Probability: judge decisions, not results

Pot odds, equity against a range, and judging decisions, not results.

You call a river bet, they show a better hand, you lose the pot. Was the call a mistake? Not necessarily. Poker has luck in every hand, so the result of one hand tells you very little. What you control is the decision, and that's what the app scores.

In short

• Judge the decision, not the result.
• Required equity is what you call ÷ the pot after you call.
• Equity is how often you win against their whole range, not one hand.
• Your read only needs to be close enough to get the decision right.
• The app flags only clear mistakes, never close spots.

A good call can lose, a bad call can win

Imagine a bet where calling wins 40% of the time and you only need to win 25% to break even. Calling is right, and you'll still lose 6 times out of 10. Now imagine a bet where you need 33% but win only 13% of the time. Calling is a mistake, and you'll still win about 1 time in 8.

If you judge yourself by results, you learn the wrong lessons from both. Judge the decision: given what you could know, was it the right play?

Pot odds: what you need to win

When they bet, the pot is offering you a price. Required equity is how often you need to win for a call to break even:

what you have to call ÷ the total pot after you call

Worked example: the pot is 10 and they bet 5. The pot is now 15, and you have to put in 5. After you call, the pot is 20. So you need 5 ÷ 20 = 25%. Win more than a quarter of the time and calling makes money in the long run.

Bigger bets ask for more:

Equity against a range, not a hand

Equity is how often your hand wins (counting a tie as half). The question is never "what do I have against their hand?" because you can't see their hand. It's "what do I have against every hand they'd play this way?" That's their range.

On the river it's simple: your equity is the share of their combos you beat. On the flop and turn, the app also counts every card that could still come.

Say they bet the size of the pot (10 into 10), and their range here is:

• AQ: 8 combos (you beat none)
• 99 and 44, sets: 3 combos each (you beat none)
• KTs, T8s and 53s, missed straight draws: 4 combos each (you beat all 12)

That's 26 combos, and you beat 12 of them: 46% equity. A pot-sized bet needs 33%, so calling is right. You'll lose this pot more often than you win it, and the call still makes money over time.

Now change their range: add Q9 (6 combos) and 77 and 22 (3 each), and drop KTs and 53s. Now they have 30 combos and you beat only the 4 combos of T8s: 13% equity. Calling is now a clear mistake, even on the nights they turn over T8s and you win.

Same cards, same bet, different range, different answer. That's why reading the range comes first.

Your read doesn't have to be perfect

No read is exact, and it doesn't need to be. What decides a call is the share of their range you beat, and a read that's mostly right usually gives the same answer as a perfect one.

Take the first river above: you beat 12 of their 26 combos (46%) and needed 33%.

• Your read left out the 3 combos of 44. You'd count 12 of 23: 52%. Still a call.
• Your read added 3 combos of 77 they don't have. You'd count 12 of 29: 41%. Still a call.

Small misses only cost you in close spots, and close spots cost little either way. A read goes wrong in a way that matters when it misses a whole part of their range: every missed draw, say, or the fact that their check means no top pair. That's why the reveal is worth studying: it shows which part you missed, not just how many combos.

And you're not the only one making mistakes. The villains' leaks (calling too much, folding too much, bluffing too often) are big, and they repeat every hand. You win as long as your mistakes are smaller than theirs, and a rough read that catches their habit is enough for that.

How the app scores your decisions

Because the villain plays by known rules, the app knows their real range at every moment. After each call or fold it works out your exact equity against that range and compares it with the equity you needed.

• Calls and folds get a verdict: Clear mistake, or Fine.
• Bets, raises and checks show their numbers, but get no verdict yet.

The rule, as the app puts it: A clear mistake is calling with less than half the equity you needed, or folding with more than double it. Close spots never count.

With a pot-sized bet you need 33%:

• Calling with less than about 17% (half of 33%) is a clear mistake.
• Folding with more than about 67% (double 33%) is a clear mistake.
• Anything in between is never marked a mistake, whichever you choose.

So in the first example above, folding with 46% isn't marked a mistake, even though calling was better. The app only flags the spots that are clearly wrong, not the close ones.

The Math setting decides how much you see afterward. Off shows only the verdict. Equity adds your equity against their range and what you needed. Odds + EV adds the expected value of each choice and how their range would respond. On the flop and turn, EV counts only this street, so it's marked approximate. Your calls and folds are scored the same way whichever you pick.

Variance: why the short run lies

Variance is the gap between what should happen on average and what actually happens over a few hands. Flip a coin ten times and you might get seven heads. That doesn't make it a bad coin.

Poker is the same. A 46% call loses more often than it wins, and you can lose it four times in a row without doing anything wrong. Over hundreds of hands, the good decisions add up and the luck evens out. That's why the stats screen counts your clear mistakes, not how many pots you won.

Try it

When they bet, before you act, ask three questions:

• What do I need? Bet size against the pot gives you the required equity.
• What's in their range? Roughly how many combos of value, how many draws and bluffs.
• How much of it do I beat? That's your equity.

If you have more than you need, call. If you have much less, fold. Then let the result go, and look at the verdict instead.