How the drills work

Counting the Pot What is actually in the middle

What it asks: The action is on you. How many chips are sitting in the middle?

Every other drill in here starts by telling you the size of the pot. This one does not, because at a table nobody tells you. The dealer will say it in a tournament if you ask and will not say it in a cash game at all, so the number every other calculation in this app is built on is one you have to arrive at yourself, in your head, while it is your turn.

It is the first drill because it is the one underneath the others. A price worked out perfectly against a pot that is fifteen chips light is a wrong answer arrived at carefully, and that is the worst kind, because nothing about it feels like a guess.

How it works

You are shown a hand as it was played, seat by seat, and stopped at the moment it is your turn. Add up what is on the felt. Two rules do almost all of the work, and both of them are things people get wrong in the same direction.

The first is that every number on the felt is a total. "Raise to 35" means that seat now has 35 in front of them for the round, however much they had in before: a limper who was in for 5 has just put in thirty more, not thirty-five more. It is not only about raises, and the first place anybody meets it is smaller and quieter than that. The small blind who posted 1 and then calls 2 has put in one more chip, and has 2 in front of them, not 3.

The second is that chips do not leave. A seat that folds leaves everything they have already put in behind them, and it stays in the middle for somebody else to win. The player is gone; the chips are not.

A raise is a total. A fold leaves the chips behind. Your own call is not in yet.

An example

The number almost everybody gets

Read every number as chips going in rather than as what a seat has in front of them and that pot comes to 122. Two chips, on one hand, which is nothing. The trouble is that it is two chips for every seat that acted twice with money out, every hand, always in the same direction, so the pot is always bigger than it really is. Four raises deep in a three-bet pot it is a full blind or more, and a pot that is a blind too big prices a marginal call as a good one.

It is worth meeting this on the smallest hand it happens on rather than on that one. Nobody raised at all, the blinds are 1 and 2, three seats limp and the small blind completes: the answer is 10 and the miscount is 11, one chip, because the blind’s call of 2 was heard as two more on top of the one already up. The drill will tell you that is what you did.

One more worth naming, because it is not really a mistake. Adding your own call in gives 180 here, and 180 is a real number: it is what you would be playing to win if you call, and it is exactly what Pot Odds wants. It is just not what is in the middle, because you have not put it in yet.

What the levels do

One thing at a time, and none of it is harder arithmetic. Level 1 is blinds and limpers, where the only way to be wrong is to forget the blinds. Level 2 has seats leaving the hand with chips in it. Level 3 is raises over raises, which is where reading "to" as "more" comes apart fastest. Level 4 puts money up before the deal, an ante or a straddle, and gives the hand a second round to carry forward. Level 5 is all of it at once, with somebody all in for less than the bet.

That last one adds a fact rather than a sum. Their chips are in the middle like anybody else’s and the total is the total, but they can only win the part everybody matched. The rest is a side pot they are not in, so the number you are counting is not all one prize. The drill tells you so after you have answered, because it changes who collects rather than what is there.

Reading the Board The hand you actually hold

What it asks: Seven cards you can see, and five of them are your hand. Which five?

Every other drill here hands you a hand and asks for a number. This one asks for the hand. It is the drill the rest of the app has been assuming since the first question it ever put on a screen, because an out is a card that takes you from behind, or level, to strictly ahead, and all three of those words are a comparison between two five-card hands.

It is also the one most people think they already have. Reading a board is not hard; reading it under a bet, at a table, with the dealer waiting, is where it goes. The mistakes are not exotic. They are the same four every time.

How it works

Your hand is the best five of the seven you can see: your two and the five in the middle. Not your two plus whatever helps. The best five, chosen from all seven, and some of your seven are simply not in it.

That is the sentence the whole drill is built on, and it has a consequence people resist. You do not have to use either of your cards. About one river in twenty the best five you can make are the five lying in the middle, which means you are holding nothing that anybody else at the table is not.

The best five of the seven. Sometimes both of yours are in it, more often one, sometimes neither.

An example

The four ways it goes wrong

Every wrong answer this drill offers is a real five-card hand made of cards on the table. None of them is invented, because a button naming cards nobody holds could be crossed off by counting suits rather than by reading a hand, and that would be a different skill.

The second is forcing both of your cards in. You have a seven and a four, so surely both are doing something. One of them is not, and which one is the question. The third is reading their hand instead of yours, which sounds careless and is the commonest error at a real showdown, because their cards are the ones you have been staring at. The fourth is the opposite: reading the board and stopping there, when your card does play.

What the levels do

One fact at a time, and the fact is always the same one asked harder: how many of your two cards are actually in the five. Level 1 is both of them, on a board with nothing going on. Level 2 is one of them, where the other has to beat something in the middle to get in and does not. Level 3 pairs the board, so three pairs are on the felt and only the top two play. Level 4 puts the board one card from a straight or a flush, where whether you have it is a real question. Level 5 is neither of them.

That last one is worth the climb. When the five in the middle are your best five, you are playing the board, and so is everybody else who cannot beat it: the pot is split, and it is split whatever you were holding. It is the one place in this app where a chop is not a fraction of an answer but the answer itself.

The showdown is printed under every answer, whether you got it right or wrong and whether the pot went to you, to them or down the middle. That is on purpose. A line that only appeared on the hands that split would tell you they had split before you had worked anything out.

Counting Outs How many cards win it

What it asks: How many of the cards still to come would put you in front?

This is the one most of the others are built on. You are behind, or level with them, there are cards to come, and before you can work out whether a call is worth making you have to know how many cards put you in front. A card that would put you in front is called an out, and counting them is a skill you can learn in an afternoon and use forever.

How it works

There are 52 cards. At a table you would see five of them, your two and the three on the board, which leaves 47 you cannot see, and 47 is the number the percentages on this page are worked out over. This drill turns their two cards face up as well, because an out only means anything against a hand you are trying to beat, so only 45 of those 47 can actually arrive and 45 is the number the screen prints under the question. Your job is to find the cards among those 45 that win it for you.

The counting is not quite as simple as it looks, which is why it is worth drilling. A card has to actually win to be an out. A heart that completes your flush and also pairs the board, handing them a full house, is not an out. And a card sitting in their hand cannot come at all, so it does not count either.

An example

The shortcut

Multiply your outs by 2 for one card to come, or by 4 for two. It has a name, the Rule of 2 and 4, and that is the name the drill uses when it marks your answer. Nine outs times four is 36%, and the real answer above is 34.97%. Two things to carry with it. The times four figure is for both cards, so it only answers a call nobody can bet into again: an ordinary flop call buys the turn alone, which is 19.1% here. And it runs high once the outs pile up, about six points out at 15 outs and fourteen at 21. The drill prints the shortcut and the exact figure side by side so you learn where it drifts.

What the levels do

Level 1 is one clean count: every card you are counting makes you the same hand. Level 2 lets a second kind of draw into the same hand, so some of these ask you to count two groups without double counting the cards in both. Level 3 always has more than one group, and it is where some of your outs start turning up in the other player's hand. Level 4 stops protecting you from anything, including hands where the honest answer is zero. Level 5 does the same on the turn, with one card to come instead of two, so the shortcut is times 2 and the count runs against 46 cards rather than 47.

Outs Against You How many cards take it away

What it asks: You are ahead. How many of the cards still to come beat you?

The same count from the other chair, and the one worth being able to do, because this is the hand you replay on the drive home. You had the best hand, a card came, and it felt like being cheated. It was not. It was a number you could have known.

How it works

Exactly like counting your own outs, except you are counting theirs. A card in somebody's hand cannot come, which you already know, and from this side it works both ways: the cards in their hand are off the deck, and so is any card in your own hand that would have beaten you. What changes is the direction of the mistake. Count too many here and the danger looks bigger than it is, so you fold a hand that was ahead.

An example

That survival figure is not worked out by subtracting. The app deals out every possible way the last two cards can come and counts the ones that do not leave them in front, a split pot included, because the two answers are not the same: there are runouts where one of their cards arrives and you win anyway, and runouts where neither arrives and you lose to something nobody was counting.

What the levels do

Levels 1 and 2 are clean counts. Level 3 starts putting cards that would have beaten you in your own hand, where they cannot arrive at all, so the count comes out shorter than their draw looks. Level 4 stops protecting you from anything, including the spot that is the whole point of this drill: nothing at all beats you on the next card, and you still lose sometimes, because two cards are coming and they can arrive together. Level 5 moves to the turn.

Charging the Draw What it costs to price them out

What it asks: They are drawing and you are ahead. What is the biggest bet their draw can call?

Outs Against You teaches you to count the cards that beat you. This is the question that comes next, and it is the one nobody at a home game has ever worked out: those cards are going to come some of the time, so what does it cost you to make them pay for the privilege? You are ahead, they are drawing, and for once the chips going in are yours.

How it works

It is Pot Odds solved backwards. There, you know the bet and work out the share it demands. Here you know their share and work out the bet that demands it. The thing being solved for has moved to the other side, and that is the whole difference.

The catch is what the bet is buying. You have chips behind, so you can bet again on the next street. That means their call is paying for one card, not two. Everything in this drill follows from that sentence.

An example

The number almost everybody uses

A flush draw is "about 35%". Every player who has done any reading at all knows that figure, and on this hand it is 39%. It is also the answer to a question nobody asked, because it is what the draw is worth by the river, across two cards. Your bet is buying them one.

The difference is not small. Priced against 20%, the line is 50. Priced against 39%, it is 275, which is nearly twice the pot. A player working from the bigger number looks at a pot-sized bet, decides it is nowhere near enough, and checks instead. That is where the belief that you cannot charge a flush draw comes from: not from the arithmetic being hard, but from it being done against the wrong card count.

A bet with chips behind it is buying one card. Price it against one card.

There is a rule underneath it that you can do at the table. With one card to come and forty-five cards that can arrive, a draw with a given number of outs needs the pot times that number, over forty-five less twice that number. Nine outs is the pot times nine over twenty-seven, which is a third of it. Fifteen outs is the pot times fifteen over fifteen, which is the whole pot.

What the levels do

The draws get bigger, and the bet needed to charge them grows much faster than they do. Level 1 is a fifth of the pot. By level 4 it is the whole pot, which is a bet almost nobody makes. By level 5 it is past the pot and you will not have it: the stack runs out before the answer does, and the drill shows you what is behind so you can see it happen. That is the real lesson at the top, and it is not a failure of arithmetic. Some draws cannot be charged at any price you are able to pay.

Past a certain size they cannot be charged at all, by anybody. A hand that wins half the pot or more makes money from every chip that goes in, so there is no bet that prices it out. On one card that is about twenty-two outs, which is more than any real hand has, and it is why the numbers run away so fast as you climb.

Pot Odds What the price is asking for

What it asks: Two things. What share of the time do you need to win for this call to break even, and is the hand you are holding worth that much?

Somebody bets, and you have a draw. Calling costs money now and pays off later, and pot odds is the name for working out whether the trade is any good. It is the single most useful calculation in poker and it is arithmetic a ten year old can do.

How it works

Look at what you have to put in, and at what the pot will be worth once you have put it in. Your money as a share of that total is the share of the time you need to win. That is the whole thing.

An example

Saying it as a ratio

The price is often said as a ratio. Half pot lays you 3 to 1, meaning there are three units in there for every one you are adding, so you need to win 1 time in 4, which is 25%. Both ways of saying it are the same number.

What the levels do

Bet sizes get more awkward, so the arithmetic stops being quarters and thirds. From level 2 the seat is dealt with the cards, and on a flop it is being all in, rather than acting last, that buys both remaining cards: from either live seat your money buys the turn and nothing more. From level 3 up some hands are dealt on the turn instead, where one card is all anybody is buying whatever seat they are in.

Equity Estimate What share of the pot you win

What it asks: Two hands, face up. What share of the pot is yours?

Equity is just a word for your share of the pot: if you win a 200 pot 40% of the time, your equity is 40%, and your share is worth 80. Hands that tie count too, and a tie counts as half: two hands that always split have 50% each and neither of them ever wins outright. So the number this drill wants is your share of the pot, not how often you take the whole thing. It is not really about arithmetic either. It is about calibration, getting your gut close enough to the truth that the answer you feel is the answer you would have calculated.

How it works

You are shown two hands, and from level 3 a board as well, and you set a percentage. It starts at 50 and you move it with the step keys, five at a time or one at a time, and then you lock it in. Before the flop there is nothing you can work out in your seat. Once there is a board, a hand that is drawing can count its outs and use the Rule of 2 and 4 from the other drills, and on most of those spots that lands inside the band. Everywhere else you guess, the app tells you what it really is, and you do it again. After a few hundred of them your guesses get good, which is the only way anybody has ever learned this.

You are marked against a band rather than an exact figure. At level 1 your guess counts as right if it lands within 12 percentage points of the true figure, either side, and the band tightens as you go: 10 at level 2, then 8, 6, and 4 at level 5.

An example

What the levels do

Levels 1 and 2 come before the board does. Some of the match-ups are the ones everybody quotes, aces against kings or a pair against two overcards, and the rest are two hands off the top of the deck, king-five against suited ace-three, which nobody has a figure memorized for. Later levels put cards on the board, where the answer moves around a lot more, and the band you are marked against gets tighter at every step.

Against a Range When you cannot see their cards

What it asks: What share of the pot is yours against everything they could be holding, rather than against two cards you were shown?

Every other drill here turns the other player's cards face up, which is the one thing a real table never does. This is the drill that fixes it. Instead of two cards you get a range, which is a written description of every hand they might have, and the answer is your average against all of them.

How it works

Ranges are written the way players say them. JJ+ means a pair of jacks, queens, kings or aces. AQs+ means suited ace-queen and every suited ace above it, which here is only suited ace-king. 99-66 means the pairs from nines down to sixes.

The part everybody skips is that the cards you can see remove some of theirs. If you are holding a queen, only three queens are left, so the six ways they could hold a pair of queens drop to three, and some of the hands in their range are impossible before anything else happens. The drill puts that count on screen because it changes the answer and nobody does it in their head.

An example

What the levels do

Ranges get wider and harder to average through the first four levels, from a couple of dozen combinations at level 1 to several hundred at level 4. Level 5 moves to the turn instead: there are four cards on the board, the range is usually narrow again, and there is one card left to come. The band you are marked against is two points wider than the equity drill at every level, because averaging a hundred hands is a coarser instrument than reading one off the table, and it would be unfair to mark the harder skill to the tighter standard.

The Combinations How many of the hand you fear are left

What it asks: How many ways can they still have the hand you are afraid of?

Against a Range tells you what your share is against everything somebody could be holding. This asks the question underneath it, and asks for a count rather than a percentage, because a count is much harder to wave away. Told your equity went up two points, a player shrugs. Told that the six combinations of kings they were worried about are down to one, they have something they can use at a table.

How it works

A pair is six combinations. Any two different ranks are sixteen: four of one by four of the other. Suited is four of those sixteen and offsuit is the other twelve. Those four numbers are the whole of what you have to know, and the drill is what happens to them once cards start coming off the deck.

Every card anybody can see is a card nobody can hold. That includes the five in the middle, which everybody subtracts because they are face up, and it includes the two in your own hand, which almost nobody subtracts at all.

A pair is six. Two ranks are sixteen. Every card you can see takes some of them away.

An example

Where the counting goes wrong

The other two are halves of the same subtraction. Taking the board off and forgetting your own hand is what nearly everybody does, because the board is face up and your cards feel like yours rather than like cards that are gone. Taking your own hand off and forgetting the board is rarer and is usually somebody who has just learned about blockers. The drill prints both under the answer, next to each other, so it is clear that neither is enough.

What the levels do

Level 1 puts the rank in the middle, where the removal is face up. Level 2 puts it in your own hand instead: the same sum, the same answer, and the cards come off from the place nobody looks. Level 3 asks about two ranks rather than one, so the count is a product instead of a triangle. Level 4 asks about one suitedness only, where a single card can take a quarter of the suited combinations away and leave the offsuit ones alone.

Level 5 asks about every set the board allows rather than one of them. Nine is the number most players carry around, and it is right exactly when none of the three ranks is in your hand. When one of them is, it is seven, and when two are it is five. That is the same lesson as level 2 with the volume turned up: the hand you are afraid of is rarer than you think, and you are the reason.

Multiway Your share against the whole field

What it asks: Three or four of you saw the flop. What is your share of the pot now?

Every other drill in this app deals you one opponent, because one opponent is what a question with an exact answer looks like. This one deals you two or three, which is what a home game actually deals, and asks the same question about a pot that several people are still in.

The reason it gets a drill of its own is that nobody estimates this by estimating it. They pick the opponent they are most worried about, work out their share against that one hand, and use the answer. That figure is real, it is just an answer to a different question, and it is always too high.

How it works

You do not beat the field by beating the hand you are afraid of. You beat it by beating all of them at once, and every extra seat is another way for the hand to be lost. Two opponents means the runout has to miss both of them, three means it has to miss all three, and the shares of everybody at the table have to add up to a hundred however strong your hand feels.

That is why the drop is so much steeper than it seems it should be. A hand that is a heavy favorite against any one of them can still be under half the pot against the three of them together, and the pot is paying you on the second number.

Your share against the field is not your share against the scariest hand in it.

An example

Where the estimate goes wrong

The drill prints your share against each seat on its own once you have answered, next to the real number, because the distance between them is the whole lesson and it is much larger than anybody expects.

What the levels do

The ladder cannot climb on arithmetic here, because a share against three hands is no harder to estimate than a share against two, it is only smaller. So it climbs on the shape of the misreading instead. Level 1 gives you two opponents and a made hand that is ahead of both, which is the friendly case where the heads-up figure feels safe and is still wrong. Level 2 gives you a draw, where counting outs stops being enough because there are now two hands to get past rather than one.

Level 3 puts one of them ahead of you, which is the case that catches people: the hand you instinctively price yourself against is the one you are not afraid of. Level 4 adds a third opponent, and level 5 gives you three of them while you are the one drawing, which is the family pot every home game deals and the shape none of the other drills can show you.

Bad Runs How often a favorite loses anyway

What it asks: Play the same hand several times. How often does the whole run go badly?

Tilt is what this drill is about, and it is where the app gets its name. Every other question here is about one hand, and one hand is not what ruins anybody's evening. Getting your money in as a big favorite and losing is a shrug. Getting it in as a big favorite four times and losing three of them is the thing that makes people throw their phone, and almost nobody has ever worked out how often that actually happens.

How it works

Each hand is the same spot dealt fresh, so the hands do not affect each other. The chance you win one is printed on the table, so the chance you lose one is whatever is left out of a hundred. Then you combine it, and the question comes in one of two shapes. Losing every single one is your losing chance multiplied by itself, once for each hand. Losing at least one is the other way about: work out how often you win them all, and take that off a hundred, because at least one loss is everything except a clean sweep.

An example

What the levels do

Levels 1 and 2 deal on the turn, with one card still to come, and ask about the two ends of a run: losing every single one, or losing at least one. Level 3 moves back to the flop, where two cards are still to come and more can go wrong. Levels 4 and 5 start asking about a threshold inside the run, as in how often you lose two or more out of five, which is several outcomes added together rather than one step, and which is exactly why it is worth having met before.

Implied Odds What the call needs from later streets

What it asks: The price says fold. How much extra do you need to win later for calling to be right anyway?

Pot Odds prices a call against the money in the middle right now, and on a flop, unless the bet puts somebody all in, that price only buys you one card. Price a flush draw against that one card and it says to fold to anything bigger than about a third of the pot, which is most of the bets anybody ever faces. Everybody calls anyway, and they are often right, because of the one thing that calculation leaves out: the money they pay you on the river, on the times your card does arrive. This drill asks for that money, in chips.

How it works

Work out what the call loses on the price alone, the way Pot Odds does. Then ask how often the card you need actually arrives. Divide the first by the second and you have the chips the river still has to bring.

What the call loses on average, divided by how often your card comes, is what the river has to bring.

An example

The number is the size of the ask, not a forecast. It assumes they pay you in full every time your card comes, that you lose nothing more when it misses, and that a missed turn is the end of the hand. Real poker moves it both ways. They do not always pay, and a flush that arrives on the turn can still lose to a full house, which asks for more. But if you are last to act and the turn gets checked through you see the river for nothing, and a draw that missed can still win the pot by betting it, which asks for less. Hold the figure against the chips behind: if there are nowhere near that many, no river was ever going to pay for this call.

What the levels do

Bets get bigger and stacks get shallower. At level 1 the river needs to bring a fraction of the pot and every stack covers it. At level 5 it is usually somewhere between two and four times the pot, and the stack almost never covers it, which is the point of the whole drill: some calls are not bad arithmetic, they are arithmetic that needs money nobody at the table has.

Fold Equity How often the shove has to work

What it asks: You are moving all in with a draw. How often do they have to fold for that to break even?

Every other drill here leaves the betting to somebody else: you count, you price, you estimate, and the chips going in are theirs. This is the other chair. You are the one putting the chips in, and the question is how often that has to take the pot down uncontested before it is worth doing. Fold equity is the name for the value you get from the times they give up.

How it works

It is the same fraction you already learned in Pot Odds, said from the other side: what you are risking, over what you are risking plus what you stand to win. The twist is what "what you are risking" means. With a hopeless hand you are risking the whole bet. With a draw you are not, because some of the time they call and you win anyway, and that cuts the risk down before you take the fraction.

An example

The figure everybody quotes

Shoving 40 into 60 with absolutely nothing needs to work 40% of the time, and that fraction is the number most players have heard. It moves with the size of the shove: half the pot has to work a third of the time, a pot sized shove half the time, twice the pot two thirds of the time. Here is the part almost nobody applies correctly.

Your hand does not come off the answer. It comes off what you are risking.

Your hand took the risk from 40 chips down to 21, and then the same division was done with that smaller number: 21 out of 81, rather than 40 out of 100. Subtracting your equity from 40% is not that calculation. On this hand the two land close, 26.6 against 26.1, which is why the habit survives. At level 5 they come apart: the subtraction says 34% where the shove needs 25%.

There is also a point past which the shove cannot lose at all. In this spot it is 28.6%: a hand worth more than that makes money when they call, so no amount of folding is required and there is nothing left to work out. That line moves with the shove too, a quarter at half the pot and a third at a pot sized shove, higher again above that. A flush draw shoving half the pot into one pair or two pair is already past it. Against a set it sits on the line, a point either side of it depending on the cards, and that is the one hand most likely to be calling. The app shows you where the line is after every single hand, because it is the most useful thing in the drill and you will not meet it any other way.

What the levels do

The shove gets bigger and the hand behind it gets better, together, because a big shove cannot ask an interesting question unless there is a real draw behind it. As they climb, the figure everybody quotes gets further and further from the truth.