## Fewer Decks are Better. Do You Know Why?

When it comes to the number of decks in a blackjack game, the fewer the better. Most players have heard this fact somewhere along the line, but many of them don’t know why fewer is better.

I often get this question by email, where players will note that the proportion of each rank of card is the same whether the casino uses a single deck or shuffles six decks together. Regardless of how many decks are in play, we start out with one thirteenth of the cards being Aces…

## You Get More Blackjacks in Games With Fewer Decks

Despite the initial card proportions being equal, in games with fewer decks you will be dealt more blackjacks. You will also be more successful in your double downs. How can that be, when all the ranks are equally represented no matter how many decks are used? It is because removing cards has more impact in a game with fewer decks.

## How Often Will You Draw a Blackjack From a Single Deck?

To get the probability of drawing a blackjack from a single deck, we multiply the chance of drawing an Ace by the chance of drawing a ten-value card. In a single deck of 52 cards there are 4 Aces and 16 ten-valued cards (4 each of Ten, Jack, Queen, and King).

p(Ace) = 4/52 = 1/13

p(Ten) = 16/51

Note that the second line reduces the number of cards in the divisor to 51, to account for the removed Ace. And that’s where the difference lies.

We also need to double the result since we could draw either (Ace,Ten) or (Ten,Ace). Our final result is:

p(Blackjack) = p(Ace) * p(Ten) * 2 = (1/13) * (16/51) * 2 = 4.83%

**The probability of drawing a blackjack from a single deck is 4.83%.**

## How Often Will You Draw a Blackjack From Two Decks

Same idea with two decks, with different numbers. 104 total cards, including 8 Aces and 32 ten-value cards…

p(Blackjack) = 8/104 * 32/103 * 2 = 4.78%.

**The probability of drawing a blackjack from two decks is 4.78%.**

More decks means slightly fewer blackjacks. In six decks, the probability drops further yet to 4.75%.

## Double Downs Work Better in Fewer Decks Too

The same effect impacts double downs. If you double your initial hand of (6,5) for a total of 11, then you are slightly more likely to draw a face card to make 21 if the game uses fewer decks.

Astute readers may notice that the dealer gets the benefit of these changes as well. That’s right, the dealer gets more blackjacks in single deck, and the dealer draws to 21 more often just like the player. But note that a player wins 3:2 for blackjack, while the dealer gets only even money. And for hands like the double down example, the player wins twice the initial bet. So while both player and dealer get more of these good hands, the player is rewarded more handsomely for his.

## But You Get Fewer Pat 20s in Fewer Decks!

It’s not all good news with less decks. For the same reason, you will get fewer dealt hands of 20! Once you remove the first ten-value card, there are only 15 tens left in 51 cards in single deck, while in double deck your chances are better with 31 out of 103.

This impact of fewer pat 20s affects players and dealers equally, so it’s really a wash.

The bottom line is that, all other things being equal, you should play in games with fewer decks. Just make sure they pay 3:2 on blackjack!

all chinese are crooked…never trust a chinamen…

Sorry to contradict your dream of winning a house . In Philippines ,they don’t just use 6 decks but all use CSM !!

Thanks for clearing this up!

I play a lot here in The Philippines where I’m living, and I’ve noticed the casinos here are all using 6 decks. I’d always wondered why, and now I know.

My grandad won his house in a game of blackjack in the 80’s (yes, I’m serious), and I’ve always had a love for the game since I started playing. Let’s hope I can win a house, too 😀

Actually, the lower the number of decks, not necessarily the better. Though if you’re lazy, it’s more appealing. It depends on 3 things – how many decks are in the shoe, where the cutcard is, and what the minimum bet is. In most places I have been, in the pacific northwest and in Indian casinos in the midwest of the US, there are 2 games you’ll see standard. The 2 deck game and the 6 deck game. Typically, the cut card will be one deck before the end in EITHER ONE. Which means that in the 6 deck game, you’ll be suffering through 5 decks before you get to the cutcard, but in the 2 deck game, you’ll only go through 1 before you get to a new shoe. But the thing is, the standard deviation OF the truecount, right before the cutcard, is actually higher in the 6 deck game than the 2 deck game. Meaning a larger fraction of the time, the truecount will be more than 5, or more than 7, or more than 9, when there is 1 deck left. AND the minimum bet of the 6 deck game is typically 3 or 5 dollars (3 is very good, 10 is very bad), and the minimum bet of the 2 deck game is typically 15 or 25 (15 is very good, 50 is very bad) dollars. If you can maintain a standard of accuracy in keeping track, then the 6 deck game is often better than the 2 deck game. Especially since they will be more off their guard in the 6 deck game. They usually don’t allow mid shoe entry in the 2 deck games, but they don’t care in the 6 deck game, and they often require the 2-deck game be dealt face-down, whereas the 6 deck game is generally always face-up. Why? because they are unaware that they have a vulnerability in the 6 deck game, they are only concerned about the 2 deck game.

How does the standard deviation OF the truecount vary through the deck and with number of decks in the shoe? Well, the regular count on the first card dealt is the same no matter how many decks, and then the variance as a function of position through the shoe is a parabola intersecting the line y=0 at x=0 and x=(52*number of decks), and of course standard deviation is square root of variance. In other words, the count is 0 before the first card has been dealt, and after the whole shoe has been dealt. Naturally the peak of the parabola is halfway through, but that’s the regular count, not the truecount. The truecount is that parabola divided by number of decks remaining, and that increases all the way to the end. The way I count is 2-7 get one point, 9 10 and A get -1. The regular count, on the first card dealt, is (12/13)^0.5, the square root of 12/13. So now you have 3 points that define the parabola entirely, you have y=sqrt(12/13) at x=1, and y=0 at both x=0 and (52*number of decks). What is the result you get? Well, one result is that halfway through a n-deck shoe, the truecount is sqrt(40/n). So in a 2-deck game with the cutcard 1 deck before the end, the standard deviation of the count right at the end there will be sqrt(20) or about 4.47. So 16% of the time, the truecount will be more than that. Allowing for some error resulting from discretization of a normal distribution, that is. But what is the standard deviation of a 6-deck game, 1 deck before the end? It’s sqrt(40), or about 6.32. Better than 4.47 by a factor of the square root of 2. So 16% of the time, the truecount will be more than 6.32 right before the cutcard in the 6-deck game, but one standard deviation is only 4.47 right before the cutcard in the 2 deck game. The detriment is that you have to suffer through 5 decks to get there instead of just 1, but the upside is that all the while, you’ll be betting the minimum bet, which is probably 5 times smaller in the 6-deck game. Plus you’ll see less heat. Almost always, the 6-deck game is going to be better. It just needs more patience and more precision, because if you can’t accurately keep count, then you might as well give up and go home. If you’re lazy and not good enough to count through 6 decks though, then the 2 deck game is for you. It’s higher risk, but you’ll see the reward more quickly. Possibly.

Under these conditions, what you should do to minimize risk of ruin (and the math I used to calculate this was unpleasant) is in the 2 deck game, bet the minimum bet PLUS 2*(the minimum bet) for every 1 the truecount is past 1.8, and in the 6 deck game, bet the minimum bet PLUS 3*(the minimum bet) for every 1 the truecount is past 1.8. And I’ll generally just use 2 instead of 1.8 because I don’t have all the time in the universe to be that precise. This is supposing they allow double after split, no hitting on split aces, double on any but only after first 2 cards, blackjack pays 3 to 2. So if you’re playing a 2-deck game and the min bet is 25 and the truecount is 3, you should bet 75 dollars, since 25+(3-2)*2*25=75. If you’re playing a 6-deck game, the count is 11, there are 3 decks left, and the min bet is 3, you should bet 18 dollars, because 3+(11/3-2)*3*3=18. This also shows you why it’s much lower risk playing the 6 deck game.

Oops. Correction – the VARIANCE is the function that has the parabola, not the standard deviation. So the 3 points that define the parabola are x=0 and y=0, x=52*(number of decks in show) and y=0, and x=1 and y=12/13. The STANDARD DEVIATION of the count after the first card has been dealt is sqrt(12/13), the variance of the count after the first card is dealt is 12/13.

It’s now 10/5/16 PM(Pre-Matthew) and it’s not fixed at all. The recommended casinos pop-up hides the free game! I’m not a competent computer programer, but surely you could find one.

Wheelmarks

Hi Mark,

We’ve narrowed down the issue and it shouldn’t be happening anymore. Thank you for your patience and my apologies for any inconvenience caused.

Cheers,

Tim

they are doing a promotion of an UNLIMITED 1% deposit rebate and that means if you play single deck game with a house edge of 0.3%,you will end up with a player edge of 0.7%.Now I know what “when its too good to be true,it probably is” means.

Its simple…. you are prob playing a game with even money black jack

i would love anyone who saw my post to share it with other players in other casino forums.Even if you think i am just a paranoid soar loser who got pissed by nothing but simply regular bad luck,at least get this information talked about and debated on so as to either prove me wrong or warn others. If any Chinese blackjack players can see this,Please be cautious ever after or PM me if you have anything else related you would like to share with me（中国的朋友看过来！）

there is a rogue casino i felt much obliged to report: the www_188bet_com——-Chinese version. According to them,they are legally regulated and licensed by the Isle of Man,which,as most of us know, is one of the most reputable gambling regulation authority.However,there is something odd about this.when you enter the webpage of its “table games”,the little icon of Isle of Man at the bottom of the main page suddenly turns into the icon of First Cagayan.I shared with them this confusion I had and they gave no explanation. When I play their microgaming single deck black,something even weirder happened.I won in a long string when i bet small like 10/20.But When I started to increase my bets,the odds just seemed to be all against me.i lost like 30 out of 40 times when i bet big and my bankroll just reduced from 10000 to 1500 while the maximum bet i made was no more than 450. Seriously,when i bet big,i just kept losing and losing and losing, and no one would not feel the same as i did if you ever were me there.Since there is no law in China to regulate online gambling ,I strongly suspect that they are exploiting some loophole to install a rigged game for the Chinese players,which probably is why they don’t show any information about relationship with Isle of Man at the Chinese version’s table game page.Because they know you have no authority to turn to even if you are cheated by an unfair game. I mean I don’t have any statistics here but as a seasoned blackjack player who has been playing this game in many other brick and motar casinos,I just got this instinct.The experiences are so apparently different to not be noticed.So here i sincerely encourage all players located in jurisdictions where online gambling is not in any way regulated not to play online blackjack on 188bet or ,if you can, any online blackjack without a live dealer.

I played live one night. Lost 20k, bout 73% of the cards were 7 or lower so every time i doubled i would get a 2 or 3 45% of the time at almost even time, so i ADJUSTED!! I stopped Doubling, keep hitting the 10 or 11 n get to 21 the hard way but I watched 32 cards come out n only 3 pictures, right!?.. Wasnt mad that i lost, but watched the next 60 cards come out, n told the dealer to watch with me., 8 picture cards came out, he started shaking his head i jus looked, shook my head n went about my buisness. End if the day ” i dont have to cheat to win, so i didnt like being cheated to lose”. Learn from this post cause Discipline is Key ?

Yo guy i absoloutely agree with you 100%

Weather it’s 20k or 2 k

It’s nothing to beat me fair and square

But to cheat me????

I just left the casino

Out of Four tables

Everyone of the tables first card

Was a face a ten a seven or an ace

They just cheated me out of 2k today

I bet a $600 dollar hand and bet $25 on lucky ladies

The dealer delt me a 20

Two jacks

So she paid the hundred from betting $25

On lucky ladies

Her turn up card was a face

And the turn down card was a 6

She flipped the next card and it was a 5

Today 3 times I had 20

And she beats me with a 21

It’s not fair

Like I said it’s nothing to beat me straight up

But to cheat me

Is disrespectful

I was told by a casino dealer in Vegas that those ShuffleMaster machines shuffle the cards Numericly ! Hmm, Food for thought. Any reaction are appreciated. Thanks