I thought I would post this here to see if there's anyone interested and possible discussion. I consider this the most important idea in my book Cardrooms: Everything Bad and How to Make Them Better; An Analysis of Those Areas Where Poker Rooms Need Improvement.

Mason

.......................A Proper Balance of Luck and Skill


This is not a statistics text book and to read and understand it you’re not expected to have a background in statistics. But there is an idea that comes straight out of the world of statistics and statistical theory that deserves its own introductory chapter and has already been mentioned. And that idea is what I call “the proper balance of luck and skill.” So, without getting into any heavy statistical theory, here’s an explanation of the proper balance of luck and skill in (I hope) easy to understand language.

It turns out that in games like poker which are grounded in statistical theory (that includes probability theory) there are two parameters that drive the success of the games: The success (or lack of it) of the best players, and much of the enjoyment of the recreational players who, while losers in the long run, will still come back to play again and again. These parameters are luck and skill. And both are required in the right proportions for poker games to be successful in the long run.

First, let’s address skill. You’ll often hear that poker is a “skill game.” But this isn’t exactly true. A better statement is that poker is a form of gambling that has a strong skill element. And this skill element allows the expert players to win money in the long run. And since they win, they’ll come back to play again and again including helping to start games and to keep games going.

Now this idea is very important. Without winning players who act as game starters and help to keep games going, it’s doubtful that poker would be a successful casino game. But there’s also more to it.

In addition, there’s also a problem. If skill was the only parameter, these expert players would never have losing sessions, which means that the non-experts would never win, and if this was the case, there would probably be no poker games.

So, this means that there needs to be a fair amount of short-term luck in poker for the games to exist. And what this short-term luck does is that it’ll allow the recreational players to also have some winning sessions, and on those nights where they end up loser, they’ll be able to think about when they were ahead, and this short-term luck is the hook that keeps these people playing. However, it’ll also mean that the experts will have some losing nights, and many recreational players love beating the experts.

To be specific, David Sklansky and I feel that the proper balance of luck and skill will allow a strong player to win two out of three four-hour sessions, and the moderately weak player to win one out of three four-hour sessions. So, that’s a rough guideline when this book talks about a proper balance of luck and skill. And for a poker room to be successful, this idea of a proper balance of luck and skill can’t be stressed enough.

But there’s another important point that statistical theory tells us. It’s the fact that over time the short-term luck factor will dissipate and the expectation (win rate for the experts and loss rate for the recreational players) will dominate, and this is exactly the way it’s supposed to be.

But when saying “supposed to be,” I’m also referring to those games in which the expectation of the experts and the luck factor is in sort of a balance. That is, to say it again, the experts will be sure of doing well after a reasonable amount of playing time, and the recreational players will have their winning sessions to remember. And when this is the case, you can expect the games to thrive in a well-run poker room. Furthermore, games like this are the type of games that the poker room management should strive for. It’s also the type of games that the experts should want to play in to maximize their long-term success, even if it means that their expected win in their current session might be lower.

In this book, this idea of a proper balance of luck and skill will frequently come up. So, keep this chapter in mind, and if needed, please read it again to make sure that what is written is understood. Also, if you’re a cardroom manager, this idea should guide many of your decisions. To see why, please keep reading.

I'm not sure where I got this from, it may well have been you or one of your earlier books.

But whenever I talk to people (poker friends, non-poker friends, coworkers, family, etc.) about the construction of poker, the theory of poker as a game, and why poker works as a long-term casino game, I basically always say the same thing. Poker only works as a gambling game because you have imperfect, asymmetric information, and because skill is only 60% of the outcome, leaving 40% to chance/luck, unlike chess, go, or other skill games.

If skill mattered more, fewer people would play, and fish would get wiped out quickly. Pretty soon you'd end up with something like chess, where there is a group that is quite serious about it, and kids learn it, but there's a big gap of recreational adults playing, definitely not enough to support a permanent room for playing. (Online is perhaps a different story.)

If skill mattered less, it's basically the lottery and you wouldn't have regs, so same problem. It's right in the sweet spot.

This was also an interesting, though not dispositive, read: https://thegammonpress.com/comparing...-skill-chance/

I think the premise that there needs to be winners in poker is wrong. If you look at virtually all other casino games, no one can be a long term winner playing by the rules the casino sets (yes, one can card count, but the casino will eventually throw those out). People play slots even when nobody can be a winning slot player. However, those other games have lots of people playing them, far more than play poker. I forget which gambler said it but there is truth in the statement, "Winning isn't important. Losing isn't important. The act of gambling is important."

The reason promotions are out there is because it is the chance that the average player is thinking, "I could hit it." That keeps them playing as well. I can understand that a gambling book publisher wants a game to be potentially profitable so they can sell the knowledge to other, but the casinos couldn't care less.

This is true. But how the skill and luck are proportioned depend entirely on the type of players and the community where players come from.

I played in the 20/40 LHE at Foxwoods for a number of years. The game was basically one of the best in the country. There were roughly 200 players who were regulars and almost nobody came to play as a newcomer. New players were either players who were moving up from 10/20 LHE or were people who moved into the northeast and were regulars somewhere else.

The luck and skill balance was great. The game was hyper aggressive. I would estimate that about 25% of the players were winners over time. The factor that kept the fish coming was that they would win big now and then and also that some were business owners, lawyers, doctors, etc. and had money to burn.

Then Black Friday happened. And some online professionals who played 4 to 10 tables at once online descended. Luck was no longer a factor. The fish couldn't win ever. The skill level of the online pros was so high that the winning regulars at FW could no longer win over time. At least most of us. I became a fish. Within a year the number of tables dropped from 4 to 7 over the weekends to 1 or 2.

As a result I play NL tournament poker mostly. When I go to Foxwoods I look to see if the 20/40 LHE game is running and now after Covid it basically isn't even on weekends.

Another factor that should be considered is that aside from luck and skill most rooms have some kind of jackpot situations going. Many of the older retired players who are regulars come and play because they get casino points so they can eat for free and they look forward to possibly winning the bad beat jackpots or high hand contests. So poker in this sense is more like slot machines for the lower end (like 1/2 NL or 3/6 LHE). They are going to lose over time but its a way to spend their days and to possibly win a jackpot.

Hi dinesh:

In some ways you're saying the same thing I'm saying. It's the fact that both luck and skill help to determine the outcome. Where I differ from what you're saying is that your 60%/40% numbers are not hard and fast ratios. That is, the longer you play, the effect of luck will dissipate meaning that after enough time has passed your results will not be influenced (very much) by luck. But in four hour sessions, that won't be the case.

Mason

But there is a long time winner. And that winner is the casino who is always there to help start games and keep games going. That is in these other casino games, the casino serves the same purpose as the regular poker players (most of whom are winners).

I agree with this and we do discuss promotions in different places in some of our books. Generally, when a large jackpot is offered, the casino/cardroom can rake at a higher rate and still attract many players.

Mason

My only comment here is that the rise of no-limit probably also had something to do with the demise of the $20-$40 limit games. What you're describing happened everywhere.

Mason

I agree that there was a decline over time of LHE games nationwide. However, that wasn't the case at Foxwoods. This happened as a direct result of the skill/luck ratio of the 20/40 LHE game changing dramatically when the online players descended.

Now its possible that after Covid the 20/40 LHE game would have disintegrated because many of the players were older. And also because of the expansion of NL and PLO games. But this happened at Foxwoods in about 2013. On a good weekend we had 7 tables of 20/40 LHE going. The decline to 1 or 2 tables happened within 6 to 12 months.

The way it happened was that the absolute worst players stopped playing because they were never winning anymore. There were now no sessions where they could win money. Aside from the 2 to 3 professionals who were making money at the table there were now several amazing online professionals. So once the worst players dropped out, the regulars who played started dropping out because they were unable to win. And it escalated to where many of the professionals (like me) dropped out. It is true that some of the fish left to play in NL games but it wasn't because of the rise of NL. It was because they could no longer have winning sessions at 20/40 LHE.

I've never played at Foxwoods so I'm sure what you're describing is exactly what happened. This is also what you would expect when the balance of luck and skill is destroyed. And very few poker room managers understand this.

Mason

I'm not sure about the 60/40 ratio, perhaps as an overall mean/average across the Player Pool?

I think that you could really break down each Player type and generate a Luck Factor based on how they play the game. Obviously a winning Player relies on +EV/high equity spots and then it comes down to running above or below the EV line to determine how 'lucky' they've been running.

Fish, Card Players, OMCs and the various levels of 'Gamblers' should all rely on luck differently since some of them 'need' luck more than others.

The concept of luck is short term in poker, which may be the whole point of 'the point'. A Pro knows that they will win in the long run if they play a certain way and each pot is the same size as before with the same EV.

Can we say a Pro needs less luck to reap the rewards of their skill level? I hope so.

I can certainly say that our PLO Player pool is greatly reduced due to the increased skill of of a larger portion of the pool .. which no longer needs 'as much' luck per hand as they did 3-6 years ago. Regs fold more often, thus preserving their chips stack .. preventing some of the less skilled Players from fully realizing their 'luck' profits, which in turn prevents them from lasting longer in the games.

Are we just calling variance 'luck'? I think so. Why are we dragging poker 'back' into the gambling realm? Perhaps the 'gamble' is just short-term variance .. I can go with that. Or are we just gambling on how we surmise the 'incomplete' information that each hand presents?

Pros make the same decisions more often whereas Recs and Whales make more emotional decisions.

I'm kind of lost in what I'm even trying to say at this point. I guess I'm wondering why we even need to discuss luck (variance) other than the straight forward thought that if the less skilled Players have limited resources they will need to rely on 'running good' (above EV, get lucky) in order to remain in the game.

I think there's a relatively larger portion of the Player Pool who just wants to 'play' and don't necessarily care about 'luck'. Yes, bad luck may result in a shorter session for some, but how often a Player 'needs' to win (get lucky) is going to be different for each Player type. GL

How does this not have more up votes?

Is it wrong to consider variance as luck?

Luck is a description of what has happened in the past.

I’m not sure it is wrong per se, especially in common usage of the terms, but variance and luck are not the same, although they are related. Variance is a mathematical quantity that measures the deviation of actual outcomes from the mean value. Luck, especially in this context, is used to refer to the degree to which it is possible for a lesser skilled player to actually win. They are related in the sense that a zero variance game would not have luck as a factor (think of chess as an example - the better player always wins). Variance works both ways though. Variance for a bad player could result in the bad player winning, but it just as likely could result in that player losing more than expected based on skill level alone.

Good luck plus bad luck = variance

People can and do win at slots over small sample sizes. So long as it is only a week end or so Las Vegas odds are set such that in a group of 6-10 buddies coming to play one or two should be winners. The group of course is down but important that they can look and see one winner or more most of the time to get returning visitors.

So what does this mean with regards to running it multiple times? And what is the ideal STD Dev of a poker game from the perspective of striking the right balance of skill and luck? What is the n0 of live nlhe poker?

There are absolutely winners at -EV games. Probably not many typical grinders on lifetime heaters. Win a big slot progressive, probably going to be some lifetime winners. Occasional recreational craps player who happens to be at the hot table, some won't give it all back.
Poker is a -EV game (rake), but many players can beat the rake and have a +EV lifetime, assuming the games remain stocked with lesser skilled players.
Heck, even a bad player who hits a BBJ might end up a lifetime winner, even continuing to play on a regular basis. Lotteries are hugely -EV, and some big winner do end up broke, but about two thirds don't. Of those that don't I'm sure some give back what they won, but most do not.

Absolutely agree that losing players need to win occasionally to keep playing. Intermittent rewards drives a lot of animal behavior. Poker does have that sweet spot. Plus there are literally hundreds of wins and losses that make up a session and it's easy for many humans to rationalize what choices and/or luck could have made a losing overall session into a winner.

I'll concede that a few people can win at slots, just like the lottery. However, that is all based on luck, not any significant skill those winners possess. Mason's point was that a game needs needs people using skill to be long term winners to make then game viable. Add a BBJ and I'd argue that people will play poker even if the only way you could be a winner is by winning the BBJ.

Variance is a statistical measurement of luck. However, the measurement that's used is actually the square root of the variance which is known as the standard deviation. And the best way to look at this for some period of time (or number of hands) is to compare your expectation (whether it's positive or negative) with the standard deviation. And the smaller this ratio of expectation to standard deviation is (for that length of time) the more the short-term luck factor (as measured by the standard deviation) can impact your results in a relative sense.

For more discussion, plus a technique to estimate the standard deviation, see my book Gambling Theory and Other Topics - Expanded Edition.

Mason

I don't agree. A better definition is that luck, as measured by the standard deviation, is a measurement of how much your results might differ from your expectation. (Keep in mind that even if there is a high short-term luck factor, it doesn't mean that your results will differ by a lot from your expectation, only that they can differ by a lot.)

Mason

You're hitting upon something important. Casino games are successful because they are highly fluctuating which means that over the short term there will be some winners. Remember, that in casino games, the house is the winning player but it still loses often enough in short playing sessions so that the long-term losing customers will be encouraged to play again. Just like the recreational players in a poker room.

Mason

I believe that running it multiple times is long-term bad for a poker game. What's happening here is that the better players are trying to reduce the standard deviation to a low number so that they will only rarely have a losing session. And if the better players never lose, the bad players will never win and the balance of luck and skill will not be appropriate for the long time survival of that particular form of poker. There is more discussion about "running it once" in my book Cardrooms: Everything Bad and How to Make Them Better.

As for the ideal standard deviation, there is discussion of this in my book Gambling Theory and Other Topics - Expanded Edition. While it's more complex than this, for live play, having, for the best players, a standard deviation that's 10 times larger than the expectation, for one hour of play, should work well.Or put another way, the ratio of the expectation to the standard deviation is 10 percent. For 100 hands this is equivalent to having a ratio of the expectation to the standard deviation 17.32 percent. See "Topic No. 4: The ideal game" starting on page 129.

Mason

i disagree. the value of running it multiple times is as an escape hatch for worse players. long term, both good and bad players will realize their equity. in the short term, luck as antithesis of skill is going to disproportionately favor bad players, who are either going to be chopping or getting quartered where they would have flat out lost, or winning in unlikely run outs. it's only a positive for the game