Mixing
Why not always bet the queen?
The middle card can use two plans
The situation
You act first
No betting yet
- Pot now
- 2
- Cost to continue
- 0
The short answer
Checking and betting finish almost even, so this strategy keeps both choices available.
The saved strategy
How often it uses each choice
Choose an action to inspect what happens next.
These are approximate frequencies from the saved solution. A higher percentage does not turn a close choice into the only correct choice.
Why
Follow the evidence
- Before anyone acts, the opponent has a jack 40% of the time, a queen 20%, and a king 40%.
- Across every possible public card and later choice, the two plans are only 0.0015 chips apart.
- The saved strategy checks 48% of the time and bets 52%. These percentages are approximate, but the near-tie is the useful lesson.
Opponent's possible card
Actions change the range
These chances use only what you can know: your card, the public card, and the actions so far.
After choosing Check
How the hand ends
After this choice, both players return to the saved strategy.
- Expected chip change from now
- +0.865
- Whole-hand result, including chips already paid
- -0.135
Exactly what these numbers mean
An action value is the average result if this situation repeats, you choose that action once, and then both players follow the saved strategy. It is not a promise about one hand.
“From now” leaves chips already paid in the past. “Whole hand” counts the ante and every earlier bet. The difference between two actions is the same either way.
This is Leduc poker, a two-player teaching game. Its percentages do not transfer directly to a normal hold'em table.