Relative Skill Anlaysis BJ question

Hi all,

Firstly, I hope I came to the right place to ask such a question and I have looked around the forum a bit and could not find a similar thread to the one I am writing now.

I'm writing my thesis on a relative skill analysis on blackjack. I'm trying to find out if blackjack is a game of chance or a game of skill (of course we all know BJ is a game of chance). To conduct such a relative skill analysis I will need to define three different players: a beginner, an optimal player and a fictive player. The beginner just learned the rules of the game and follows a (naive) strategy, for example always standing when dealt a 15 or higher and never doubling, splitting or surrendering. An optimal player has mastered the game and always follows a strategy that will maximize his or her expected gain, i.e. follow the basic strategy. Finally, the fictive player has also mastered the game and follows basic strategy, however he or she knows the cards that will be dealt beforehand, without influencing the game. So, the player knows which cards will come next and how the hand will be played, but cannot influence the game in any way.

With the help of Michael I have found the optimal strategy of a blackjack game with infinite decks, as this was an assumption of mine. I also found the house edge and the expected gain of a player when he or she follows the optimal strategy. So, the optimal player can be defined. The beginner is also easy to code, since I can just program that the player will always hit when the total value of the cards is 14 or below and always stand on 15 or higher. The problem arises when I need to define the fictive player as I do not have a clue ow to program this. So, after some days contemplating on what to do I thought why not ask it here and see if someone can help.

I have used these two videos from Michael's YouTube channel for reference purposes: /watch?v=jCF-Btu5ZCk&t=959s and /watch?v=wJsGnXgrGvg.

If someone has any idea on how to tackle this problem, let me know. If I have to provide more details in order for it to be more understandeable let me know.

Thank You,

Murut99

Quote: Murut99

I have used these two videos from Michael's YouTube channel for reference purposes: /watch?v=jCF-Btu5ZCk&t=959s and /watch?v=wJsGnXgrGvg.

link to original post

Welcome to the forum.

I am relinking the videos here:




What playing options are the three hypothetical players "allowed' to alter in your comparison?
There seem to be some arbitrary limitations imposed.

Also I would like to thank Michael for helping me a lot with his videos. I am forever in your debt sir!

Thank you for linking the videos here! The optimal and fictive player can split, surrender, double, hit or stand, so basically everything in their arsenal. They will most of the time do the same as the optimal player and fictive player both follows basic strategy. However, the fictive player can "see" if the next card is going to bust him or not, leading to a presumed higher expected gain in the long-run, as hitting a 17 can now be valid strategy if the next card is a 4 for example. Or the fictive player doubles with an 9 against a dealer's 10 since the next cards are an ace and 7 for example.

The beginner player I have defined as a player that does not split, double or surrender and either hits or stand. This was my own interpretation and this will be explained further in my thesis of course.

Quote: Murut99

define three different players: a beginner, an optimal player and a fictive player.

The beginner just learned the rules of the game and follows a (naive) strategy, for example always standing when dealt a 15 or higher and never doubling, splitting or surrendering.

An optimal player has mastered the game and always follows a strategy that will maximize his or her expected gain, i.e. follow the basic strategy.

Finally, the fictive player has also mastered the game and follows basic strategy, however he or she knows the cards that will be dealt beforehand, without influencing the game. So, the player knows which cards will come next and how the hand will be played, but cannot influence the game in any way.
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Basically, the beginner plays imperfect basic strategy, the optimal player plays perfect basic strategy.

The fictive player - I don't think there is such a player who sometimes knows what card comes next, but does nothing about it. "Cannot influence the game in any way. " And who follows basic strategy only, even knowing what card comes next? The fictive player knowing what card comes next could definitely influence the game in every way and would not necessarily follow basic strategy at all times.

I think you should make your third category a player who follows perfect basic strategy at most times, counts down the deck, and from the count sometimes alters the basic strategy to suit the count.

You could then create a fourth category of a player who follows perfect basic strategy at most times, counts down the deck, sometimes knows what card is coming next and from the count sometimes alters the basic strategy to suit the count or based on what card comes next. You won't find too many players in this category.

You also made no mention of amount bet. The advantage player will alter his bet based on whatever advantage is in play at that time, whether it be the count, or that the dealer in question is exposing the hole card, or the player somehow knows what card is coming next before the hand is played and is in the position to receive that card.

Edit: I see that you added the following criteria too: "The beginner player I have defined as a player that does not split, double or surrender and either hits or stand." That's...entering the realm of criteria definitions that might not relate to reality. I think I'll leave this thread to others, at this point. Good luck getting someone to spend the time on this.

Quote: Murut99

Hi all,

Firstly, I hope I came to the right place to ask such a question and I have looked around the forum a bit and could not find a similar thread to the one I am writing now.

I'm writing my thesis on a relative skill analysis on blackjack. I'm trying to find out if blackjack is a game of chance or a game of skill (of course we all know BJ is a game of chance).

Maybe contact Bill Zender. Long ago he did a survey from surveillance of a large number of players to find sample the error rates for various types of hands. This allowed him to get a very precise estimate of the skill of an "average player." As an aspiring academic, you may find he is willing to share some of his results, but I can't say that for certain. That said, short of what Bill did, or real-time sampling in a casino, anything you come up with is speculative. But, you may also find you can't distinguished highly skilled play from idiots -- namely a hole-card player or edge sorter or ace tracker or skilled cutter may look like an idiot to you, even thought they may be the most skilled player in the casino.

And you are wrong in your initial paragraph (as quoted above) saying that blackjack is a game of chance. Everything about Blackjack, no matter the knowledge level, is a demonstration of skill. The only way to make it "not skill" would be to use a random number generator to decide all hit-stand-double-split decisions.

Roulette is a game of chance. My dog could play just as well as you, in fact, you and my dog would have the exact same skill level, no matter your "strategy."

I overlooked the "game of chance" versus "game of skill" (semantics - a theoretician would get caught up on that), but after looking over what he wrote, I couldn't overlook all the strained and conflicting criteria imposed on the different categories of players he created, which a real blackjack player would have a hard time running with.

Hi again,

Based on all the replies I think I have to add a little bit more context on what I am doing. Basically I am determining if blackjack is game of skill or a game of chance. To do this I will use a proposed measure of skill mentioned in the Lecture Notes of one of my classes. Here, the three players are introduced and formula's are given to find a level of skill on a scale fo 0 and 1. 0 being a pure game of chance, like roulette, and 1 being a pure game of skill, like chess. Of course, one cannot find a beginning strategy that every beginning player will play, as everyone plays differently. That's why I have assumed, for simplicity reasons, that the beginning player will not split, double or surrender and always hits when the toal value is below 15 and stands otherwise. My question solely focuses on the fictive player as I have no clue on how I could program a player that would know all the cards dealt beforehand.

Regarding the comment I made on blackjack being a game of chance I acknowledge that, for example, roulette is much more a game of chance. However, if we would compare it to chess could one safely say that blackjack is a game of skill? Of course, the expected gain of a player can be increased when certain strategies are followed but it will not make sure the house edge is gone, making it somewhat of a game of chance. Nonetheless, I am not looking for a discussion on bj being a game of skill or chance. I should have made that more clearer, I'm sorry.

Also I would like to add that I had not considered the bet size that can change depending on the outcome. I am sure that an assumption will be added on the bet limit or an assumption on bet size always being the same.

Regardless, thank you for the replies all.

I hope I have explained myself better this time.

Assumptions are needed for my research and of course there is no correct way to define skill and chance.

So just have two categories of players. One plays perfect basic strategy, the other deviates from it somehow. Make the deviations fixed of course. Then run the simulations, and a posteriori you will establish that the perfect strategy comes out on top over time, proving therefore that blackjack is a game of skill.

Don't have to do much more than that.

I wish it was a simple as that. I have to support my thesis with theories, lemmas and prepositions I learned during my studies. So, I have to somehwat link it to the lecture notes. If this proves to be too diffcult I will see if I can alter the formula to make it easier or to merge the optimal and fictive player into one player as mentioned by you in a comment above.

I was thinking to deviate between a certain loss (let's say the player has a 16 against a 10 and the next card is a 10) and the times where a fictive player would win and a optimal player would not (let's say a 17 against a 10 with the next cards being a 4 and a 6; the optimal player would stand and lose and the fictive player would hit and at least push). But I think this would prove to be too difficult to handle, so I was hoping someone could help me find a better way in doing this.

Nevertheless, thank you for replying so quickly!

I don't know if you're trying to prove BJ is a skillful game or trying to show students that some casino/card games have a skill element. For instance bridge and poker are skill games, where in the long run the better players will tend to win, but the skillful player knows how to play some scenarios better than the average player. However you can still have a "rotten run of cards" (although in competitions it is how you handle them compared to how others do).

In Blackjack, ignoring counting, card tracking, peeking at cards etc. the best player can learn and adopt the optimum strategy and just let luck play its part. There are some versions of Blackjack (e.g. Switch) and also some casino games, where there is a computer-calculated correct strategy but typically no-one knows all the details perfectly.

Perhaps a simpler game to think of is 3-card poker. There's a simple strategy, play Q64 or better; nevertheless many players follow hunches or play blind. As it happens if you could see all the players' hands, it has some advantage on marginal cases, and can easily be run as a simulation (just look at the cards and from the cards left, determine what hands the Dealer could make).

Thnking of bridge competitions, you could simulate, say 15-hand knockouts, and see how a skillful player does compared to a novice.

Quote: Murut99

Assumptions are needed for my research and of course there is no correct way to define skill and chance.
link to original post

The difference between chess & blackjack is that chess is a "full information" game, both sides can see and use all the information available. Likewise with Backgammon, it is also a full information game. Partial information games include bridge, rummy, poker, blackjack and many novelty casino games. Full information sports include golf and pool. Partial information sports include baseball and football (hence the signaling).

The availability of partial or full information is irrelevant when it comes to the game having an element of skill. The only time there is no skill in a game is if it is a no-information game, like roulette, baccarat, slots or keno. Even then, a knowledgeable player may be able to get some information, like wheel bias, but most would be oblivious to the possibility.

Every game that uses information (even if partial information) in making decisions is a game of skill. There, that's your Ph.D. (or masters) thesis.

I think you have a profound misunderstanding about the fundamental nature of casino games and the meaning of skill. Please take this feedback, you don't want to embarrass yourself by writing a thesis with your current level of understanding of skill in casino games. I recommend you begin by reading everything you can about skillful play in casino games (not just blackjack).

I just spent 3 hours playing the Wizard's site game of Black Jack using my best strategy for a $1,000 buy-in and lost 5 times in a row, or I'm down 125 hands. Somebody put a spell on me and my luck has gone so damn negative.

Duplicate

Quote: teliot

...I recommend you begin by reading everything you can about skillful play in casino games...

I am not an AP but am grateful to Eliot for many of his writeups and the types of analysis that can be done. He makes a valid point that there is a lot behind the scenes about casino games. There's also knowing about House Edges and, where applicable, play and betting strategies.

His website is an excellent read and shows some advantages by tracking cards. He introduces a nice "countability" measure - the profit someone with perfect information (i.e. counting cards seen) could make, on average, which watching 100 hands and making $100 bets when it's in the Player's advatange. (I have done this analysis on some of my ideas for new games.)

I also suspect you might need to get into writing your own simulation software; there are some fun challenges in generating random numbers, how to shuffle cards properly, and testing your games against known House Edges.

btw you may have to make an educated guess how a "ploppie" plays, but many of them will split Aces and Eights and even double 11. I suspect some of them always stand on 15, some on soft 17s, but some do stand earlier on dealer's 2-6s, others stand on 12s vs 2-6. And they always take Even Money!

Quote: charliepatrick

btw you may have to make an educated guess how a "ploppie" plays, but many of them will split Aces and Eights and even double 11. I suspect some of them always stand on 15, some on soft 17s, but some do stand earlier on dealer's 2-6s, others stand on 12s vs 2-6. And they always take Even Money!

With deference to our own late Alan Mendohlson, I am going to not use the term "ploppy" as he was very insulted by the use of that term.

Quote: Murut99

Hi all,

I'm writing my thesis on a relative skill analysis on blackjack. I'm trying to find out if blackjack is a game of chance or a game of skill (of course we all know BJ is a game of chance).

You need to know how Blackjack has both chance elements and skill elements. It is not a simple either/or. Probabilities are constantly in play in the game, and house edge derives from that. For example, after the cards are shuffled, there is a chance that the player is dealt a dozen winning blackjacks in a row and could not lose if he didn't even know the game. Or maybe he was incredibly skilled and the dealer was dealt a dozen unbeatable hands.
You need to understand that as cards are dealt, how probabilities and the house edge change, sometimes in the players favour. The infinite deck derivation of house edge breaks slowly as the game progresses. The player's optimal play also changes. You need to understand how skilled players, card counters, constantly monitor the remaining deck constitution and modify their hand play to suit. E.g. knowing when to play 'index variations' to get the best probability of profit. It seems you do not yet understand how card counting works. Card counters are the skilled ones that have a player advantage. You absolutely need to know how they exploit their advantage by bet value spread and wonging in and out. There's also psychology skill where the card counter avoids detection by observing game supervisors.

Quote:

To conduct such a relative skill analysis I will need to define three different players: a beginner, an optimal player and a fictive player. The beginner just learned the rules of the game and follows a (naive) strategy, for example always standing when dealt a 15 or higher and never doubling, splitting or surrendering. An optimal player has mastered the game and always follows a strategy that will maximize his or her expected gain, i.e. follow the basic strategy. Finally, the fictive player has also mastered the game and follows basic strategy, however he or she knows the cards that will be dealt beforehand, without influencing the game.

Those three player types are pretty arbitrary and not recommended. Beginners can't surely all be categorised with the same flawed strategy. If you watch such beginners, they seldom play consistent same set of errors.
What you define as the optimal player is not quite right. A player that uses correct basic strategy is only playing optimally to the extent that he's not card counting. He will NOT have an advantage over the house, but will lose less slowly than your bad playing beginner.
Your fictive player is a bit of a nonsense in as much as 'what's the point of such a player'? It's like saying will a horse race bettor have an advantage if he knows which horse will win. You need to have card counter in your group. He's the guy with the skill to overcome the house advantage completely. He still is at the mercy of random chance, but wagers so as to manage his risk of ruin.
If your thesis does not cover card counting, risk of ruin, kelly criterion, index play, spread, then it will show total ignorance of the game in the real world.
Oh. And if you ever think. "Wow I could become rich, counting cards' then you have failed in your understanding.

Quote:

...he or she follows the optimal strategy. So, the optimal player can be defined.

I have used these two videos from Michael's YouTube channel for reference purposes: /watch?v=jCF-Btu5ZCk&t=959s and /watch?v=wJsGnXgrGvg.

That's an estimation of basic strategy. It's still sub-optimal and why would you think the player will achieve a gain by using it. He won't. Basic strategy is a beginners level of play with enough skill to achieve close to the house edge and lose less slowly than a less skilled player.

Quote:

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So, with the Fictive player, any action taken based off of his next card knowledge would invariably change the game. The fact that he hits a hard 17 means that the next player or dealer's hand changes.

Also I am not sure why you would chose 15 arbitrarily, just have the novice either stand on all hands or follow the exact same rule as the dealer within whatever rule set you are assuming.

If you want a better than basic strategy player I would suggest calling out a SPECIFIC type. so, a hole-carder for example. Otherwise, you need to pick a specific type of card counting and run with it. Assuming that the novice and basic strategy player do not vary bet size. This shouldn't be too difficult as the + expected value is very well defined for this type of player.

If it is not too late however, I might suggest a different path. Video poker with a progressive available that could bring the EV more positive with an altered play strategy. I.E. the novice plays with common mistakes at a significant -EV. The skillful player plays basic strategy. The optimal player plays with the best strategy based off of the board-state (the fact that the Royal is paying more than the standard payable).

Concerning your chess example, consider the following: Computers are now demonstrably better than humans at chess. Chess could now be made as a "skill based" casino game, with a house edge, and even the most skillful player in the world would be at a negative expectation with an even money bet in that game (I fully agree to this argument being used in your thesis without citation as long as you come back to this thread and say thanks :P [after it is used and published]). Consider the implications of that to your arguments put foreword here.

Quote: teliot

Quote: Murut99

Assumptions are needed for my research and of course there is no correct way to define skill and chance.
link to original post

The difference between chess & blackjack is that chess is a "full information" game, both sides can see and use all the information available. Likewise with Backgammon, it is also a full information game. Partial information games include bridge, rummy, poker, blackjack and many novelty casino games. Full information sports include golf and pool. Partial information sports include baseball and football (hence the signaling).

The availability of partial or full information is irrelevant when it comes to the game having an element of skill. The only time there is no skill in a game is if it is a no-information game, like roulette, baccarat, slots or keno. Even then, a knowledgeable player may be able to get some information, like wheel bias, but most would be oblivious to the possibility.

Every game that uses information (even if partial information) in making decisions is a game of skill. There, that's your Ph.D. (or masters) thesis.

I think you have a profound misunderstanding about the fundamental nature of casino games and the meaning of skill. Please take this feedback, you don't want to embarrass yourself by writing a thesis with your current level of understanding of skill in casino games. I recommend you begin by reading everything you can about skillful play in casino games (not just blackjack).
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I think golf, at least competitive tournament golf, is not a ‘full information’ game. If I am on the 17th hole lining up a 70 foot putt for birdie, my strategy on whether I should ‘lag’ or definitely not leave it short WOULD vary depending on how my competitor who is on the 18th hole is doing. I certainly wouldn’t have the information on his distance to the green, his lie, etc…. I MAY have partial information, but not full information.

As far as the OP, I am not sure how analyzing his ‘fictive’ player in any way allows him to determine if BJ is a game of skill or not. It seems like a total waste of time to include any analysis of it.

The answer as to whether BJ is a game of skill or not is plainly staring you in the face. You need to compare the decisions of a RANDOM player to that of a ‘skilled’ player. NOT comparing the ‘skilled’ player to your made up ‘do the exact same thing’ player.

Thesis writing/preparing/defending is HARD!