Daily Brains · one Pot-Limit Omaha hand a day. Four cards, exactly two of them, pot-limit bets: price every call and play it the way the maths says.
Daily PLO is the Omaha puzzle in Daily Brains (/daily), the four-card sister of Massachusetts Hold'em. Every day everyone is dealt the same Pot-Limit Omaha hand at a deep, six-handed penthouse table and plays it against one opponent whose range of possible hands is defined in advance. You make every decision, street by street: fold, call or raise the pot when they bet; check, bet half the pot or bet the pot when they check; fold or call when they re-raise. You can also guess your equity on each street. A real Omaha evaluator grades every play by expected value against their range and explains the right answer. It is a decision puzzle played with play money only: there is no wagering of any kind.
STORY & LORE
The room
A penthouse game above the city, late: sapphire felt in a black leather rail with a platinum trim, ivory cards in a four-colour deck (spades black, hearts red, diamonds blue, clubs green, because in Omaha you read suits all night), oxblood card backs. Everyone sits with 200 big blinds. Five regulars, all MeWows drawn by the site's own avatar maker, rotate through the seat opposite you: Nora from Norfolk (the nut peddler), Lyle from Lincoln (tight), Kay from Kearney (calls everything), The Baron from Bellevue (balanced) and Pot-Limit Pat from North Platte (pots every street). Everyone else folds; it is always you against one of them.
Why Omaha plays differently
Each player holds four cards, so there are six two-card combinations in every hand and the equities run much closer than in Hold'em: AAKK double-suited, the best starting hand, is only about a 71% favourite against a random hand (Hold'em aces: 85%). Draws are often favourites, a flush that is not the nut flush is a liability, and the cards you hold change what your opponent can have. Hold the ace of a suit and they can never have the nut flush in it: that is a blocker. Bets are pot-limit, so the most you can raise is the pot after you call.
The check-down maths
Real poker EV depends on every future street. To keep each decision a clean puzzle the game scores each play as if the hand checks down from that point, so your equity already counts every redraw. It is the same simplification every pot-odds lesson uses, and it is stated in the rules and in every breakdown.
CHARACTERS & ENEMIES
Norafrom Norfolk · Nut peddlerVILLAINOnly bets when she has close to the nuts. Never bluffs. Folds the rest the moment you push back.
Lylefrom Lincoln · TightVILLAINPlays solid hands, bets the good ones, rarely bluffs, gives up on bad turns.
Kayfrom Kearney · Calls everythingVILLAINHates folding a draw. Small bets, few bluffs, and she will see the river.
The Baronfrom Bellevue · BalancedVILLAINBets value, semi-bluffs his draws, bluffs in sensible doses and defends by the book.
Pot-Limit Patfrom North Platte · Pots every streetVILLAINOpens wide, bets the pot with anything, bluffs a lot and calls a little too much.
HOW IT PLAYS
Exactly two, exactly three
Your five-card hand is always exactly two of your four hole cards plus exactly three of the five board cards. Four hearts on the board and one in your hand is not a flush; a straight on the board does not play for you; three aces in your hand count as one pair of aces. The evaluator applies the rule as written, the best of all 60 combinations on the river, and the test suite checks it against a naive best-of-60 on 200,000 random deals and on the classic traps.
A day's hand
The hand is generated from the puzzle number, so it is the same for every player. Preflop you face a pot-sized raise: an open from an earlier seat, a small-blind raise while you are in the big blind, or (Thursday on) a pot 3-bet after you open. After the flop the opponent always acts first and you close the action. You make every decision; the hand ends early only if someone folds or the chips are all in.
Your options
Facing a bet: fold, call, or raise the pot (to their bet + the pot after you call, capped at all-in). Facing a check: check, bet half the pot, or bet the pot. If they re-raise the pot over your raise, the call-or-fold is your own next decision on the same street, priced and graded like any other (no equity guess). Keys 1 to 4 pick an option and the arrow keys nudge the equity slider.
How the opponent plays
Their range is a fixed sample of 1,100 concrete four-card hands drawn from their opening (or 3-bet) range by an Omaha preflop order (pairs, suits, connection, danglers). The sample is public: their strategy is decided on the whole sample, but only the hands that miss your cards are live, so your blockers really change how often they fold and what they hold when they continue. After the flop they read every hand by how many random four-card Omaha hands it beats on this board and how many next cards turn it into a top-5% hand. They bet their strong hands, semi-bluff big draws if that is their style and bluff a fixed share of the rest. Against your bet they continue with the strongest stickiness x (pot / (pot + bet))^0.6 of their range (a little more preflop, where Omaha hands run close), but never with less than a minimum strength that rises with your bet size; the top of what continues re-raises the pot instead. Their actual cards are drawn from the range they end with, so they always take the action their range takes.
The maths
Equity is computed against every live hand in their range: exact enumeration of every turn and river on the flop, every river on the turn, a straight comparison on the river, and a seeded Monte Carlo of about 110,000 boards preflop (identical on every device). EV of fold = 0; check = equity x pot; call = equity x (pot + call) - call; bet or raise = fold% x pot + call% x (equity against the calling hands x final pot - chips added) + re-raise% x (the better of calling or folding to the re-raise). The test suite rebuilds every equity on 150+ spots with an independent evaluator, re-derives the opponent's read and policy from these rules, recomputes every option's EV and checks that the best play and every grade follow. Preflop spots are rerun with a different seed and twice the samples to prove the grades are stable.
Scoring
Each street: 150 for a Perfect play (the best EV, or within 2% of the pot of it), 90 for Close (within 10%), 0 for a Leak, plus up to 50 for your equity guess (full marks within 3 points, nothing beyond 25). Win the pot (they fold, or you win the showdown) for a 200 bonus; a split pot pays 100. The maximum is 1000. If the hand ends early, the streets not reached copy your last street's score. Score 400 or more to keep your streak.
The day book
Every hand is chosen by a search that deals candidates for the day and walks the main line (the best play at every decision) through the engine. A day is kept when every main-line spot is a real decision (a clear best play, at least five live hands, nobody drawing dead), there are at least two pot-odds spots, the day's theme turns up on the main line and the weekday's lesson is there. The search's choice and the opponent's real hand for 420 days are stored in days.js (lightly obfuscated) so a phone deals in one pass.
GALLERY
THE WEEK
| Day | Level | Theme | Pots | Opponents | Clear best play by |
|---|---|---|---|---|---|
| Monday | Gentle | Nut flush draw: called at the right price | Facing an open | Nora, Lyle, Kay | 4% of the pot (price shown) |
| Tuesday | Easy | Drawing hands | Open, or blind vs blind | Nora, Lyle, Kay, The Baron | 3% (price shown) |
| Wednesday | Steady | Made hands | Open, or blind vs blind | Nora, Lyle, Kay, The Baron | 2%, one move to find |
| Thursday | Tricky | Redraws | Any, pot 3-bet pots appear | Lyle, Kay, The Baron, Pat | 2%, turn folds possible |
| Friday | Tough | Wraps | Mostly 3-bet pots | Lyle, Kay, The Baron, Pat | 2% |
| Saturday | Hard | Blockers: a bet that leans on the nut-flush blocker | Mostly blind vs blind | Kay, The Baron, Pat | 2% |
| Sunday | Fiendish | Blockers, redraws, wraps or made hands, with pot-limit sizing | Mostly 3-bet pots | The Baron, Pat | 2%, two moves to find |
THE REGULARS
| Opponent | Style | Opens | Bets for value (strength) | Bluffs | Stickiness | Calls light |
|---|---|---|---|---|---|---|
| Nora from Norfolk | Nut peddler | 0.7x standard | top 5% / 5% / 4% | never | 0.85 | never (floor x1.15) |
| Lyle from Lincoln | Tight | 0.85x | top 10% / 10% / 8% | 4% | 1.0 | rarely (x1.05) |
| Kay from Kearney | Calls everything | 1.2x | top 12% / 10% / 10% | 5% | 1.45 | often (x0.6) |
| The Baron from Bellevue | Balanced | 1.0x, semi-bluffs draws | top 14% / 12% / 10% | 14% | 1.15 | by the book (x1.0) |
| Pot-Limit Pat from North Platte | Pots every street | 1.5x, semi-bluffs draws | top 22% / 18% / 16% | 38% | 1.3 | a lot (x0.8) |
VERSION HISTORY
- First version: one Pot-Limit Omaha hand a day at a 200-big-blind penthouse table, four decisions or more, graded by EV against a defined range.
- Own Omaha engine: five-card lookup tables, the exactly-two-plus-three rule, exact flop / turn / river enumeration and a seeded preflop Monte Carlo; checked against an independent evaluator on all 2,598,960 five-card hands, 200,000 Omaha deals and exact preflop matchups.
- Opponents read hands against random four-card hands (the real Omaha yardstick) and decide on a public range sample, so your blockers change their folds.
- 420-day book in days.js; weekday ramp from Monday's nut flush draw to Sunday's blockers, redraws and sizing.