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Frequently Asked Questions about Blackjack

Last update: January 18, 2007

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Blackjack FAQ

Does it make any difference in which seat I sit in at blackjack?

No.

Is it true an idiot at third base will cause the other players to lose too?

No. This is just a myth. He is just as likely to help you as hurt you. On average it makes no difference. If anyone rebukes you for hitting a stiff hand at third base tell them you'll keep doing so when the odds favor it and if they don't like it they can find another table.

BlackjackInColor.com has a very good page on this topic.

I disagree. I've seen idiots take the dealer's bust card too many times.

Meanwhile you never remember the times he took a card that would have helped the dealer, resulting in the dealer busting on the next card.

I'm going to Vegas for the first time soon and you have convinced me to play blackjack. How should I prepare myself?

Memorizing the basic strategy is a good first step.

Why is the house edge for one deck different than for multiple decks? If I'm not counting cards why does the number of decks matter?

The answer has to do with the fact that once a card is played it has an impact on the distribution of the remaining cards. For example the single deck basic strategy calls for standing on two sevens against a ten, with two more decks the player should hit. In the situation with one deck the probability of drawing a third seven on the third card is only 2/49, or 4.08%. With two decks this probability rises to 6/101 or 5.94%. With the lower probability of catching a 3-card 21 in single deck (the only total that can beat a dealer 20) the best play is to stand. The effect of removing a single card increases as the number of decks decreases. The player has the option to hit or stand on a stiff but the dealer must hit once. In other words stiffs hurt the dealer more than the player. Also, with fewer decks more blackjacks are probable, which pays 3-2 to the player but only 1-1 to the dealer.

I'm trying to weigh the pros and cons of the various card counting strategies? Which one do you use/recommend?

I both use and recommend Stanford Wong's plus/minus, as explained in Professional Blackjack. This strategy counts 2 through 6 as +1 and tens and aces as -1. There is no side count of aces. I think this is a good balance between power and ease of use. This also seems to be the most widely used strategy and there is more literature about it than any other strategy. Bluejay prefers Knock-Out because it's easier to use.

What is the probability of winning any given hand in blackjack?

Under Atlantic City rules the probability of a net win is 43.31%, a tie is 8.80%, and a loss is 47.89%. For more information visit my blackjack appendix 4.

What do you think of the idea of mimicking the dealer in blackjack? If I follow the same dealer strategy of hitting to 17 I should have the advantage because the player gets paid 3-2 odds on a blackjack and the dealer only wins even money. This seems so obvious, I can't believe all the blackjack experts have overlooked it.

You seem to be forgetting that if both you and the dealer bust then YOU lose. The mimic the dealer strategy results in a house edge of 5.48%, according to my calculations.

What is the probability of getting a blackjack in blackjack?

It depends on the number of decks; here are the probabilities for 1 to 8 decks:

0.048265
0.047797
0.047643
0.047566
0.047520
0.047489
0.047468
0.047451

How did you calculate those numbers?

The general formula is 2*(probability of 10)*(probability of ace). The reason for the 2 is that there are two ways to order the two cards; either the ace or 10 can come first. The probability that the first card will be a 10 is always 4/13, regardless of the number of decks, because there are 16 out of 52 tens in the deck and 16/52 = 4/13. The probability of an ace, given that a 10 has already been removed from the deck is the number of aces divided by the number of cards left. Let n be the number of decks. There are 4*n aces and 52*n-1 cards left. So for n decks the probability is 2*(4/13)*(4*n/(52*n-1)), which is conveniently about 1 in 21. For example for 6 decks the answer is 2*(4/13)*((4*6)/(52*6-1)) = 192/4043 = 0.047489.

Why is the basic strategy different for 12 vs 2 (hit) and 13 vs 2(stand)? The value of a 12 and 13 should be exactly the same because both will lose to any pat hand and win if the dealer busts.

Yes, the value of standing on 12 and 13 is almost the same. Assuming six decks and the dealer hits on soft 17 my blackjack appendix 9 shows the value of standing on 10+2 vs 2 is -0.289435, and 10+3 vs 2 is -0.289352. So the value of standing is indeed almost the same. However you are overlooking the value of hitting. The expected value of hitting 10+2 vs 2 is -0.252224, and 10+3 vs 2 is -0.307973. So hitting 12+2 is significantly safer than hitting 12+3. With 10+2 the expected value of hitting is greater than standing (-0.252224 {hit} > -0.289435 {stand} ), while with 10+3 the expected value of standing is greater (-0.289352 {stand} > -0.307973 {hit}). So the alternative to standing is greater with 12 than 13.

I played t hands of blackjack one at a time, flat betting and religiously following basic strategy. My final outcome was a gain of r (a negative r represents a loss). The house edge under the rules I played was h. What is the probability of losing this much or more in a fair game?

Using Excel type this into any cell, substituting the correct values for h, t, and r:

=normsdist((r+t*h+0.5)/(t^0.5*1.16)).

Where, r = the number of units won or lost, t = the number of hands, and h = the house edge.

The 1.16 is the standard deviation per hand. This will vary slightly from one set of rule to another but I feel 1.16 is a good benchmark. Let's take an example. Suppose the number of hands is 1000, the house edge is 0.41%, and the player lost 100 units. The formula for the probability of losing this many units or more is =normsdist((-100+1000*0.0041+0.5)/(1000^0.5*1.16)) = normsdist(-2.600700765) = 0.004651712 .

I disagree with you and all the other blackjack experts about splitting 8's against a 10 or ace. Why turn one losing hand into two?

Under typical U.S. blackjack rules with two 8's against a 10 the following is the expected loss on a $100 bet for each possible play:

Stand: $53.69
Hit: $53.54
Double: $107.07
Split: $47.55

Splitting has the smallest expected loss. There is no sound bite answer that explains why this is so, but if you consider the millions of ways the hand can play out splitting will result in losing less. Here are the numbers for splitting 8's against an ace.

Stand: $66.33
Hit: $51.36
Double: $102.71
Split: $36.44

Please see my blackjack appendix 9i for more information.

I disagree with your advice that the player should stand with two sevens against a dealer 10 in single deck blackjack.

Following is the expected loss on a $100 bet for each possible play in this situation.

Stand: $50.97
Hit: $51.48
Double: $103.47
Split: $61.97

Standing saves the player 51 cents per $100 bet. The reason is largely because the player needs another 7 on the third card to make 21, the only total which will beat a dealer 20, and half the 7's are already out of the deck. For larger numbers of decks this factor is less important and consequently the odds favor hitting. Please see my blackjack appendix 9b for more information.

I disagree with another play in your basic strategy charts.

My blackjack appendix 9 indicates the expected value of every play for every hand under almost every set of rules. Just look it up and you'll see that by following the basic strategy you either win the most, or lose the least, for every possible situation. There is no good sound bite explanation as to why one play is better than another. To get the correct answer you have to have a computer play out every possible outcome (as I do) or a simulation of millions of hands (as Stanford Wong does) to see which play is best.

The flaw in your basic strategy is that you are trying to maximize the player's return per dollar bet. So you foolishly forget that the player must bet twice as much money when doubling or splitting. For example in the case of splitting eights against a dealer 10 you are losing a slightly smaller share of a much larger bet.

No, I'm afraid not. My basic strategy, and that of every respectable blackjack authority, is based on maximizing the net win of each hand. My blackjack appendix 9i shows the expected loss by hitting two eights against a 10 is -0.536853 and by splitting is -0.475515. In other words you can expect to lose 54 cents by hitting and 48 cents by splitting, and that is combined over all the split hands. If we assumed the player split to an average of 2.15 hands then the expected value of each one of them would be -0.475515/2.15=-0.2212. So I fully consider that the player is wagering more money.

What is the house edge in blackjack if you don't have enough money to double or split?

Removing the option to double and split increases the house edge by 1.9%. The normal house edge in blackjack is usually 0.4% to 0.6%, depending on the rules, so if you can't double or split the house edge would be 2.3% to 2.5%.

Once I saw myself/the dealer get x cards in blackjack without busting. What is the probability of that?

Assuming a 6-deck game, where the dealer stands on soft 17, double after split allowed, surrender allowed, resplit aces allowed, player may resplit to four hands, a cut card, and only one player I get the following results. Each hand from a split hand is counted individually.

Player Hand Probabilities
Event	Observations	Probability
Player busts	276659980	0.1299584409
Player surrenders	92261962	0.0433391947
Player blackjack	97936983	0.0460049828
2 cards	1193785045	0.560769372
3 cards	325677353	0.152983894
4 cards	120180207	0.0564535295
5 cards	19891981	0.0093440722
6 cards	2248456	0.0010561912
7 cards	181767	0.0000853834
8 cards	10128	0.0000047575
9 cards	376	0.0000001766
10 cards	10	0.0000000047
11 cards	1	0.0000000005
Total	2128834249	1

Dealer Hand Probabilities

Event Observations Probability

Player busts first 276659980 0.1339737001

Player surrenders 92261962 0.0446782235

Dealer busts 469895050 0.2275485544

Dealer blackjack 97940000 0.0474278361

Player blackjack, no dealer blackjack 87823688 0.0425289716

2 cards 406164309 0.1966866886

3 cards 453039024 0.2193859565

4 cards 151522915 0.0733755767

5 cards 26606271 0.012884193

6 cards 2903511 0.0014060368

7 cards 205782 0.0000996508

8 cards 9253 0.0000044808

9 cards 268 0.0000001298

10 cards 3 0.0000000015

Total 2065032016 1

Why don't you create a list of shame of casinos that have 6 to 5 blackjack?

For one thing this dreadful game has become so pervasive in Las Vegas that almost every casino on the Strip would be on the list. Second, I give players 90% of the blame for this game for playing it in the first place. So the list of shame should also include every player who has ever played it. For more on 6 to 5 blackjack I recommend www.6to5blackjack.org.

What are the index numbers for Spanish 21/Blackjack Switch/Lucky Ladies/any other blackjack variant?

I don't know. It is one of my ideas to do index numbers for all the major blackjack games and countable side bets. However at this time I have nothing except standard blackjack, and those index numbers are available from numerous books and programs.

What is the house edge for the following set of blackjack rules...

Between my blackjack house edge calculator and my effect of rule variations you should be able to figure it out for yourself. If you find a rule variation that is not addressed you may ask about it.

What is the probability of winning x hands of blackjack in a row?

According to my blackjack appendix 4 the probability of a win is 43.31%, a loss is 47.89%, and a tie is 8.80%, give or take depending on the exact rules. Assuming you are ignoring ties the probability of a win is 47.49%. So the probability of x wins in a row is 0.4749^x - For example the probability of 5 wins in a row is 0.4749⁵=0.0242.

What is the probability of the player/dealer busting in blackjack?

The following table shows the probability in a single-player game. Remember, the dealer will not play out his hand if the player busts first. If you add players the dealer's probability of busting will go up because there will be a greater probability of at least one player not busting.

Bust Probabilities
Decks	Soft 17	Player	Dealer
6	Stand	15.72%	24.07%
6	Hit	15.68%	24.40%

There is a weird rule where I play blackjack in which the dealer doesn't check for blackjack and if the player doubles or splits he only loses his original bet if the dealer does have blackjack.

This is the mathematically equivalent to the dealer peeking for blackjack. So everything I say about blackjack, except European rules, is true under this rule.

There is a weird rule where I play blackjack in which the player only gets one card to split aces, he can't resplit and he can't draw more cards.

That IS the normal rule for splitting aces.

Also see my main blackjack section and the Ask the Wizard blackjack section.

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