Poker math

Your accuracy

Where you go wrong

How it works

You estimate equity. That is the share of the pot a hand gets on average when the players are all in and the cards simply run out to the river: every win plus its share of the split pots. Two or three hands are face up on a flop, and the percentages are hidden. The hands are not random: they are drawn from the real ranges of the GGPoker NL100 field for the scenario named under the question – who opened and who called. So these are hands people actually take to the flop, not J4 against 83. The question is about one hand – it is outlined and named in the question. Set the slider to your estimate and answer. Then the turn comes and the question is asked again: the slider sits on the exact flop figure, and your job is to see where one card moved it. Both figures come from running through every remaining card.

The score is not right or wrong but the miss: how far your estimate was from the exact figure. You said 40%, the exact figure is 35% – off by 5. Strictly these are percentage points; the page writes them as per cent for short. The traffic light shows your average miss over the last 20 answers: green is up to 3, then 4–6, 7–10, 11–18, and red from 19. The boundaries come from a measurement on 3,000 deals of the same kind. The rule of 4 and 2 with the outs counted exactly misses by 3 on average. The rough “ahead – 70%, behind – 25%” misses by about 10. Splitting the pot equally between the hands misses by 26.

Every deal has a type, named after what the trailing hand can catch up with: flush draw, open-ended straight draw, gutshot, combo draw, made hand behind, overcards against a pair, no pair on either side, no pair and no overcards; three hands are a type of their own. The trainer keeps your miss for each type and shows where you are furthest off and which way – too high or too low. “Train…” deals only spots of your weakest type until you switch back. After you answer, the outs are shown as the cards themselves. False outs are listed apart: cards that improve the hand but do not put it ahead.

After you answer you see the exact numbers, how many cards change who is ahead, and what the rule of 4 and 2 would have said: outs times 4 on the flop, times 2 on the turn. “Share my result” draws an image right in the browser: on a phone it goes to the system share sheet, on a computer a panel opens – copy the image, download it, or open a post on a network. Your answers live only in this browser: no cookie and no server, so on another device the count starts again.

Outs and pot odds

Two tabs for simpler counting. “Outs”: two open hands from real ranges, flop or turn; the question is how many cards on the next street put the trailing hand in front on its own. Both hands and the board are already out of the deck, and a card that improves you but leaves your opponent ahead is not an out – after the answer such false outs are listed apart. There is also a check by the rule of 4 and 2: outs times 4 on the flop and times 2 on the turn, next to the exact equity. The traffic light has its own scale here: missing by a single out already shows. “Pot odds”: no cards, only arithmetic. How much equity a call needs when your opponent bets – the bet given in big blinds or as a share of the pot; and how often your opponent must fold for a pure bluff to break even. The answer is always exact: what you put in divided by the final pot. Each tab keeps its own statistics.

Combos

The “Combos” tab asks the questions combos are actually counted for at the table: are there enough weaker hands for a value bet to pay, and does your opponent have enough bluffs for a call. Those questions come up in narrow ranges and on later streets, so every deal here is a 3-bet pot, and the question is asked on the turn or the river. There are three kinds of question. On the turn: how many combos in your opponent’s range beat your hand right now. On the river, value: how many combos weaker than your hand would call a bet – any hand with a pair or better from its own cards calls, and a hand that only plays the board folds. On the river, calling a bet: your opponent bets every hand that beats you and every missed draw – a hand with no pair of its own that had a flush draw or an open-ended straight draw on the flop or turn; how many bluffs are in that bet. Who calls and what he bets with is the rule of the question, printed in the hint. It is an assumption, not a measurement: almost only called bets reach showdown, so this data cannot honestly say how often the field bluffs the river. The opponent’s range is his preflop line; it is not narrowed by the betting on the flop and turn. It is drawn on a 13×13 matrix right away, before you answer: this is the field’s average range, a particular player’s may differ, and nobody needs to know it by heart. If you would rather carry the range in your head, as at the table, switch to “Range in your head” – the matrix then opens only after you answer; each mode keeps its own statistics. Counting is simple: a pocket pair is 6 combos, a suited hand 4, an offsuit hand 12, minus the cards already on the board and in your hand. After the answer you get a breakdown by hand group, a verdict on whether the bet or the call pays at that bet size, and the blockers: how many combos of his range your cards removed. The flop and pots without a 3-bet stay with the “Equity”, “Outs” and “Pot odds” tabs: there the decision rests on equity and pot odds, not on counting combos.

The ranges are real, not solver output: this is how the GGPoker field plays at NL100 – Rush & Cash fast-fold, six-handed tables, $0.50/$1 blinds, over 60,000 hands from the project’s closed archive. The width of each range is measured exactly; the composition comes from hands opponents showed down, corrected for strong hands reaching showdown more often. For counting, the range is rounded: a hand is either fully in or out. The range takes the most frequent hands of the line – just enough for its width to match the measured one. The real frequencies are not thrown away: under a turn answer you see how many combos beat you by the measured frequencies and which hands sat on the rounding edge. Your opponent holds one specific hand from that range, face down until you answer; then it is turned over and you see whether you were ahead this time. After the answer the matrix is coloured: red cells beat you, green ones are weaker (on the river – weaker and calling), yellow ones are bluffs, grey ones fold or are not in the bet. In 3-bet pots fewer hands are shown down, so the range there is shared by several neighbouring seats, and the deal names one of them. Opponents in the archive are anonymous. The tab keeps its own statistics, counted in combos.

Your blitz runs

How the blitz works

The blitz asks the trainer’s questions against the clock. There are four kinds of blitz, switched on the start screen. “Equity”: ten deals, a random street – flop or turn. “Outs”: ten deals, the question from the “Outs” tab. “Pot odds”: ten questions on the arithmetic of calls and bluffs. “Combos”: ten deals from the “Combos” tab – a 3-bet pot, turn or river. The pace is yours to pick as well: equity and pot odds – 5, 10 or 20 seconds per question, outs – 10, 15 or 25, combos – 20, 30 or 45 with the range matrix and 10, 20 or 30 with the range in your head. The hands come from the field’s real ranges. Every kind-and-pace pair keeps its own record, and a challenge link opens the same kind at the same pace. The score is the same as in the tab of the same name: how far your answer is from the exact figure, on average. If time runs out, whatever the slider shows is your answer. The time in the result is only the time spent answering. Blitz results are kept apart and do not feed the traffic light or the spot-type breakdown: people miss differently under a clock. Leave the tab mid-blitz and it resets. “Share my result” gives a challenge link: it opens the same ten deals, and after the run the two results are shown side by side. The opponent’s result travels in the link itself and is not verified – this is a game, not a tournament. Deals you have already played do not count towards your record a second time. Everything is stored only in your browser.

Your warm-ups

How the warm-up works

The poker warm-up is ten questions a day, the same for every reader: three on pot odds, three on outs, two on equity and two on combos in a 3-bet pot, easy to hard. There is no timer; the time is simply counted. Each answer earns up to 10 points on the same traffic-light scale as the tabs: spot on – 10, close – 7, near – 4, far off – 2, guessing – 0; outs use a stricter scale, since missing by one out already shows. The first run of the day counts towards the score and the streak; you can repeat as often as you like. After the warm-up comes a question-by-question review: your answer, the exact figure, the cards and how the figure is worked out. The streak is how many days in a row you have done the warm-up; miss a day and it starts again. New questions arrive at midnight by your device’s clock. You can share your result: the image is drawn right in your browser. Everything is stored only in this browser.

How to play

While the timer runs, tap the hand you think takes the pot. Tap again to remove the bet; you can back several outcomes at once: every tap is a separate bet, and the total is shown under the buttons. “Deal” opens the cards without waiting. “Auto” bets for you every hand – on the favourite or on the underdog – and the betting window shrinks to 5 seconds.

The “Straight+ · Flush+ · Full+” row is a bet on which hand rank wins the pot, whoever holds it. Only the winner’s rank counts. Deals where one hand has under 1.5% or over 88% are skipped; that does not affect fairness, because the odds are computed for the deal you actually see.

Checking a deal

Before bets open the game shows a SHA-256 of the card order plus a random salt. After the hand it reveals the original string – you can recompute the hash and confirm the cards did not change after you bet.

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Recent hands

This is not gambling: there is no money, no prizes and nothing to buy. The balance lives only in your browser.