Definition
A mixed strategy is when a player takes different actions with the same hand at certain frequencies. Instead of "always bet" or "always check," it's "bet 60%, check 40%."
Mixed Strategy = Randomizing between actions with the same hand
Pure vs Mixed Strategies
| Pure Strategy | Mixed Strategy |
|---|---|
| One action, 100% | Multiple actions at frequencies |
| AA = always raise | J9s = bet 55%, check 45% |
| Deterministic | Randomized |
Why Mix Strategies?
The Indifference Principle
When two actions have the same EV, you're indifferent:
| Situation | Logic |
|---|---|
| Bet EV = Check EV | Either is equally good |
| Mixing | Prevents exploitation |
| Opponent can't adjust | You're unpredictable |
Example
Hand: K♠ Q♠ on A♥ T♣ 7♠ 5♦
Bet: Makes weaker hands fold, charged for draws Check: Pot control, showdown value
If both are equally profitable, mix them to stay balanced.
When Mixing Occurs
| Scenario | Why Mixed |
|---|---|
| Borderline hands | Close between actions |
| Multiple sizing options | Different sizes similar EV |
| Defense decisions | Some hands borderline call/fold |
How Solvers Show Mixing
K♠Q♠:
Bet 75%: 45%
Bet 33%: 20%
Check: 35%
This means with K♠Q♠, you should:
- Bet 75% pot 45% of the time
- Bet 33% pot 20% of the time
- Check 35% of the time
Practical Mixing Approaches
In-Game Randomization
| Method | How |
|---|---|
| Clock second | 0-5 = action A, 6-9 = action B |
| RNG app | Use random number generator |
| Card memory | Remember last card dealt |
Simplification
| Approach | Trade-off |
|---|---|
| Pick one action | Slightly exploitable |
| Round frequencies | 60% → always, 30% → never |
| Split by combo | AhKh bet, AsKs check |
When Not to Mix
| Situation | Just Pick One |
|---|---|
| Significant EV difference | Clear best action |
| Exploiting opponents | Deviation from GTO |
| Difficult to implement | Simplify |
Common Mistakes
| Mistake | Problem |
|---|---|
| Never mixing | Predictable, exploitable |
| Random guessing | Not strategic |
| Overcomplicating | Can't execute in-game |
| Ignoring mixes | Missing balanced play |
Key Takeaway
Mixed strategies arise when actions have similar EV. Mixing prevents opponents from exploiting your patterns. In practice, simplify where possible, but understand why solvers mix to appreciate balanced play.