Frequencies & mixed strategies: why solvers play a hand two ways

A solver doesn't fold AJo from under the gun *every* time and open it *every* time — it might open it 35% of the time and fold it the other 65%. That's a mixed strategy, and the number is a frequency.

Why would a perfect player flip a coin? Because at the edge of a range a hand is roughly indifferent: the EV of opening and the EV of folding are almost identical. When two options are worth the same, *any* mix between them is fine — and mixing makes you impossible to read. If you always opened exactly the hands a solver opens half the time, an observant opponent could pattern you for free.

The key word is *indifferent*. A mixed hand is one the math can't separate. That's completely different from a clear mistake, where one option is plainly better than the other.

A simple chart shows a hand as in or out — open or fold. That's a useful simplification, but the real picture is a *band* of mixed hands around the frontier. Deep inside the range you open almost always; just outside it you fold almost always; right on the line it's blurry.

This is exactly why the Range Builder shades the boundary cells a lighter green — those are the mix-it-up hands. And it's why the in-game coach tags some opens *"a close, mixed-frequency spot — strong players play it both ways."* Being a single hand off at the edge costs almost nothing, because those hands were nearly indifferent to begin with.

Here's the liberating part: you don't have to mix. Pick the simpler pure choice on a boundary hand and you give up a tiny fraction of a big blind. Across a session it's noise.

The mistakes that actually cost you chips are core errors, not edge frequencies:

• Folding a hand that's a *clear* open, deep inside the range.
• Calling a raise with a hand that's a *clear* fold.
• Stationing off your stack postflop — or never bluffing at all.

That's why this trainer weights your leaks by EV lost: it surfaces the expensive, obvious mistakes first and waves you past the close ones. Spend your attention where the chips actually are.

Frequencies start to matter when:

• Your opponent is strong and observant. Against good regs a purely predictable strategy gets exploited; varying your edge plays keeps you balanced. The bots here adapt to *your* tendencies, so don't show them the same pure pattern every hand.
• The pot is big or the stakes are high. A fraction of a BB at the edge adds up fast when you're playing for a pay jump.
• You're building a study habit. Knowing *which* hands are mixes tells you where the genuinely close decisions live — and where it's safe to simplify.

For most spots, most of the time: play the clear hands clearly, simplify the edge, and never let a "wrong" on a 55/45 hand dent your confidence.