Level three
The maths that decides how much to bet, the parts of the game no amount of good play protects you from, and where every model on this site stops being true.
Even a genuinely winning player loses often. Swings of thirty or forty big blinds in a session are ordinary, and losing months happen to good players at small stakes. This is not a sign that anything is wrong, and reacting to it is how people turn a small edge into a loss.
A winning player, over eighty sessions. The edge is real and the line still spends a long stretch below where it started. This is normal, and reacting to it is how a small edge turns into a loss.
The practical version is bankroll. The bigger your edge and the calmer your game, the less you need behind you. As a rule of thumb, twenty to thirty buy-ins for a cash game means a bad run is uncomfortable rather than fatal.
The house takes a cut of most pots. Typically a few per cent up to a cap, and almost always with "no flop, no drop", meaning nothing is taken from a hand that ends before the flop.
Two consequences follow. First, the price you need to call is slightly worse than raw pot odds suggest, because winning does not pay you the whole pot. Second, stealing the blinds before the flop is worth more than it looks, because that pot is not raked.
Rake is the main reason a break-even player is a losing player. At small stakes it can be several big blinds per hundred hands, which is larger than many players' entire edge.
A bet of any size is a threat that has to be answered. Work out the answer and the right size falls out of it.
Say you bet 10 into a pot of 10. You are risking 10 to win 10, so if they fold more than half the time the bet is free money whatever you hold. To stop that being true they have to keep playing at least half of their hands. Bet a quarter of the pot and you risk 2.5 to win 10, so they have to keep playing 80% of it. The rule is short:
That is the trade. A bigger bet wins more when it is called and folds out more of the hands that were going to pay you. Somewhere between those two the money is highest, and it is usually not at either end. The table on the play page works this out for every size, and the peak is often in the middle:
| Size | They fold | Worth |
|---|---|---|
| a quarter pot | 0% | +0.22 |
| half pot | 0% | +0.28 |
| three quarter pot | 1% | +0.19 |
| pot | 3% | −0.06 |
Two warnings come with it. That defence figure is a floor: it is the least they can get away with folding, not a description of anybody real. Most people defend a big bet with more than the minimum, which is why the biggest size is rarely right at a real table. And it assumes nobody raises, which they will.
Everything so far describes an opponent who responds correctly. Almost nobody does, and the money is in the gap between the two.
Against someone who folds too much, bet more often and size does not much matter, because you are being paid by the folds rather than the calls. Against someone who calls too much, stop bluffing entirely and bet your good hands larger than the model says, because every extra chip goes in against a hand that was never folding. These are opposite adjustments and they are both large. Getting the read right is worth more than getting the size right.
This is also the honest limit of every figure on this site. The equity is measured, the price is arithmetic, and both are exact. The range they are put on is a guess, and everything downstream inherits it. A confident number computed against the wrong range is still the wrong number, which is why the table tells you which read it used.
The practical order never changes: watch what they do and how often, decide what they could hold, then price your decision against that. Skipping the first two steps and going straight to the arithmetic is how people end up distrusting arithmetic.
A bluff is not a mood. It is a bet with a break-even point, and the point is set by the size exactly the way a call's is.
A bluff of a given size risks that much to win the pot, so it has to work bet ÷ (pot + bet) of the time. Bet bigger and it has to work more often, which is why a huge bluff is a worse bluff, not a scarier one.
So a pot-sized bluff has to get through half the time. Ask yourself honestly whether the hands they can hold fold that often, and most of the time the answer is no. This is why a huge bluff is usually a worse bluff rather than a braver one: the bigger it is, the more often it has to succeed and the more suspicious it looks.
The bluffs that work are the ones where the story fits. A bet that represents a hand you could actually have, on a board where that hand is plausible, against somebody who can fold: the size is the last part of it and the smallest.
The largest single decision in poker is who you sit down with, and it is made before a card is dealt. A modest player at a soft table makes more than a good one at a hard table, every time, and no amount of study closes that gap.
This is why the opponents here are configurable rather than fixed. Practising against experts teaches you to survive against experts, which is worth something, but if the game you actually play is five casual players then a table of five casual players is the one to practise against. Set the seats to the game you are in.
The most expensive leak is not technical. It is playing on after the point where you have stopped making decisions and started reacting to them.
It follows from variance. If a winning player can lose for twenty sessions, then losing today tells you almost nothing, and the instinct to win it back is an instinct to play worse at exactly the moment you can least afford to. The hands you play to get even are the hands you would fold on any other day.
The session report separates how you played from how you ran for this reason. A losing session where the coach graded every decision correct is a good session, and reading it that way is the habit that keeps a bad hour from becoming a bad month.