Measuring the duel instead of arguing about it
I could not win the poker duel against Country, so I filed a difficulty bug. A simulation of 3000 duels per cell showed the win rate tracks chip share almost exactly, so the right change to the numbers was none.
Written up later from the repo's history and dated to the days it describes.
On August 21 I played the desperate version of The Lien's Country duel several times and could not win it. I filed it as issue #120. The write-up showed the math and made an argument, and it ended by asking for exactly the right first step, which was to simulate the matchup before moving anything.
What the duel is
In the duel, your stack is your health. Country sits down with a fixed 75 chips, and the game does not scale that to you. Arriving at full health is 75 against 75, and a hard run in the desperate scenario is 30 against 75, with a floor of 12. A tier rule also moves her play with her own stack, so she plays loose and exploitable when she is flush and plays her best poker in the last quarter of her chips.
That last rule was the heart of the complaint. It meant she played boss-tier poker exactly when I was closest to winning, which sounds like a rule built to take wins away.
What 3000 duels say
A duel is gambler's ruin. I ran 3000 duels per cell with both seats driven by the real opponent code and her tier recomputed on every decision. The win rate for the player came out as their share of the chips and almost nothing else.
| Stacks | Chip share | Player wins | Hands |
|---|---|---|---|
| 75 v 75 | 50.0% | 49.9% | 40 |
| 30 v 75 | 28.6% | 30.2% | 29 |
| 12 v 75 | 13.8% | 14.8% | 18 |
I then crossed three player profiles with four house configurations at three stack sizes. Every cell landed within about three points of chip share. Chip share moved the result by 21 points, and everything else combined moved it by about four. The desperate scenario is a 30% proposition, not a broken one, and losing four in a row at 30% happens about a quarter of the time.
The tier argument was backwards. Against a flat Elite opponent the rule is worth 2.6, 3.6 and 2.0 points to the player, because the same rule hands her the loose, exploitable profile for the whole first quarter of her stack. That phase is longer and richer than the last one. The reasoning is recorded next to the rule in the code, because it is a good argument and someone will make it again.
So I changed no constant. The real content of the issue is that the duel has no skill term to tune around. Moving her starting stack does not adjust a difficulty curve, it sets a win rate directly, which makes the next step a design call and not a tuning one.
The harness stayed
An identical simulator had been written on August 21 to settle a different question, which was how large the ante should be. It found that win rate stayed flat from an ante of 2 to an ante of 15, at 29.6% for an ante of 2 and 27.5% for an ante of 10. The ante controls how long you sit there. Hands per duel went from 40.7 at an ante of 2 to 14.9 at 6 and 8.8 at 10. That result went into the code as a comment, and the harness was thrown away.
Issue #120 asked the same class of question a few days later and paid for it again. This time the simulator is committed. It is pure code with no engine dependency and compiles only in debug builds. A test of about eight seconds pins three things: win rate tracks chip share, the tier rule is not a punishment, and, as a deliberate tripwire, chips still dominate play. The last assertion will fail the day the poker becomes skill-expressive. That would be good news with the wrong shape of test, so its failure message says to reread issue #120 instead of loosening it.
What is left
The question underneath is still open. A duel that is always a weighted coinflip is a legitimate design, and so is one where skill matters, and the simulation cannot say which one The Lien wants. It only says that nudging a number is not how to get there.