What is the mathematical expectation in poker?

What is the mathematical expectation in poker?

 If we talk about poker on the Internet, the most important factor for success here is not mathematical abilities (poker calculators, hand charts, auxiliary tables of chances can replace them), but decision-making skills with a positive mathematical expectation.
    Before each draw, all players have equal chances of both winning and losing. Specific hands increase the chances of winning some players, and reduce the chances of others. To understand the deep meaning of the expectation (the estimated income from the bet in a particular situation at the gaming table), you need to know some poker terms: variance, winrate and ROI.
    Dispersions are called deviations from average mathematical values. Let’s return to our favorite occupation: tossing a coin. If the “eagle” falls more often than “tails,” this will be a prime example of dispersion. Such a deviation does not reduce the chances of “tails” falling out. This is a simple deviation from the norm, which will be corrected by further tossing the coin. Why is it important to know? The answer is simple. Losing in poker can be profitable if it is a consequence of variance. Such losses are easier to perceive, realizing that all actions were correct. A bet with a positive matt expectation always makes a profit. Even if the player has lost a specific distribution.
    It is important to continue to act mathematically correctly and the distance will correct the deviation. Prolonged dispersion to the negative side is called downswing or downstream. In positive – upstrikom.
    Winrate is a very important statistic in cash games, showing the profit of a particular player in a distance of 100 hands. Counting is done in the big blinds (BB). An excellent indicator is the winrate from 2 to 5 BB. Winreat reflects the general level of the player’s skill and shows the value of the mathematical expectation from his game.
    ROI is a return on investment. In fact, this is the percentage of money spent on the game and the player’s net profit. ROI may be different. This indicator depends on the type of poker, the format of the game (tournaments or cash), the level of opponents, limits. The more money invested in the game, the larger the winnings. But the ratio does not change. Record ROI can also be available at microlimits. It all depends on skill or luck.
   Professional players have ROI from 10-20% (in tournaments) to 30-35% (in cash games). But they are experienced players.