Variance, bankroll and judging decisions

On this page

• Judge a decision by its expected value, not by how the hand ended.
• Work out all-in EV and compare it with the money you actually won.
• Explain why a small sample says little about your real win rate.
• Set bankroll and stop-loss rules you will keep to.
• Recognise tilt as a rise in mistakes after big losses.

Concepts used: EV, EV loss and how Rail grades, Pot odds

Results are decisions plus luck

Every result mixes two things: the quality of your decisions and the cards that came. Over one session, the cards win easily. A good call can lose and a bad one can win, and how the hand ended says nothing about which it was.

All-in EV: the result you earned

When the money goes in before the river, you can measure what the decision earned instead of what the cards did. The EV of the call is your equity times the final pot, minus what you put in.

Say there is 10 bb in the middle and your opponent shoves 40 bb more, so the pot is 50 bb and the call is 40 bb. If you call, the final pot is 90 bb. With 50% equity the call is worth 0.5 × 90 − 40 = 45 − 40 = +5 bb, whether you win this particular hand or not. It needs 40 / 90, about 44.4%, to break even.

Rail's stats graph has an all-in EV line: your results with every all-in runout paid at equity. When it sits well above your real results, you ran badly in those pots; the decisions were fine.

How long luck lasts

Results settle down slowly. A few thousand hands can swing a long way up or down for a player of any skill, and even much larger samples leave plenty of room for luck.

Your EV loss per 100 hands settles much faster, because it does not depend on which cards came. It compares each decision with the alternatives in that same spot, and a hand usually holds several decisions. That makes it Rail's best signal of how well you are playing.

Bankroll and stop-loss: rules you set

Swings are normal, so decide in advance how you will handle them, while you are calm. These are personal rules, and only you can set the numbers.

• Keep the money you play with separate, and only use money you can afford to lose.
• Play stakes where a normal losing stretch does not change how you play. If a loss makes you play scared, the stake is too high for you right now.
• Pick a stop-loss for a session, in buy-ins or big blinds, and stop when you reach it, however the session feels.
• Decide when you move stakes up or down before the swing comes, not during it.

Tilt shows in the numbers

Tilt is not just anger: it is your decisions getting worse after something goes wrong. That makes it measurable. Your progress page can split EV loss by session, and the sessions after a big losing hand are the ones to compare.

If your EV loss per 100 jumps after big losses, that is the clearest case for a stop-loss rule. The cards are out of your control; how you play the next hand is not.

Rules of thumb

• Judge a decision by its EV at the moment you made it, never by how the hand ended.
• The EV of calling an all-in is equity × final pot − call.
• EV loss per 100 hands is a faster, steadier signal of skill than results.
• Set your bankroll and stop-loss rules before a session, not during a swing.

When they break

• All-in EV only removes luck from all-in pots; luck in hands that end in a fold or reach showdown without an all-in stays in your results.
• EV loss compares you with a reference, so a profitable exploit can raise it while your results improve.