The EV curve against variance
What the yellow EV (chips) curve really takes out of variance, and what it still leaves in.
Gandalf
Co-founder of Poker Sciences
In the chapter The Chips curve (CEV), you learned how to read the yellow EV (chips) curve: the one that neutralizes all-in luck, and that acts as the ultimate judge of whether you're a winning player at your stake.
This chapter picks up that same curve from another angle: variance. No longer "how to read it", but how far to trust it.
Because plenty of players run into the same paradox: their yellow curve is going down, even though they feel like they're playing well, and even though that curve is precisely the one that's supposed to have taken luck out.
We'll answer this question in particular:
Why is it sometimes negative on a small sample of Spins, even for winning players?
To answer it, this chapter breaks down the sources of variance the yellow curve cannot neutralize, and gives you a ballpark for what's normal on a small sample.
If variance, CEV or sample percentiles are new concepts to you, start with the Variance in Spin & Go chapter of our free course. This chapter is its logical follow-up, on the Poker Spin Tracker side.
On forums and in other trackers, the yellow curve usually goes by "chips adjusted" (or "all-in adjusted"). That is exactly what Poker Spin Tracker calls the EV (chips) curve: a chip curve with all-in variance taken out.
1. A reminder: what the yellow curve neutralizes
You saw it in the chapter The Chips curve (CEV): on every all-in, the yellow EV (chips) curve replaces the actual result with the mathematical expectation of the hand (your equity multiplied by the pot).
Example. You go all-in with AKs against QQ at equal stacks, and your equity is around 46%. Two possibilities:
- you lose the flip: the green curve drops by the stack you lost ↓
- you win the flip: the green curve rises by the opponent's stack you won ↑
In both cases, the yellow curve only moves by the expectation of the spot (46% of the opponent's stack, minus 54% of your own). That number is the same whether you won or lost the flip.
On every all-in, the yellow curve always records the expectation of the spot, never its actual result. That's what makes it immune to all-in luck.
It's powerful, but it's also everything the yellow curve does. It neutralizes all-in variance, and only all-in variance.
The gap between the green curve and the yellow curve (precisely that all-in luck the yellow curve neutralizes) is in fact quantified automatically on the Dashboard by the Run Luck Badge. We'll come back to it later in this module.
2. The three variances it leaves intact
On a small sample, three sources of variance keep pushing your yellow curve around. The tracker can do nothing about it: these variances can't be corrected with a formula.
2.a The cards you're dealt
You don't get every hand at the same frequency, and on a small sample, that frequency sometimes drifts a long way from its theoretical average.
A pair of AA comes up on average once every 221 hands. Over 500 Spins (roughly 6,000 hands), you should be dealt around thirty of them. In practice, on that same sample a "lucky" run and an "unlucky" one can differ by a factor of two: 18 on one side, 36 on the other.
Multiply that gap by every playable hand, by every position, and by every opponent profile you run into: genuinely favorable combinations (strong hand + good position + weak opponent) thin out even faster than hands taken in isolation. The yellow curve has no way to invent EV on spots that never happened.
The yellow curve captures the EV of the spots you did play. It doesn't correct for the fact that the favorable (or unfavorable) spots never came up.
2.b The all-in confrontations
The yellow curve neutralizes the outcome of the flip, but not which hand you end up all-in against. You shove A8 in a spot where your opponents are supposed to fold most of the time, and call with a range you dominate (weaker Aces, Kx, suited connectors, and so on). The bad luck is when they call anyway with AT+: you're dominated. Over 300 games, those calls with the top of their range can turn up more often than their theoretical distribution predicts.
The yellow curve records your actual equity against their actual hand. If your confrontations have gone against you, it drops, even though your decision to shove was +EV against their theoretical range.
The yellow curve neutralizes the luck at showdown, not the luck of the ranges you run into.
2.c The spots that do not go all-in
The yellow curve only corrects all-ins. Everything that gets decided without going all-in stays in the curve, exactly as it happened:
- a 3bet that gets a fold vs a 3bet that gets a call: the result depends on the opponent
- a river call that pays off or doesn't
- a bluff that goes through or gets picked off
In Spins, most big pots go all-in before the river, so this source is less brutal than in cash games. But it's there: the deeper the effective stack, the more non-all-in decisions pile up, and the more their variance shows on the yellow curve.
The yellow curve is blind to everything that gets decided before the chips go in the middle.
When your yellow curve starts sliding, the question gnawing at you is always the same: is a leak creeping into my game, or is this one of those three sources of variance the yellow curve can't neutralize?
The only honest way to settle it is to look at the 90% confidence interval from the chapter The Chips curve. It alone lets you judge how close your CEV in Poker Spin Tracker is to your true skill level.
Key takeaways
The yellow curve is the most powerful tool on the Dashboard for judging your level, but it's not infallible. It only neutralizes the outcome of all-ins, and three other sources of variance keep moving it for as long as your sample isn't big enough.
The only honest way to settle it remains the 90% confidence interval, covered in The Chips curve (CEV).
