Big Two · Dai Di · Deuces
Most card games just beat you. This one tells you why. Turn on the advisor and every legal move in your hand is ranked by how often it wins, what it's worth, and what can still beat it — so a game you lose is a game you learn something from.
Free · 2, 3 or 4 players · scored across deals to 100
median in-browser, 14 ms at the 95th percentile
32.7 M for the 4-player network, 35.5 M for the 3-player one
win probability, expected score, and the reasoning
against the odds bot, where an even table is 33.3%
What you get
Full Big Two for 2, 3 or 4 players, scored across deals to 100 points. The awkward rules are all in: the A-2-3-4-5 straight ranks lowest, suits break ties, the 3♦ opens the first deal, two players draw from a pile when they pass, and three players set one card aside face-up.
Start a gameOpen the panel mid-game and every move you could make is listed with its win rate, its expected points and how many turns you'd have left. It names the cards that still beat you — and when nothing can, it says so outright instead of guessing.
Analyse a positionPut two combinations side by side and it tells you which one wins and which rule decided it — the arguments people actually have, like whether A-2-3-4-5 is the top straight or the bottom one, and which suit takes a tied flush.
Compare two handsUnder the hood
You choose who you sit down against. One reasons about the cards; the other has a feel for them. They pick different moves often enough that watching them argue is half the fun.
It works out which cards are still unseen, then asks what they could do to you. For a single card the answer is exact — a closed-form probability over the remaining deck, not a guess — and it can sometimes prove a play is unbeatable, or that your whole hand can be run out without ever losing the lead. Everything else it settles by playing the position out thousands of times.
This is the engine behind the advisor, which is why the advisor can show you a probability rather than an opinion.
A network trained the way DouZero learned Dou Dizhu: play yourself millions of times, remember what each position turned out to be worth, and learn to predict it. At the table it calculates nothing — it looks at every legal move at once and picks the one that feels best, in about 3 ms.
Its published win rates come from evaluations against a deliberately cheap version of the odds bot, so read them as training progress rather than a claim that it dominates.
Why two players is different
At a two-player table the neural option is switched off and you play the odds bot instead. The network was trained for 3–4 players, and heads-up Big Two is a different game: the other 26 cards form a draw pile, passing costs you a card, and the loser doesn't go negative. The 2-player network that exists loses to the odds bot, so it isn't shipped — and the option is greyed out with a reason rather than quietly swapped behind your back.
How it learned
There is no book of good Big Two moves to copy, so the network was never shown one. It was made to play itself, told only who won and by how much, and left to work out the rest — the same recipe DouZero used for Dou Dizhu, called Deep Monte-Carlo. Two runs, one for the 3-player table and one for the 4-player table, 6 hours each on a single machine.
01
Each round it deals 512 fresh games and plays them out. Its opponents are its own earlier selves — a pool of 6 past versions — so it can't win by exploiting one fixed rival. One move in 10 is picked at random, which is what stops it settling into a rut and never trying anything else.
02
Nothing is judged while the deal is running. When it ends, every move made along the way is labelled with what the deal was actually worth to the player who made it — cards left over, doubled and tripled as the rules say. No guessing at the value of a position from another guess: the label is the real result.
03
Those labelled moves go into a buffer of the last 500,000, and the network is trained to predict the score from the position and the move alone. That is the whole trick — at the table it runs no simulations. It scores every legal move at once and plays the highest.
Every 10,000 rounds the run stopped and played 800 deals in seat 1 against a cheap version of the odds bot. Above the dashed line it is winning more than its share of the table.
training rounds
| Round | 3-player run | 4-player run |
|---|---|---|
| 10,000 | 51.9% | 38.2% |
| 20,000 | 56.6% | 42.8% |
| 30,000 | 56% | 43% |
| 40,000 | 56.9% | 39.6% |
| 50,000 | 57.1% | 43.9% |
| 60,000 | 59% | 43.5% |
| 70,000 | 57% | 44.6% |
| 80,000 | 61.3% | 47.1% |
| 90,000 | 58.1% | 43.6% |
| 100,000 | 58.2% | 44.8% |
| 110,000 | 58.1% | 44.4% |
Median training error per 700 rounds; the band is the best and worst in that stretch. Every point is from the 3-player run's own per-round log.
training rounds
Why up is not broken. It is not fitting a fixed answer sheet. As it improves, its opponents improve with it and the deals get sharper, so the thing it is trying to predict keeps getting harder. Error climbing from 0.047 to 0.155 while the win rate climbs too is the shape a healthy run of this kind has; what would worry you is error falling while the win rate flattens.
Both runs used the same network and the same settings; only the table size changed.
| Measure | 3 players | 4 players |
|---|---|---|
| Deals played | 35.5 M | 32.7 M |
| Wall clock | 6 h | 6 h |
| Deals per second | 1,756 | 1,611 |
| Best deal-win | 61.3% | 47.1% |
| An even table would be | 33.3% | 25% |
| Error at the end | 0.1548 | 0.2135 |
One caveat, stated rather than hidden: only the 3-player run's per-round log survived, so the error chart is that run alone. The 4-player figures are the eleven evaluations its console log printed. Both runs' logs are in the repository if you want to read them.
Why the numbers are worth trusting
An advisor is only useful if it is right. All of this began as a Python project, and none of that could ship to a browser — so it was rewritten in TypeScript and WebAssembly, then held against the original: the Python code dumps a record of what it actually does, and the browser engine has to reproduce it.
Recorded games for 2, 3 and 4 players — including one run 102 deals to the 100-point finish — play out identically in the browser.
300 complete games checked on every single turn: cards conserved, moves legal, scoring correct. No illegal state was ever reached.
The single-card beat probability uses exact integer arithmetic and matches the original to twelve decimal places.
154 tests cover the rules engine, including the corners people argue about — the low-ace straight, flush tiebreaks and same-size-only beats.
Every weight round-trips bit for bit, and the move it picks in the browser is the move PyTorch picks.
The rollout kernel is the original C source compiled to WebAssembly, so the bot in your tab runs the code that was benchmarked, not a re-interpretation.
All of it is open source — read the engine, the training pipeline and the test suite
Questions
Pick a table size and an opponent. It takes about ten seconds, and you can leave the advisor open the whole time.
