Definition
Poker solvers find game-theory optimal (GTO) strategies that can't be exploited. Often, these strategies involve mixing—taking different actions with the same hand at certain frequencies.
The Core Reason: Indifference
Solvers mix when:
Two or more actions have identical expected value
| If... | Then... |
|---|---|
| Bet EV > Check EV | Always bet |
| Bet EV = Check EV | Mix betting and checking |
| Bet EV < Check EV | Always check |
Why Equal EV Happens
Equilibrium Logic
In Nash equilibrium:
- If one action were clearly better, everyone would take it
- Opponent adjusts, making the action worse
- Eventually, actions reach equal EV
- Mixing is the stable solution
Example
If you always bet bluffs on the river:
- Opponent always calls (because you never check bluffs)
- Your bluffs become -EV
If you never bet bluffs:
- Opponent always folds (because you only bet value)
- You should bluff more
Equilibrium:
- Mix bluffs at a frequency that makes opponent indifferent to calling
What Mixing Achieves
| Goal | How Mixing Helps |
|---|---|
| Balance | Range isn't obvious |
| Unexploitable | Opponent can't adjust |
| Protection | Checking range has strength |
| Flexibility | Multiple viable lines |
Reading Solver Output
Example Output
A♥K♥ on Q♣T♠ 5♦:
Bet 75%: 62%
Bet 33%: 15%
Check: 23%
Interpretation:
- This hand mixes between three actions
- Big bet most frequent (maybe value + draws)
- Sometimes small bet or check (deception/balance)
Why Specific Hands Mix
| Hand Type | Why It Mixes |
|---|---|
| Borderline value | Could bet thin or check |
| Medium draws | Semi-bluff or check |
| Pairs with SDV | Bet for protection or pot control |
| Bluff candidates | Need correct frequency |
Simplifying Solver Mixes
For Practical Play
| Solver Says | Practical Approach |
|---|---|
| 70%+ one action | Just do that action |
| 50/50 split | Pick one, stay consistent |
| Complex 3-way mix | Simplify to primary action |
When to Respect Mixes
| Situation | Importance |
|---|---|
| High-stakes | More important |
| Tough opponents | They'll exploit patterns |
| Key spots | River decisions matter |
Common Misconceptions
| Misconception | Reality |
|---|---|
| "I must mix perfectly" | Close is good enough |
| "Mixing is always better" | Clear actions don't need mixing |
| "Ignore mixes entirely" | Understanding helps study |
Key Takeaway
Solvers mix because multiple actions have equal EV at equilibrium. This creates balanced, unexploitable play. In practice, simplify mixes but understand the logic—it reveals when hands are borderline and helps you think in ranges.