Before we begin, I will need to define a couple of terms to ensure we’re all on the same page:
- Game of Skill- A game where the outcome is determined predominantly by mental and/or physical skill, rather than by pure chance
- Game of Chance- A game where the outcome is determined predominantly by randomness
- There is no rake
- The players play at the same stakes* the entire time
- Each player gets dealt an infinite amount of hands
- The decisions that a player makes in each hand materially affects that player’s monetary results.
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| Image taken from TournamentTerminator.com |
Example 1: Player A decides to fold every single hand he is dealt. Let’s say Player A decides that he is going to fold every single hand he is dealt. Well, this decision has guaranteed Player A will lose money. Chance will play absolutely no role in his results. If there are 10 players at the table and the blinds are $5/$10, Player A has guaranteed he will lose exactly $15 every 10 hands. He will have to pay the small blind and the big blind each time the blinds come around (called an orbit). Even though the average winnings of the players at the table will be $0 over these 10 hands (remember it’s a zero-sum game!), Player A will lose $15 during these same 10 hands. His decision to fold every hand has caused him to have below average results.
Example 2: Player A decides to call a river bet with 3 high. Let’s say Player A gets dealt two cards, a two and a three of spades (2s3s). The first 7 players fold, leaving the Player B, the small blind, and the big blind. Player B raises to 30 (blinds are $5 and $10). The small blind folds. Player A decides to call with his 2s3s preflop:
Full Tilt Poker $5/$10 No Limit Hold'em - 3 players
DeucesCracked Poker Videos Hand History Converter
Player B (BTN): $1000.00
Seat 2 (SB): $1000.00
Hero (BB): $1000.00
Pre Flop: ($15.00) Player A is BB with 2
3Player B raises to $30, 1 fold, Player A calls $20
Okay so now the flop (the first 3 community cards) gets dealt. Since Player A, who has 2s3s, is in the big blind (BB), he must act first after the flop. He decides to check, which is essentially the decision to do nothing until your opponent acts. The other options are to bet or to fold, but since Player B has not bet anything on the flop yet, it would make no sense to fold. Instead you can check and see what Player B does. If Player B bets, player A must make a decision to call, raise, or fold. If Player B checks, the turn gets dealt.
Player B decides to bet $30 and Player A calls with a flush draw and a gutshot.
Flop: ($65.00) 5
6 7
(2 players)Player A checks, Player B bets $30, Player A calls $30
The Turn is another 5. Player B bets and Player A calls.
Turn: ($125.00) 5
(2 players)Player A checks, Player B bets $60, Player A calls $60
The river gets dealt and a final betting round exists. The River is an 8 of diamonds (8d) so Player A plays the board. His hand is a pair of 5s with a 678 kicker. To make his best 5 card hand, he uses zero of the cards that were dealt face down to him (the 2s and 3s). He uses all 5 community cards. This is called playing the board
River: ($245.00) 8
(2 players)Player A checks, Player B bets $100, Player A calls $100
Final Pot: $445.00
Hero shows 2
3Player B wins $445.00
On the river, Player B bets $100 and player A decides to call. Now will his decision to call this river affect his monetary results? Of course. Player B can absolutely never be losing to him. No matter what two cards player B holds he will always have something as good or better than Player A. If Player B has a 2 and a 3 as well, the two players will tie and split the pot. However, if Player B has any other two cards, his hand will be better than Player A's and he'll win the pot. By making this river call, player A has essentially thrown away $100. This clearly illustrates that a player’s decisions will impact his monetary results.
Making the decision to fold every single hand or to call the river with nothing will materially affect your results. This distinguishes poker from zero-sum games of chance alone. Take flipping a coin for example. If two people are flipping a coin and wagering $1 on the outcome every time (a zero-sum game), there is only one decision to be made. The player chooses “heads” or “tails” and in the long run, this decision will not affect the players’ results. Each player will win 50% and lose 50% and end up breaking even.
Poker is fundamentally different because in its essence, poker is a strategy-based game of decision-making. In the long run, the players that consistently make better decisions will win money and the players that consistently make worse decisions will lose money.
If each player in our hypothetical cash game is dealt an infinite number of hands, then each player will be placed in the same exact situations – each player will get outdrawn when they have the best hand the same number of times; each person will be dealt aces the same amount; each person will hit their flush draw on the river the same number of times, each person will lose kings to aces preflop the same number of times, etc. The point being that if everyone plays an infinite number of hands, everyone will get into the same exact scenarios, and only what the players control -their own decision making- will impact their results. The short-run luck inherent in poker will even out, and 100% of the variability in players’ earnings will be explained by differences in ability rather than differences in luck. If Player A makes 100k and Player B loses 100k over an infinite hand sample, this difference can be explained ONLY by Player A consistently making better decisions than Player B.
This demonstrates that poker is theoretically a game of skill in the very long run. Of course, this hypothetical game can never exist in reality. In reality, nobody gets dealt an infinite number of hands and thus chance does play some role in players’ results. The fewer hands a person plays, the higher proportion of the results will be explained by randomness rather than skill differences. In order to mimic this hypothetical infinite hand game, professional poker players generally try to play as many hands as possible. For example, I try to play 150,000 hands per month. By increasing my sample size, I effectively increase the impact my own decision-making has on my results and reduce the impact of luck on these results. Playing a large amount of hands reduces the volatility of my earnings and allows me to make a fairly predictable income stream.
A good analogy to drive home this concept is to look at how a casino makes money. Over a few spins of the roulette wheel, it is very possible the casino gets “unlucky” and loses money. They have an edge against the players (remember they make roughly 5 cents on every $1 bet), but in the short run randomness might prevail over this mathematical edge, and the casino will lose money. However, given enough spins of the wheel, the actual results will eventually converge to the expected results, and the casino will win. The concept is the same for poker players. Over a few hands, the more skilled poker players, who have an edge just like the casino, may lose to the less skilled players. However, as the number of hands increases, the players’ actual results eventually converge to their expected results (EVs), and the better players will win money from the worse players.
Though this post far from proves that poker is primarily a game of skill over a few hands or even a few hundred hands, it demonstrates that in the long run, poker is a game of skill. Over a long enough time horizon, the quality of the players’ decisions, not the quality of their cards, will be the main determinant of their results.
In my next post, I’ll take a look at why it shouldn’t really matter that poker is subject to short-term randomness, and how many other industries are subject to similar short-term randomness.
* Stakes refer to the size of the small blind and big blind in a given game. There is a wide variety of different stakes. Online these stakes range from 0.01/.02 (one cent, two cent) where you can play for a long time with a few dollars to $25/$50 (and even higher) where you need thousands of dollars to play.
The reason I included this as an assumption is because in poker there are a few different ways that you can get "unlucky" or "lucky". One of these ways to get lucky is if you play a wide variety of stakes and only play a fairly small sample at certain stakes. Let's say you play a large sample of hands at $5/$10 and very small samples of hands at $1/$2 and $25/$50. During the large sample of hands at $5/$10, the results will be explained largely by your ability since over a large sample your expected results and actual results will converge. Luck will play very little role in these results. However at the smaller samples at $1/$2 and $25/$50, randomness will play a significant role in your results. If you run well (get lucky) at higher stakes and run poorly (get unlucky) at lower stakes, your overall results will be biased upwards towards your true expected value. The poor results from running bad at low stakes will matter very little compared to the good results from running well at high stakes.
