11 May 2024 mindset mental game bad beats discipline downswing variance Poker is a game of both luck and skill. Have you ever experienced not cashing in a tournament despite playing well, or losing five consecutive all-ins in a cash game despite making good plays? Such things are common in poker, and anyone who has played poker for a long time has likely experienced them. Luck is uncontrollable, so let's learn how much luck influences poker and how to prepare for situations when luck is not on our side! What is Poker Variance? In poker, variance measures how far the actual results deviate from the expected probabilities. For example, let's say you go all-in with AA, and your opponent has KK, creating a $100 pot. How much profit can you expect on average? AA is the strongest hand, so it generates a lot of profit. However, you don't win the $100 pot every time. AA loses to KK approximately once every five times (18.05%). Even in this seemingly overwhelmingly advantageous all-in situation, you can lose $100 about once every five times. Moreover, there is a 1 in 25 (about 3-4%) chance that you will lose $100 twice in a row, and the difference between -$200 may deviate significantly from the +$160 you should have earned. Variance is inherent in poker, and despite having a good expected value, losing is quite common. Cash Game Variance In cash games it is possible to calculate how much you can expect to win on average based on your win rate (how many big blinds you win per 100 hands), and the number of hands played, as well as the best and worst-case scenarios. Let's calculate based on 100,000 hands and a win rate of 2.5bb/100: Looking at the calculation results, we can see that out of 20 times, we won +11,135 bb in the best case and lost -8,407 bb in the worst case. Normally, if you can win 2.5bb/100, you'd expect to get 2,500 bb over 100,000 hands. However, as shown by the calculations, there can be significant deviations in results due to poker variance. Even good players who can win at decent win rate of +2.5bb/100 might find themselves losing -8,407 bb over 100,000 hands. Considering such large variance in cash games, it's important to manage your mental state and bankroll. Tournament Variance Variance in tournaments is more difficult to calculate compared to cash games because there are many factors involved, such as the number of players and the prize distribution structure. However, it's important to remember that variance increases as the number of players increases and as prize distribution becomes more top-heavy. This time, we will calculate the case where there are 100 participants, the ITM zone starts from 15th place, the buy-in is $50, the rake is 11%, the ROI is 10%, and 1,000 tournaments are played. *ROI (Return On Investment) is a measure of how much profit is returned per investment (buy-in). ROI of 10% means that you will get back an average of +10% of your buy-in, so if the buy-in is $100, you will get an average prize of $110. In our simulation, with a 10% ROI, the expected value is: EV = $50 x 10% x 1,000 = +$5,000 However, due to variance, the actual results can vary significantly. Out of 20 outcomes, in the worst-case scenario, you could lose nearly $10,000, while in the best-case scenario, you could win nearly $25,000. Therefore, even a player who could normally win $5,000 might lose $10,000 in some instances. This could potentially lead to a loss of self-confidence, but as shown by the calculations, this is a realistic outcome that can happen 1 in 20 times. In poker tournaments, only the top 10-20% of participants get money, and since the distribution is top-heavy, variance is more severe compared to cash games. It's difficult to determine whether you lack skills or simply had bad luck just from losing 200 buy-ins. It is impossible to understand a player's true skills just by looking at the results of 1,000 tournaments. Understanding this level of variance and continuing to play through it while learning and striving for better plays during downswings is crucial. Prepare for Variance Accepting variance is crucial in poker. Whether it's an upswing where you're lucky and winning continuously, or a downswing where you're unlucky and losing continuously, being able to identify the situation accurately is important. Upswing Everyone who plays poker hopes for an endless upswing that keeps them winning. In the cash example above, a player with a true win rate of 2.5bb/100 might experience an upswing where they win 11 bb/100 over 100,000 hands 1 out of 20 times. During an upswing, it's important to realize your true skill level. Rather than being complacent with results, continuously improve your poker skills, analyze other players, and keep learning the game. Downswing In a downswing where you're unlucky and losing continuously, some people may believe that they are not good enough and may quit playing poker or become desperate. However, losing around 40 stacks in cash games or 200 buy-ins in tournaments is bound to happen at some point. Every poker player experiences downswings, and it's unavoidable. If you truly lack skills and keep losing, you need to focus on learning more about poker or lowering your stakes. But if you have enough skill and are still losing, it's important to keep playing without losing confidence. It's a good idea to remind yourself that these losses fall within the range of variance, strive to learn, and view downswings as opportunities to acquire better playing skills! Conclusion Variance is an inherent part of poker. In fact, you'll probably experience more losses due to variance than you imagine. This is because poker is not just a game of skill but also involves a significant element of luck. During severe downswings, it's crucial to accept them as part of the game and continue playing!