Reconsidering the unit of play, and the propriety of card counting
May 22nd, 2015 at 12:38:53 PM
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I'll make this quick, because Dan has been pretty vocal about the issue of card counting in the other current thread (here) as well as several others.
Here's the thought. House-banked poker games, including pai gow poker, Caribbean Stud, Three Card Poker, Ultimate Texas Hold'em, etc., are -- like virtually all player-banked poker games -- dealt from a single deck. More importantly, that deck is shuffled between every hand. In many cases, like player-banked 7-card stud or house-banked Caribbean Stud, there simply aren't enough cards in the deck to play two hands before shuffling. In others, like player-banked Texas Hold'em or house-banked Three Card Poker, while there may be enough cards in the stub to physically deal two hands, the number of outs would so dramatically shift based on the prior hand's discards that it would completely change the game. Poker players understand this as a matter of course because counting outs is what they do. In any event, I've never seen a single-deck poker game deal more than one round without shuffling. As a result, the play of a single hand in a poker game is equivalent to the play of a single shuffle of the deck.
But in blackjack that equivalence does not hold. Even single-deck games deal multiple rounds per shuffle. The effects of card depletion on blackjack are well-understood (and have been discussed for decades) but two important points fall out. One is that basic strategy is essentially correct for the first hand dealt from a new shuffle. Two is that the expectation of the second hand is almost invariably different than the first, either better or worse, and as a result basic strategy may not be correct for that hand. The expectation often shifts even more dramatically as the hands progress after the shuffle, either in a single deck or in a multi-deck shoe.
Unlike blackjack, the expectation in baccarat doesn't fluctuate much as the cards come out. This has also been studied extensively and card counting in baccarat is, for all practical purposes, ineffective. Most regular baccarat players use scorecards to keep track of prior hand results and it's very common to see a baccarat player sit out one or more hands during a shoe while they wait for the patterns to take a certain shape. Baccarat players also tend to evaluate the course of their play on a shoe-by-shoe basis. "That shoe had 10 more banker than player wins," or "I won $200 on that shoe," etc. In other words, the "unit of play" in baccarat is the shoe (that is, the shuffle), not just one hand.
That leaves blackjack as the only card game in the casino where the effective "unit of play" is not the shuffle of the cards. I submit that if you consider the "unit of play" in blackjack to be the shuffle, rather than any individual hand, the question of the propriety of card counting becomes moot. Of course it makes sense to vary your strategy and bets during the course of the shuffle: the deck composition is changing as the hands are dealt. Like reading a table in poker, reading the deck in blackjack (that is, "counting cards") is simply the best way to play the shuffle, whether it's one deck or multiple decks. From that perspective, playing a fixed strategy at a fixed betting level for the entirety of a shuffle is decidedly not the optimal way to play. It might be near-optimal, but it's not actually the best way to play.
In video poker, there are several shortcuts that can make for a quick near-optimal strategy, but it takes a lot more effort to play according to optimal strategy. Similarly, in a shuffle of blackjack, top-of-the-deck basic strategy is a shortcut that makes for a quick near-optimal strategy, but it takes a lot more effort to play according to optimal strategy. That optimal strategy, for the shuffle of a blackjack deck, involves understanding how the deck composition changes from hand to hand and playing (and betting) accordingly.
The real bottom line is that optimal strategy in blackjack is actually player-favorable so a casino can't afford to tolerate too many optimal players. So they may employ countermeasures or rule changes. Those interventions may change the relative theoretical expectation of optimal strategy play, but they cannot change what optimal strategy actually is.
For what it's worth, I am not an optimal blackjack player. :)
Here's the thought. House-banked poker games, including pai gow poker, Caribbean Stud, Three Card Poker, Ultimate Texas Hold'em, etc., are -- like virtually all player-banked poker games -- dealt from a single deck. More importantly, that deck is shuffled between every hand. In many cases, like player-banked 7-card stud or house-banked Caribbean Stud, there simply aren't enough cards in the deck to play two hands before shuffling. In others, like player-banked Texas Hold'em or house-banked Three Card Poker, while there may be enough cards in the stub to physically deal two hands, the number of outs would so dramatically shift based on the prior hand's discards that it would completely change the game. Poker players understand this as a matter of course because counting outs is what they do. In any event, I've never seen a single-deck poker game deal more than one round without shuffling. As a result, the play of a single hand in a poker game is equivalent to the play of a single shuffle of the deck.
But in blackjack that equivalence does not hold. Even single-deck games deal multiple rounds per shuffle. The effects of card depletion on blackjack are well-understood (and have been discussed for decades) but two important points fall out. One is that basic strategy is essentially correct for the first hand dealt from a new shuffle. Two is that the expectation of the second hand is almost invariably different than the first, either better or worse, and as a result basic strategy may not be correct for that hand. The expectation often shifts even more dramatically as the hands progress after the shuffle, either in a single deck or in a multi-deck shoe.
Unlike blackjack, the expectation in baccarat doesn't fluctuate much as the cards come out. This has also been studied extensively and card counting in baccarat is, for all practical purposes, ineffective. Most regular baccarat players use scorecards to keep track of prior hand results and it's very common to see a baccarat player sit out one or more hands during a shoe while they wait for the patterns to take a certain shape. Baccarat players also tend to evaluate the course of their play on a shoe-by-shoe basis. "That shoe had 10 more banker than player wins," or "I won $200 on that shoe," etc. In other words, the "unit of play" in baccarat is the shoe (that is, the shuffle), not just one hand.
That leaves blackjack as the only card game in the casino where the effective "unit of play" is not the shuffle of the cards. I submit that if you consider the "unit of play" in blackjack to be the shuffle, rather than any individual hand, the question of the propriety of card counting becomes moot. Of course it makes sense to vary your strategy and bets during the course of the shuffle: the deck composition is changing as the hands are dealt. Like reading a table in poker, reading the deck in blackjack (that is, "counting cards") is simply the best way to play the shuffle, whether it's one deck or multiple decks. From that perspective, playing a fixed strategy at a fixed betting level for the entirety of a shuffle is decidedly not the optimal way to play. It might be near-optimal, but it's not actually the best way to play.
In video poker, there are several shortcuts that can make for a quick near-optimal strategy, but it takes a lot more effort to play according to optimal strategy. Similarly, in a shuffle of blackjack, top-of-the-deck basic strategy is a shortcut that makes for a quick near-optimal strategy, but it takes a lot more effort to play according to optimal strategy. That optimal strategy, for the shuffle of a blackjack deck, involves understanding how the deck composition changes from hand to hand and playing (and betting) accordingly.
The real bottom line is that optimal strategy in blackjack is actually player-favorable so a casino can't afford to tolerate too many optimal players. So they may employ countermeasures or rule changes. Those interventions may change the relative theoretical expectation of optimal strategy play, but they cannot change what optimal strategy actually is.
For what it's worth, I am not an optimal blackjack player. :)
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
May 22nd, 2015 at 1:13:10 PM
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Quote: MathExtremist
For what it's worth, I am not an optimal blackjack player. :)
I am not either. I do not think there is a single person in the world that is an optimum blackjack player. Not even Rainman.
I am not even a 'Linear Optimum' BJ Player. Maybe there is such a person.
But a 'Full Optimum' BJ Player definetely not.
I have been reading recently both Fiction and non-fiction books regarding Artificial Intelligence, Technological singularities and embeded chips that will enhance us all in the future. So it is only a matter of time for an Optimum BJ player to become a reality !!!
May 23rd, 2015 at 7:25:22 AM
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Very interesting different way of looking at it.
One of the appealing aspects of BJ to many people, I think, is the element of decision making. Many of the decisions seem obvious (example standing on a hard 19... Duh...) but it's still technically a decision mid-hand. and in many cases the decision is non-trivial. The rules have been written and, indeed adjusted by each house, such that when played by the majority / average cross-section of people, the house has the edge, but an edge that is low enough to keep the players coming back. The current most common set(s) of rules allows very smart/skilled players to gain a small advantage. However even these players are not truly optimal. I've often seen a rule of thumb for counting is "use a count system that your brain is capable of using without mistakes". Thus implying that a computer player could do better than a human player.
I'm curious what would be the EV for a computer playing "optimal shoe strategy" including varying the betting unit per hand, if such an optimal strategy could be written. Assuming one player, and mandatory to play a minimum bet on every hand for the stated penetration. Penetration becomes an actual rule of the game instead of a "playing condition". How wide of a spread? How many 'index plays' if it had 100% knowledge of lost cards? would it be more advantageous to play with a larger shoe because of the greater possible variance in deck composition? (Is it even a true hypothesis that a larger shoe would have more possible variance???) Of course it's all only theoretical; in real life there are other non-mathematical factors at play.
But certainly a very intriguing way of viewing the game --- viewing strategy and EV on a "per shoe" basis rather than "per hand".
One of the appealing aspects of BJ to many people, I think, is the element of decision making. Many of the decisions seem obvious (example standing on a hard 19... Duh...) but it's still technically a decision mid-hand. and in many cases the decision is non-trivial. The rules have been written and, indeed adjusted by each house, such that when played by the majority / average cross-section of people, the house has the edge, but an edge that is low enough to keep the players coming back. The current most common set(s) of rules allows very smart/skilled players to gain a small advantage. However even these players are not truly optimal. I've often seen a rule of thumb for counting is "use a count system that your brain is capable of using without mistakes". Thus implying that a computer player could do better than a human player.
I'm curious what would be the EV for a computer playing "optimal shoe strategy" including varying the betting unit per hand, if such an optimal strategy could be written. Assuming one player, and mandatory to play a minimum bet on every hand for the stated penetration. Penetration becomes an actual rule of the game instead of a "playing condition". How wide of a spread? How many 'index plays' if it had 100% knowledge of lost cards? would it be more advantageous to play with a larger shoe because of the greater possible variance in deck composition? (Is it even a true hypothesis that a larger shoe would have more possible variance???) Of course it's all only theoretical; in real life there are other non-mathematical factors at play.
But certainly a very intriguing way of viewing the game --- viewing strategy and EV on a "per shoe" basis rather than "per hand".
May 23rd, 2015 at 4:53:44 PM
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A computer could absolutely do better than a human using a counting system because no human-playable counting system is perfect. A computer could just compute the real-time expectation based on the remaining cards in the deck and tell you which play was correct so you wouldn't technically need "index" plays at all. You'd just make the optimal play based on the deck contents. As far as bet spread, you could actually apply a given betting pattern to the distribution of EV after the fact to determine what the effect was. The highest total expectation would be "bet min whenever edge <= 0; bet max otherwise," though that's not the best risk-adjusted strategy w.r.t. bankroll.
You can approximate the answer to "what would the EV be" by looking at the distribution of true counts, the approximate EV that applies to each, and multiply through by a given betting strategy. For example:
https://blackjackincolor.com/truecount1.htm
https://blackjackincolor.com/truecount2.htm
You can approximate the answer to "what would the EV be" by looking at the distribution of true counts, the approximate EV that applies to each, and multiply through by a given betting strategy. For example:
https://blackjackincolor.com/truecount1.htm
https://blackjackincolor.com/truecount2.htm
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
May 23rd, 2015 at 5:23:18 PM
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Quote: MathExtremistoptimal strategy in blackjack is actually player-favorable so a casino can't afford to tolerate too many optimal players.
The saving graces for the house:
- Most players do not play optimally.
- Many players who do play optimally are not a threat to the casino's bankroll, because of their comparatively small bankrolls.
- Many players who attempt to play optimally miss some important aspect of optimal play
May the cards fall in your favor.
May 23rd, 2015 at 5:34:04 PM
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Counting cards is the proper way to play blackjack. Just like remembering discarded cards in rummy, or counting outs in a poker-based game (UTH, MS, etc.).
May 23rd, 2015 at 10:56:37 PM
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Quote: DieterThe saving graces for the house:
- Most players do not play optimally.
- Many players who do play optimally are not a threat to the casino's bankroll, because of their comparatively small bankrolls.
- Many players who attempt to play optimally miss some important aspect of optimal play
That's all true. Operations consultants like Bill Zender have argued for years that the cost of countermeasures are far higher than the reduction in loss from card counters. Accepting some measure of AP play is just the cost of doing business; to get rid of it altogether would be far more trouble than it's worth.
I think managing a casino game portfolio is in some respects like managing a financial portfolio. A casino GM can be risk-averse and settle for a lower expected gain or can be more risk-tolerant and expect a higher average return. There have been casino bosses in the past who were actually risk-seeking but with corporate ownership that's rarely the case anymore.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
May 23rd, 2015 at 11:46:24 PM
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Very good Stacy!
Blackjack can be viewed as a single multi-bet round, occurring between the first hand dealt to the cut card hand, with a series of raise or call bets within that window.
Good way to look at it.
As it stands now, theoretical optimal play and allowable optimal play are currently two different things in the real world, though. However, it is possible that a game can be created where the two can meet.
Here's a project.
Blackjack can be viewed as a single multi-bet round, occurring between the first hand dealt to the cut card hand, with a series of raise or call bets within that window.
Good way to look at it.
As it stands now, theoretical optimal play and allowable optimal play are currently two different things in the real world, though. However, it is possible that a game can be created where the two can meet.
Here's a project.
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
May 27th, 2015 at 7:19:01 AM
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Quote: MathExtremistThat's all true. Operations consultants like Bill Zender have argued for years that the cost of countermeasures are far higher than the reduction in loss from card counters. Accepting some measure of AP play is just the cost of doing business; to get rid of it altogether would be far more trouble than it's worth.
There have been casino bosses in the past who were actually risk-seeking but with corporate ownership that's rarely the case anymore.
A good quote that I once read (from Bringing Down the House): "It's not how much players win that bothers the casino, it's the fact that players can win that bothers the casino." Sorry if it's not exact since I was quoting from memory.
Casinos have done a wonderful job of convincing the public that card counting is wrong:
It ruins the order of the cards
It forces us to offer worse rules (no surrender, H17, 6 to 5 BJ, etc.) to non counting players
It siphons gaming taxes that go to social programs
Players who count cards try to hide money: money that could be used to buy drugs, evade taxes, or fund terrorism
Any form of advantage play (reading a hole card, optimal VP play) is really a form of cheating, even if it's legal
