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.