In comments at Volokh.com, people are discussing Blackjack trivia. In particular they are debating whether dealing an 8 deck game is a disadvantage for players. Theef started it all with this comment:
Worse, most of these measures actually harm all blackjack players, even the vast, vast majority who don’t know a thing about advantage play. (As one example, all players, counting or not, are dealt blackjacks less frequently from an eight-deck game than from a single– or double-deck game.)
A bunch of discussion ensued.
Now, without showing the math, I’ll say that it is true that players are dealt more blackjacks from 1 card decks than 8 card decks. But others in the thread go further and seem to suggest that this alone is sufficient to give the player an advantage relative to playing with an 8 card deck.
I’m not sure that’s true.
However, the reason I’m not sure is that I don’t know the rules for Blackjack, so I’m hoping one of my readers know. Right now, I’m only trying to understand the rules for payouts after only two cards have been dealt. In this case, I can see four circumstances:
- The player gets a blackjack, the dealer does not. In this case, the player wins 3:2 right? Meaning if the player bet $10, they keep their $10 and take $15 from the house. Right?
- The dealer gets a blackjack but the player doesn’t. In this case, the house takes the players money. So, if the player bet $10, the house takes $10, right?
- The player gets blackjack and the dealer gets blackjack. Am I correct to think the player keeps his $10?
- No one gets blackjack. In which case, the game just continues, so we don’t yet know the payout.
Can anyone confirm if these are the rules? (By the way, I know some tables don’t use the 3:2 payout. I’m mostly worried about what happens when both the player and the dealer get blackjack.
(Yes, I will be showing the math up to this point after someone confirms.)
Here’s Wikipedia:
Normally, the highest possible hand is a “blackjack” or “natural,” meaning an initial two-card total of 21 (an ace and a ten-value card). A player blackjack is an automatic winner unless the dealer also has blackjack, in which case the hand is a “push” (a tie). When the dealer upcard is an ace, the player is allowed to make a side bet called “insurance,” supposedly to guard against the risk that the dealer has a blackjack (i.e., a ten-value card as his hole card). The insurance bet pays 2-to-1 if the dealer has a blackjack. Whenever the dealer has a blackjack, he wins against all player hands except those that also have a blackjack (which are a “push”).
The minimum and maximum bets are posted on the table. The payoff on most bets is 1:1, meaning that the player wins the same amount as he bets. The payoff for a player blackjack is 3:2, meaning that the casino pays $3 for each $2 originally bet. (There are many single-deck games which pay only 6:5 for a blackjack.)
BarryW
I read stuff like this. But… not to be stupid, in games like baseball, the “tie goes to the runner”. So, in blackjack, does “tie” mean no money changes hands. (This is what I suspect–but to do the math, I need to know, not just suspect.)
You can criticize particular lines of argument, but the fact of the matter is that for all commonly used rule sets, assuming perfect play based only on presently visible cards, six decks provide a very modest advantage to the player over eight decks.
You can demonstrate this very easily via monte carlo methods.
It seems very unlikely that any viable card counting system would remove the six deck advantage.
My advice to people using this information is as follows:
1. The six vs eight deck difference is insignificant in comparison to other rule changes, and will very rarely dictate where you should play. Environmental considerations can easily outweigh this difference.
2. If you have the time, patience, money and mental aptitude to make money counting cards, you should be playing poker which, despite the dramatically increased skill level of the average player since the poker explosion, offers very significantly better financial opportunities. Making money through Black Jack, even if executed extremely well, requires (what I consider to be) extremely high patience.
And yes, two black jacks is a push.
Jason-
I’m not so much trying to criticize as to understand the edge. The problem is I don’t know the rules for payouts! That makes it impossible for me to compute anything closed form or using montecarlo.
I do get that the probability of blackjack is higher with 1-deck cards than 8 deck cards and that if rules are as I described in the post, the pay out after 2 cards is better for players using 1 deck rather than 8 deck. This can be shown both closed form and monte carlo. (I compared my monte-carlo to my closed form and they agree.)
But I want to have fun doing other “what ifs”. So… I want to verify the payouts.
FWIW: I have NO intention of trying to make money playing blackjack. Counting cards sounds like it would take oodles of concentration, and I assume the edge is small. Plus, it’s legal to kick out card counters in Illinois. (OTOH, Indiana is close. Whooo!)
Fact is plenty of dealers count cards. Why? So they can reshuffle the deck when the odds start to go against the house. Back in the late 70s I went with my college team to Las Vegas for a bowling tournament and one of the fellows in our group could count cards. The dealer picked up on it and complemented him on his play. He was counting also and thought it a joke. Not much money changed hands. The dealer got plenty of tips and played it straight up. It was fun to watch.
John–
Oh, I’m sure the dealers keep some sort of count! It only makes sense.
I did find some gambling web pages with tables of optimal strategies when you haven’t counted, and have little scripts describing the house edge under various combinations of circumstances. It does look like the final answer is that 8 deck games favor the house more than 1 deck games. So, even though just computing the ratio of blackjacks isn’t enough proof, it does happen that the edge in blackjacks you get from a 1 deck game does happen to go with the case that ultimately gives you the edge if you use the optimum strategy.
You know though… the weird thing is that I can’t imagine wanting to play the game unless I thought I could at least try to count. Knowing that the house has an edge in the long run would really make the game fall in the category of “not fun” for me. So, the only way I could enjoy the game is if I were undertaking the challenge to count. But even then, it seems like such a pain in the neck to memorize the table of best strategies, then count, then spend all the time at the table! (Meanwhile, not getting drunk to avoid making mistakes. Oy!)
Lucia,
Its been several years since I was deeply into this. But FWIW:
As I understand your inquiry, you are trying to figure out why a seemingly symmetric change to the rules (the size of the deck) has an asymmetric result (larger decks favoring the house).
The argument about blackjack [it is less likely with a larger deck, and has asymmetric payouts] is correct, but my recollection is that is represents less than 50% of the disadvantage that comes from the larger deck.
The larger asymmetry (in this case) results from the player having a choice as to when he hits or stands, while the dealer does not. In a game with fewer decks, a player knows more, and gains a greater advantage from this choice, especially in those situations where basic strategy calls for the player to stand (or double down) with less than 17 [holding a 15 against a 5].
For a concrete example of this: In a game with 1 or 2 decks, if you are holding a 9 against a dealer’s 2, you should double down. In a game with 4,6 or 8 decks, you hit. This is because the three known cards provide more information in the case of a smaller deck (increasing the chance that you will draw a ten by a greater amount and decreasing the chance that the dealer will draw to 21 by a greater amount) and this additional information is sufficient to change the optimal decision.
With certain obscure exceptions, the optimal strategy does not change between six and eight decks, but the edge held by the player (mostly in those situations when you are betting that the dealer will bust) does increase.
We played hearts and spades in the dorm. Me and another guy in our group could remember the cards played. It was just a matter of practice. I would imagine four strings of cards and fill them in. I don’t know how he did it. Being able to do this didn’t help in poker where you reshuffle after every hand. Because of this poker didn’t interest me much. Some how we didn’t play 21. Counting and remembering are different skills.
We played much chess, Stratego, Risk and the above card games. I remember a four board game of Risk that went on for days. Well nights really. Do college kids still do this?
A book you might like… “The Hut Six Story” by Gordon Welchman, ISBN 0-07-069180-0.
Jason–
Yes. My puzzlement was to a large extent over the explanation involving only information on the rate the player hits blackjacks. That part of the game represents less than 10% of all plays. It’s also pretty obvious that what one does in the second part of the game matters a lot to the payouts.
So basically, the math related to the fraction of blackjacks only wasn’t sufficient to really tell me much. (That doesn’t mean the guys claims were wrong– just that the effect wasn’t entirely explained.)
Your explanation of the later part is interesting and would dominate the part of any formal computation.
It is tempting to run monte carlo on some of these things. But… hmmm maybe too much time. 🙂
“It is tempting to run monte carlo on some of these things. But… hmmm maybe too much time.”
Having actually done this, those are my thoughts exactly 🙂
Just did a monte carlo. 10 runs each of 10000 decks of both single deck shoes and 8 deck shoes. Then averaged them. Single deck shoe you get 1.254 blackjacks per deck. With the eight deck shoe you get 1.234 for each single deck.
A pretty trivial difference in a lifetime of play. Other playing rule differences and errors made dominate.
Bob–
The closed form solution is: probability of blackjack on 2 cards =
2* 16*4 *N/[(52)(52*N-1) where N is the number of decks in the shoe. This reproduces your answers for N=1 and N=8.
Of course, this alone isn’t enough to tell you the edge on the “2 card” part of the game.
So, for the 2 card part of the game, you need to account for whether the dealer gets a black jack too!
I guess for completeness, I should write this up.
As far as the idea about blackjack dealers counting cards. Forget about it. It’s so laborious they’d quickly run out dealers willing to do job. With everything else they have to do, it simply isn’t required. It’s possible the eye in the sky or the shoe itself might be fitted with a scanner to do that. But simply cutting off the last couple decks reduces some of the edge a player may have by counting anyway.
Heh. Let me see if I can get rid of that smilie by removing the spaces.
My blackjacks per deck is simply the total number in each 26 hand deck. Divide by two for player share.
Competing against the dealer, the single deck shoe gives .606 wins per deck for the player. 8 deck shoe gives .589 wins per deck for the player.
So out of 104 player bets placed in an 8 deck shoe the player edge has been reduced by
(((.606*8)-(.589*8))*1.5)/104 =0.00196154
Pretty trivial.
Actually the real life difference is even smaller since many hands are more than two cards.
Bob,
Not only are most dealers at nicer establishments trained in card counting (a Wynn dealer told me that it was a standard part of their training), but if you ask them, they are likely to tell you if the deck is heavy or light.
Amateur advantage players rarely have an actual advantage, and smart casinos appreciate their money.
BTW, I have never seen any evidence of a dealer shuffling early based on the count in a nice establishment. I’m sure I’m not the only person who would walk out if this happened to them. (And I am most definitely a net revenue source for the casinos).
You CAN observe this happening in single deck blackjack on Freemont street (which suggests that at least some dealers at low rent establishments may also be trained in counting).
Jason,
Frankly, if I was running a BJ pit I wouldn’t want the dealers being able to count. I wouldn’t want that grief. I want dealers that are friendly and just competent enough to pitch the cards and properly handle the bets. Too sharp a dealer and you’ve committed yourself to always being wary of collusion by dealers and teams of confederates. (and don’t think it wouldn’t happen) The dealer signaling when the confederates should come over and play big because the shoe is favorable.
The only one that should have an interest in the count might be the pit boss. I wouldn’t be surprised if the eye in the sky is capable of keeping track for them.
My son has been dealing poker for many years between Mohegan Sun and Foxwoods and I asked him tonight. He immediately said BJ dealers don’t count. That doesn’t mean a dealer couldn’t have made themselves capable, just that it’s not required.
The dealer you described must be some sort of special case. Maybe private one player tables?
The dealer who told me that everybody at Wynn gets this training was working a $25 or $50 six deck table that was not, in any obvious way, special.
I would guess, BTW, that a Vegas casino would rather deal with a counting group that includes somebody who they can easily keep track of, than one which does not.
Dealer misbehavior is a serious issue, but counting ought not be at the top of the list.
This links gives payoffs when playing from an infinite number of decks.
wizardofodds.com/blackjack/appendix1.html>
The blackjack house edge calculator
wizardofodds.com/blackjack/house-edge-calculator-pop.html
indicates that the difference between 1 deck and 8 decks, using optimum strategy but not counting cards, is about -0.0061 to the player.
The general rule is the player bets 1 unit. If the player mimics the dealer, the player and dealer will have an even break on the hands where both players score between 17 and 21. The payoff in these cases is 1 to 1. The house edge comes when both the dealer and player bust. Since the player busts first, the dealer wins these “ties”.
When the house pays 3 to 2 on blackjack, the net dealer
edge is about 5.5%
Another non-symmetrical rule is that players get to see 1 card of the dealer, make a reasonable inference as to what the probable hand of the dealer is, and adjust hitting and standing accordingly. If the up card is a 4,5, or 6, the player should stand on hard 12.
A third non- symmetric rule is “doubling down”. The player may have the option of doubling his bet, and receiving only 1 more card. Usually this option is restricted to cases where the player’s total is 9, 10, or 11.
A fourth non-symmetric rule is “surrender”. In some cases the casino gives the player the option of conceding 1/2 a bet, and giving up the hand.