probability of only winning 3 or less is 12.4%. This is using a standard deviation of 1.17 for a single hand and 2.68 per hand for playing three at time. My source of the 1.17 is a random simulation using Stanford Wong's Blackjack Count Analyzer and I multiplied that by 2.28 for 3 hands, based on the standard deviations for regular blackjack for 1 and 3 hands as found in my blackjack appendix 4.

This certainly does not rise anywhere near enough to make any accusations. In addition I recorded results all sorts of ways but every test came out looking normal. I would have played longer but the game play is extremely slow and I went broke. The reason I went broke is I did worse on larger bet sizes and my first few hours I didn't record results but they were not good.

So I failed on both my goals. I was too skeptical to deposit again and already wasted several hours on the game. However, if you wish to take a crack at it then be my guest.

Not being allowed to split aces increases the house edge by 0.18%. You should only double against a six, otherwise hit.

I’m sure they still make money on the game due to player mistakes. There are also forms of video poker here in Vegas that return over 100% with optimal strategy. Again, the casino counts on player mistakes to bring them under 100%. With most games that do pay over 100% the edge is so small it isn’t worth ones time to play the game as a living. However if you are going to play anyway you may as well get the best odds possible.

You’re welcome. It’s rare for online casinos to intentionally let players win in free mode. I know the Elka casinos used to do this (for which I blacklisted them), but fortunately they seem to have vanished. If anyone can show me hard evidence that a casino is intentionally allowing players to win in fun mode I would be happy to investigate it. Hard evidence means, at a bare minimum, a record of hands won and lost in each mode, for several dozen hands. Simply telling me that you lost "a lot more" when in real mode is useless.

Perhaps you misunderstood the point I was trying to make in my blackjack appendix 10. The bottom line is that unless you are a card counter shuffling after every hand, as opposed to using a cut card, is a good thing. The house edge is reduced 0.02% in a 6-deck game, to 0.11% in a 1-deck game, by shuffling after every hand.

Thanks for the kind words. So you have played 680,000/5 = 136,000 hands. According to my blackjack appendix 4 the standard deviation per hand, playing two hands at a time, is 1.91. So the standard deviation of 136,000 such hands would be 136,000^0.5*1.91 = 704 hands. Your losses above expectations are $5,500, or 1,100 hands. So you are 1,100/704 = 1.56 standard deviations south of expectations. The probability of doing this badly or worse can be found in Excel as normsdist(-1.56) = 5.94%.

At Cryptologic they use 8 decks and the dealer stands on a soft 17. According to my blackjack appendix 2, the probability of the dealer busting with a 6 up is 0.422922. So the probability of not busing is 1 - 0.422922 = 0.577078. The probability of not busing 7 times out of 7 is (0.577078)⁷ = 2.13%.

I see Bodog follows the 1-2-3-4-4-9-15-25-200-800 pay table, which is known as “Ugly Ducks” and returns 99.42% with optimal strategy. Although I don’t indicate an Ugly Ducks strategy on my site, my Not so Ugly Ducks strategy should do quite nicely, and is indeed accurate for this play. To answer your question, the strategy depends only on the pay table. The number of hands makes no difference. What is right for one hand is right for 100 hands. On average you should get about 34 coins back playing the inside straight and 32 coins back tossing everything. However, actual results will vary. I would say you’ve just been unlucky with the inside straights if you have only been getting back 25 on average.

As I read them, the rules are:

• 1 deck
• Dealer hits soft 17
• Double only on 9 to 11
• Double after split allowed (subject to 9 to 11 rule)
• No surrender
• Blackjack pays 3 to 2
• Dealer always peeks for blackjack

Here is the basic strategy.

The house edge under these rules is 0.16%.

The standard deviation per hand in blackjack is 1.15 under Vegas Strip rules (source). This can vary, depending on the rules, but since you didn’t state them, we’ll go with 1.15. So, the standard deviation of 30 hands would be sqrt(30) × 1.15 = 6.30. I don’t know what their blackjack rules are, but let’s assume a house edge of 0.4%. So in 30 bets, you would expect to lose 30 × 0.004 = 0.12 units. Your losses exceeded expectations by 21.5-0.12 = 21.38 units. That is 21.38/6.3 = 3.39 standard deviations south of expectations. The probability of that is 0.000349, or 1 in 2862. I’m afraid this doesn’t rise to the level to make any kind of accusations. If you still suspect something fishy, I would gather a larger sample size.

I agree, that does seem like a good advantage play. At the 5dimes live casino game they offer the following rules:

• 6 decks.
• One burn card at the beginning of the shoe, and one with every dealer change, which occur every 30 minutes. If the supervisor has to step in, which I’ve seen happen twice, then three cards are burned.
• Dealer stands on soft 17.
• Early surrender, except against an ace.
• Double after split allowed.
• Split to two hands only.
• No hole card, but player loses original bet only to dealer blackjack.
• Bet ranges: $5-$250, $10-$250, or $25-$500

The house edge under these rules is 0.24%.

The rules say the penetration is 75%. Twice I counted the number of cards seen per shoe, and I got 211 both times, which is 68%. Shortow, a member of my forum, placed two videos of the cut card placement on YouTube: Video 1 Video 2. It looks to me like the penetration was a little deeper in video 2. I would say it ranges from 60% to 70%, depending on the dealer.

Not only could the player easily count this game, but he could use a calculator on a separate screen to make perfect decisions. The Blackjack Real Time Analzyer is one product that does this. However, I have no idea what kind of game protection they employ. With every card scanned, it would not be difficult to determine the correlation between count and bet size and raise a red flag if the correlation was sufficiently positive.

If you give it a try, I'd be interested to know what happens.

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