More on Luck vs. Skill in Poker

I think my assessment was somewhat accurate on the luck vs. skill problem in poker yesterday. As mentioned, I am not a math guy. Despite that, the “equation” still does not look complete. It may not be accurate either.

If I were forced to draw an equation for a six-seat table, it would have looked something like the following:

Six Seat Poker Table =Player 1 (skill+luck factor) + Player 2(skill+luck factor)… Player 6 (skill + luck factor)

I had skill varying from 6-1, with the most skilled player at the table receiving the 6, and the least skilled player receiving the 1. I had the luck factor evenly distributed among the six players, so that every player is 1/6th lucky.

Problems with the formula

I have problems; however, with the formula of mine that I would have committed to had I been “forced” to commit to a formula I believed to be accurate.

First, time needs to be taken into consideration, in that the longer the game goes on, the less luck has to do with it. I did not represent that in my formula above. Second, I suspect hand strength and position would have to be taken into consideration if we are speaking of just one hand. However, we are not referring to any one hand; we are referring to a session, perhaps even a career or a lifetime of poker.

Third, I have not considered how “in tune” one is with said skill-sets, which does vary, by the way. This brings me to the next point. Skill is not something that I can represent by assigning a six to the best player at the table, and a five to the next. Who is to say that the best player at the table is not at least twice as skilled as the second best player? If that, in fact were the case, then 6 for #1 and 5 for #2 would not be mathematically correct.

Finally, I did not take into consideration the ability for lesser, unskilled players to adapt to a given game, or just straight up improve their game over time. This also stands to reason that the most skilled of player’s improvement is not accounted for. Even taking all of that into consideration, I am still unsure if it would be accurate.

Time factor
In tune with skills
Skill multiple

Luck over the long haul - the time factor

I am rather certain that despite what is said, luck still plays out over the long haul. People have said that one’s poker statistics over the course of their career shows that luck has nothing to do with their results. If they are a highly skilled poker, you will not find evidence of luck in their statistics. This is not completely true. You will in fact find luck in their statistics, as you will see instances where they sucked out on another player (who played their pocket aces poorly, perhaps), and also instances where an opponent successfully chased, despite the poor odds and unlikelihood of catching their hand.

If luck were not evident in one’s long-term statistics, then anti-luck also would not be present. This would state that throughout the course of one’s career, every hand that should hold up does hold up to the extent that it should. Or at the very least, that over one’s career, they are equally lucky and unlucky, providing they are technically sound to the extent that we “assessed” them to be.

Over time, luck has “less” impact on one’s play, but it is still sure to be present, especially when analyzing shorter-term results. If the “long term” is made up of a series of “short terms,” and luck is believed to have more “presence” over a short-term scenario, then luck must also be present, to some extent over the course of one’s complete poker career. I would argue, however, that it is less evident over the long haul than over the short-term results.

A quick thought though. We all should have seen the expected value charts for starting hands. Is time and luck factored into the equation for these EV charts? Take for example the Starting hand
EV Chart here; broken out by position for a ten-seat table, from the button, we can expect to win AN AVERAGE of 2.96 BB (big bets) per instance of receiving pocket aces on the button. Does this mean each and every time we will win exactly 2.96 big bets per instance of receiving said hand on the button? No. However, it does mean that we can expect that we will win an average of 2.96 big bets every time we are dealt aces on the button over the course of our playing career at a ten-seat limit table when we are playing optimally. Said another way, assuming we always bring the A game when we are dealt aces, sometimes we will win more than 2.96 big bets, other times less. Over our career, we can expect to win 2.96 big bets per time we get aces on the button. This takes into consideration the “suckout factor” as well, from my perspective.

I believe it also takes into consideration that we do not play these hands all the way to the river every time. The chart, from my best guess, assumes that over time, we are beat here, we win to showdown here, we lose to showdown, and we end it early by either folding our opposition or folding ourselves. This brings me to my next point, and perhaps the final point of the day:

The hand range impact on luck

If I have “standards” with my starting hand selection, relative to hand strength and position, do I “need” as much luck as those who play against me and have “less” standards or perhaps even “no standards” at all? If what I deduced above is correct, luck is already factored into the equation. I need only play the +EV hands optimally in position and over time, providing I play optimally, I “should” show a profit closely resembling the EV chart throughout my career. If this is true, or close to true, then I would suspect that a player’s hand range and skill factor would have to go into the luck vs. skill calculation.

Even so, it still does not answer the question of just how much of the game is skill and how much is luck…