The Long Run in Poker
The long run

13 years earlier, when I started playing Texas hold'em among friends, whenever someone was unlucky enough to lose with strong cards and obviously needed consolation, we kept telling each other not to worry about it because it's all going to be good in the long run.

What did we mean by this? The majority certainly meant just that, not to worry about the lack of luck because in the long run if you keep putting your money in so well you'll get all our previous losses back. This, unfortunately, isn't true. The only truth is that the more often you put in our chips well, the more likely it's going to be for you to be overall winning players.

In the first part of the article, I talked about this, and you know that you can't ever get a chip back from someone that you lost unjustly, however probably the Justice League won't break your doors down to take back all the money you've earned through your opponents' bad beats. If someone still isn't convinced by my reasoning, I'll try to demonstrate with a simple example

An example for chips forever lost

Let us imagine a really rare situation, which only occurs once or twice a year. Let the game be texas hold'em. After the turn card you get four of a kind, you go all-in but the opponent has a full-house. Let's say on a K 8 3 3 board you have 33 while the opponent has KK. Only the fourth king can help the opponent, every other card is good for you. The ratio of a good card and unknown cards is 43/44, so your chances to win are 97.7%. To reiterate, out of 44 times you are expected to lose once. We all saw or heard about games where the king came. Even if it wasn't against you, but you saw it happen. It does happen. It's expected to happen once out of 44 times.

At the beginning of the example, I said that at most you'll have 1 or 2 games like this a year, which means that during the average poker career, probably less than 46 times. Let us say you'll experience it 26 times. If you ever lost a game like this, the best possible results you can get will be winning 24 out of 25 times, which is only 96%. And that's the rest of your life.

So based on this, you can say that the player like this who suffers from bad luck in a situation like this at least once, even if he wins every other time it comes up he still won't be able to "make up for the lost chips". The percentage will surely remain under 97.7%, and the previously mentioned assumption about the long run certainly can't be applied.

All lines intersect at infinity?

A graph could be drawn from every game type which shows your actual results in either chips or dollars won. You obviously don't do this with a pencil and a calculator, a tracker software will do it for you instead. Whoever saw something like this knows that the software is also capable of drawing further graphs. The most important one out of all this is the one that calculates the odds and shows our performance like that. We call this an EV-graph. (the meaning of EV here is expected value.) The EV-graph gives you a more accurate look at our performance than the graph detailing your actual winnings, as on some level it avoids the uncertainty of randomness.

Many people including world class players often assume based on lacking knowledge that these two graphs will definitely intersect, or meet in infinity. Obviously, this question concerns the people who are running worse than their EV a lot more. Whoever runs above EV tend to hope that it's going to say that way. The two graphs definitely correlate, but them meeting isn't guaranteed.

In reality, the exact opposite happens. Over time an even bigger absolute discrepancy is expected between the actual results and the EV. However, the relative discrepancy will be lower, so you can say the following: the difference between EV and the actual results will grow the more hands you play, however the difference between the two values in percentages will expectedly be less and less.