Texas Hold’em obviously involves luck. The cards come out at random, and the same decision wins today and loses tomorrow.
But involving luck and being pure chance are two different things, and the difference is concrete: you can know your chance of winning before you push the chips in.
1. What you decide is not the result, it is your equity when you bet
You can set yourself a rule: only move all in when you are at least a 60% favourite.
That rule is what the title means by how you play it — same deck, same table, and it decides which of the two things you are doing.
The rule is enforceable because there is enough information. Your two cards, the community cards, how much your opponent put in, where they are sitting — put those together and you can work out how far ahead you are right now. That number is available before the hand is over.
Roulette has nothing of the kind. A single number, red, a whole column: for every 100 you stake, you lose 2.70 on average in the long run, and it is the same wherever you put it — you are not failing to calculate it, there is simply nothing to choose between. Hold’em gives you the choice: the same all-in can be made as a 60% favourite or as a 30% one.
That is the part of this game you actually hold: not the result, but your chance of winning at the moment the money goes in.
2. Losing all night disproves nothing about the rule
The problem is that being right does not mean seeing it.
Say you follow the rule tonight and get all in five times, a 60% favourite every time:
| What happens | Probability |
|---|---|
| Lose all five | 1.0% (about one night in a hundred) |
| Lose three or more of the five | 31.7% (roughly one night in three) |
The second row is the point. One night in three, you will get your money in as a 60% favourite and lose more than half of them — that is not a freak run of bad luck, it is a normal part of the distribution. And losing all five is no great marvel either: one time in a hundred. What it feels like at the table is “everything I touch dies tonight”; what actually happened is that five is a tiny sample.
The reverse holds too: winning three nights in a row does not prove your decisions were right either. With a sample that small, running good and playing well look identical, and people are especially quick to build themselves a theory while they are winning. The same feeling grows in front of a roulette wheel, where there is not even anything to choose between.
3. How long "the long run" actually is: thousands of hands
“The maths will tell you in the long run” is true, but the unit of time deserves spelling out.
For the same 60% all-in, here is how far off the win rate you measure can be:
| Number of all-ins | Where your measured win rate lands, about 70% of the time |
|---|---|
| 5 | Within about 22 points either way (you have measured nothing) |
| 100 | Within about 5 points either way |
| 1,000 | Within about 1.5 points either way |
Only in the thousands does the number you measure sit close to the real 60%. And getting all in and running it out — both stacks in the middle, the rest of the board dealt at once — is a rare event; a few dozen a month is a lot. Reaching a thousand of them is measured in months, or a year.
So what this game actually tests is not “did you win tonight”. It is whether you can put the money in on the right side of the odds, over and over, on incomplete information, and sit through the stretches that look like the game is mocking you. The maths does show up in the end. It does not show up tonight.
Back to the question in the title: luck and variance do not add up to pure chance. The line falls on two things — whether you can work out your chance of winning before you bet, and whether you then act on that number. Neither exists at a roulette table. Both exist in Hold’em.
(What the law makes of it is judged by an entirely different standard, one that turns on statutes and rulings. This article does not go there; that is a separate one.)
Read this next: the legal side is is Texas Hold’em legal in Taiwan — what the courts weigh is not whether the game takes skill but three concrete facts, and they have not converged on an answer yet.
For where these numbers come from in the structure of the game, see why Texas Hold’em is fun; if the rules are still shaky, start from what Texas Hold’em is.