Beginners guide

If you are unfamiliar with equity calculators and poker software like Flopzilla, then you are in the right place. Even if you are an experienced poker player.

If you are familiar with that sort of stuff, then head over to the quick guide for an overview of Premium Poker Tools that isn't nearly as lengthy.

Note: These tools are meant for studying the game away from the table. The reason for this is because it'd just take too long to sit there analyzing things with Premium Poker Tools (or any similar software) while you're at the table.

Equity calculator

To explain how the equity calculator works, let's explore a common scenario. You are playing $1/$2 No Limit Texas Hold'em at your local casino. You look down at your cards to find that you have an ace of clubs and a king of spades, which is abbreviated AcKs in the poker world. Pretty good! So you raise to $8. It folds around to the player in the big blind. This guy raises all in to $200! What do you do? Call, or fold?

I play $1/$2 No Limit Hold'em (NLHE) in Vegas, and my impression is that most players happily get it in (call) in this scenario. Presumably, they think to themselves that AKo (ace king offsuit) is one of the best starting hands in the game - perhaps third or fourth best - and so it is worth a call.

Makes some sense. But let's take the time to explore this question in more depth.

To know whether or not it is worth a call, we're going to have to dive in to the numbers and do a little math. I promise, it won't be intimidating.

The first thing that we'll want to know is called the pot odds. This is the ratio of the pot size to the size of the bet you have to call. In this case, the pot is the big blind's $200 + your $8 + the small blind's $1 = $209. And you need to call another $192. So the pot odds are 209:192.

The second thing we'll want to know is how much equity we need for it to be worth calling the bet. (For now, just think of equity as your win percentage.) To determine this, we just do 192 / (192 + 209) and get about 47.9%, which means that you need 47.9% equity in order to justify calling. (In practice, we usually just approxmiate the pot odds as 1:1 and say that we need 1 / (1 + 1) = 50% equity to justify calling.)

A simplified version of that statement would be, "if you win 47.9% of the time or more, it is worth calling". But let's dive in to what that term "equity" really means.

Basically, equity is win percentage that takes ties into account. Suppose that you only win 45% of the time, but that you also tie 30% of the time. Note that when you tie, you split the pot. 45% is less than 47.9%, so does that mean that you should fold? No. In this scenario, you would have 45 + (30 / 2) = 60% equity, which is more than enough to justify calling.

Returning to the question of whether we should call the all in bet with our AcKs, we know that we need 47.9% equity to justify calling, but that just begs the question of how we know how much equity we have. Equity calculators help us answer that question.

This is Premium Poker Tool's equity calculator:

The box to the left represents you; the box to the right represents your opponent:

You know what your cards are, so why don't we go ahead and click the AKo grid square.

That just set "ace king offsuit" (AKo) as your hand. But there are twelve combinations of AKo - AcKs, AcKh, AcKd, AsKc, etc. If we want to be even more precise and enter AcKs specifically, we can either:

1. command (⌘) + click or windows key (⊞) + click (depending on whether you're on a Mac or Windows computer)
2. Use the text selector

Now how do we set our opponent's hand? Well, we don't know what our opponent is holding, so we can't set his hand, per se. But we have an idea of what range of hands our opponent would make this play with. Our opponent wouldn't go all with with 72o, for example, so we can eliminate that from the potential range of hands that he has. He probably wouldn't even go all in with T9s, or KJo.

This is one part of poker that requires judgement - determining your opponent's range. When you are at the table, be sure to pay careful attention and observe your opponents. Have they gone all in for $200 with 66 in the past? If so, we can probably assume that they'd also go all in with 77. And 88. And 99, TT, JJ, QQ, KK and AA. It also probably means that they would go all in with AK, because AK is, in most peoples minds, a stronger hand than 66. But what about AQ? Probably. AJ? Maybe.

Determining your opponent's range is certainly not an exact science. Even if you had a record of every hand your opponent played, we are still dealing with human beings here, and humans don't always behave like they did in the past. Sometimes someone who normally folds 33 will feel like gambling. Sometimes someone who normally plays TT isn't feeling lucky. Sometimes someone studies the game and changes their strategy. (Hint: that's you!)

But this doesn't mean that all is lost. Just because someone could go all in with 72o doesn't mean that them doing so is likely. All we can do is use our judgement, make educated guesses, and play the percentages. Fortunately, if you are good at using your judgement and playing the percentages, you're going to make a lot of money.

Premium Poker Tools offers you a variety of shortcuts that you can use to set ranges. Note that they all stay in sync with each other.

Tier selector:

Note: you can configure the default tiers at Settings / General / Tiers.

Category selector:

Saved ranges selector:

Note: To use the saved ranges selector, set it at Settings / General / Included selectors. To customize the saved ranges, go to Settings / General / Saved ranges.

Slider selector:

Text selector:

Now let's put our opponent on a range, and run a simulation to see how much equity we have. Let's first suppose that our opponent is relatively tight, and that he only goes all in like this with AA, KK, QQ, and AKs.

Woah! Even though we have one of the best hands in the game, versus this range in particular, we actually only have about 33.21% equity, which is way less than the 47.9% we would need to justify calling.

Take note of the insights section:

Here is what it is saying:

• If the pot odds are 4:1, you need 20% equity to justify calling. You have more than that, so it would be worth calling with those pot odds.
• If the pot odds are 3:1, you need 25% equity to justify calling. You have more than that, so it would be worth calling with those pot odds.
• If the pot odds are 2:1, you need 33.3% equity to justify calling. You have less than that, so it would not be worth calling with those pot odds.
• If the pot odds are 3:2, you need 40% equity to justify calling. You have less than that, so it would not be worth calling with those pot odds.
• If the pot odds are 1:1, you need 50% equity to justify calling. You have less than that, so it would not be worth calling with those pot odds.
• If the pot odds are 2:3, you need 60% equity to justify calling. You have less than that, so it would not be worth calling with those pot odds.
• If the pot odds are 1:2, you need 66.6% equity to justify calling. You have less than that, so it would not be worth calling with those pot odds.

Let's continue to explore whether it is worth calling your opponent off with AKo. Maybe your opponent isn't as tight as we initially assumed. Maybe he would make that all in bet with JJ+, AKs, and AKo.

Even against that range, we still only have about 39.84% equity, which of course is way less than the 47.9% we would need to justify calling.

Would our opponent make this all in bet with an even wider range? Let's suppose that our opponent is a little crazy and makes this bet with 99+ and AQ+.

Now it finally seems that it may be worth a call with our 48.67% equity against this range. But it's still really, really close.

What if our opponent is just wild? What if our opponent is blasting all in with the top 20% of his hands?

Ok, this time we have a pretty clear call with 61.2% equity.

As you can see, Premium Poker Tools can't actually tell you what the right play is. But when combined with you're judgement as a poker player, it is a tool that can really give you some useful insights.

Now, let's explore some of the slightly more advanced features of Premium Poker Tools' equity calculator.

Multiway

Suppose that we have the same situation as above, except that there is one more player in the hand. Suppose that the player in the small blind (SB) is the one who raised all in, and that the player in the big blind (BB) called. Now, you face a different situation. Fortunately, Premium Poker Tools can help you analyze this situation too.

First, let's figure out how much equity we need to justify calling. In order to do that, we need to know what the pot odds are. The size of the pot is your $8 + $200 from the SB + $200 from the BB = $408. You need to call $192. So the pot odds are 408:192. Which means that you need 192 / (192 + 408) = 32% equity to justify calling. (Note: in the real world, we would approximate the pot odds as 2:1 and say that you need 1 / (1 + 2) = 33.3% equity to continue.)

Now let's use the equity calculator to put our opponents on some ranges, and see how our AcKs does against those ranges.

But before we start doing that, let's add a third player to the hand. To add a third player to the hand, click the "Add player" button towards the bottom left of the screen:

Let's start off by entering our hand:

Next, let's think about the range that the SB might be on. Let's start off supposing that the initial raiser is tight and has a range of AA, KK, QQ, and AKs, like we did before:

Now let's think about the range that the caller from the BB might be on. Let's also start off supposing that he is on a tight AA, KK, QQ and AKs range:

Before clicking "Simulate" and seeing how much equity we have, I have a question for you: which scenario do you think you'll be better off in - AKo versus one tight range, or AKo versus two tight ranges? Think about it before continuing.

After clicking "Simulate", you'll see that you only have about 15.64% equity. This is objectively a worse situation to be in. The expected value of having 15.64% equity in a $600 pot is $93.84, whereas the expected value of having 33.21% equity in a $401 pot is $133.17.

So it seems that versus two opponents, we're going to have an even harder time justifying call. It seems that both opponents are going to have to be relatively loose.

But don't trust the way it seems. Play around with different ranges until you are comfortable knowing how loose your opponents have to be for you to justify calling.

Postflop + narrowing your opponents range

Let's consider a new situation. Suppose that you raise $8 from the button with AcKs, and the BB calls. The flop comes AhTd9d. The BB checks to you. You bet $15 into the $17 pot. The BB re-raises all in to $200. Do you call, or fold?

As always, let's start by thinking about the pot odds and how much equity we need. The pot odds are 224:177, so we need 177 / (177 + 224) = 44.14% equity to justify calling.

Next, as we did before, let's enter our AcKs:

Now, we're going to do things slightly differently. Instead of setting our opponents range, we're going to set the flop cards to AhTd9d. Here's how:

Now, when we run simulations, the flop is always going to start off as AhTd9d, and then the turn and river will be dealt from the deck.

Next, we are going to want to set our opponent's range, but the way we're going to do so is going to be slightly different. Well, we could just ask ourselves what our opponent would make this play with and click those grid squares, but the way I'm going to show you will be easier.

Let's first ask ourselves what our opponent would call our $8 raise with from the BB preflop. Perhaps the answer to that is something like... the top 30% of hands except AA, KK, QQ and AKs (because we assume he would raise with those rather than calling). Let's start off by setting that as our opponent's range:

Now, let's click the "Narrow range" button:

What do we think our opponent would check-raise us with on this board? Perhaps two pair or better, and flush draws. Let's check that stuff off and click "Narrow range" inside the modal. When we do, it will eliminate all holdings from our opponents range that don't make two pair or better or a flush draw on this flop:

That was easier then manually inputting all of the two pair and better + flush draws, right?

Now that we have our hand, our opponent's range, and the flop set, we can simulate and see how much equity we have:

Looks like we only have about 35.90% equity. We need 44.14% equity, and so, despite the fact that it appears to be a great hand, our AcKs should actually be folded in this situation.

Hand weights

Let's consider that situation we had in the previous section. We initially removed AA, KK, QQ and AKs from our opponents range because we assumed that they would have raised with those hands rather than just calling:

But would they alawys raise with those hands?

A lot of players call with AA, KK, QQ and AKs maybe 25% of the time. Doing this makes you a lot less predictable. Suppose the flop comes J74. If someone always raises AA, KK, QQ and AKs, you know that they won't have an overpair on J74, because they would have raised preflop with the starting hands that make an overpair. But if they mix in a few calls with those hands, well, it's a lot more difficult for you to narrow their range and deduce what possible hands they may have.

Anyway, what does this mean for Premium Poker Tools? AA can either be in your opponent's range, or not be in your opponents range, right? So how can we tell the app that our opponent only has this in his range 25% of the time?

You can use the hand weight selector to do exactly that! If you command + click AA, you will see a slider. Sliding the slider tells the app how often that hand is actually in your opponents range.

If you want to apply the same weight to multiple hands at the same time, you can use the "Set hand weights" button like so:

Future streets

So far we've only examined all in situations. This kept things simple. In these situations, once you decide to call, there are no more decisions left to make for anyone. You just wait for the dealer to deal until the river, and then you see who wins.

In reality, for most situations you're in, if you decide to call, the hand will not be over and you'll be faced with more decisions to make on future streets (eg. after the dealer deals the next board card(s)). There are various implications of this, and these implications mean that pot odds and equity are just the starting point of your analysis, not the end.

But even with that said, equity is still a great starting point. You usually won't deviate too much from what the equity analysis says. You usually start off with what the equity analysis says and then adjust slightly - perhaps 5% or so - based on other considerations. But sometimes other considerations will be strong enough to require a larger than 5% adjustment.

Imagine that you are playing against an aggressive opponent. You flop a flush draw. With a flush draw, you will make a flush about 36% of the time by the river. Suppose that your opponent bets the flop, you have 2:1 pot odds, and that you only "need" 33.3% equity to justify calling.

Given that your opponent is aggressive, even if he was bluffing on the flop, he is likely to continue bluffing on the turn. This may mean that you'll have to fold. Which means you won't get to see the river. Which means you aren't fully getting a chance to see if you make your flush. That really changes things. The equity stuff we've been talking about is referring to the chance that you win the pot assuming that everything just stops and we deal to the river right now and see who wins. In reality, sometimes you get bluffed before you get a chance to see the river. That's something to consider.

Another thing to consider is called implied odds. Suppose that you do make your flush. If so, you're likely make a lot of money on future streets. So even if you don't "have enough" equity right now, once you take in to consideration that you'll win a ton more money on future streets, perhaps it becomes worth calling anyway.

On the other hand, what if you have something like top pair. Top pair seems like a great hand, but this can be a blessing in disguise, because when your opponent makes a straight or a flush, you're likely to put a bunch of money in the pot and lose. This is called reverse implied odds. The idea that you're at risk of losing a bunch of money on future streets. The opposite of implied odds.

Other things to consider

Somehow, when I'm playing live poker and I mention that I'm developing this app, there never fails to be someone at the table who starts lecturing me about the fact that there's more to poker than math and numbers. (Often times the person will even make a stronger claim that poker is all about "feel" and that math and numbers mean nothing.)

I totally agree (with the first statement, not the second one in parentheses). There are other factors to consider other than the ones I've mentioned in the scenarios above. Here are some:

• Position. If you are first to act, you are at a significant disadvantage. If you are last to act, you are at a significant advantage. Adjust how much equity you "need" to justify calling accordingly.
• Skill. If you know you can outplay your opponent postflop, you may want to call with a slight equity disadvantage preflop. Maybe you know that you could float your opponent and win a high percentage of the time. Maybe you know your opponent overvalues mediocre hands and that you'll be able to extract a ton of value if you make a strong made hand. Maybe you know that your opponent folds to re-raises on the river too often.
• Your table image. Perhaps you want to call even when you mathematically "shouldn't" so that your opponents don't start to think that they could bully you around. Or perhaps you want to avoid calling when you mathematically "should" so that your opponents get greedy, try to bully you, and lose a ton of money when you do make a strong hand.
• If you're in a tournament, you have to think about how close you are to cashing out. If you're one away from being "in the money", maybe you shouldn't call if you have 55% equity but only "need" 50% equity.
• Live reads. Did your opponent start tapping his foot? Does that mean that he's bluffing? If so, that is certainly something to consider. Although, I would say that you should use that tell as information to help you narrow your opponents range, and then base your decision on the numbers, as opposed to just "going with your gut" and calling with anything.
• Fun! Maximizing my win rate and challenging myself to make the best decision every chance I get is my definition of fun, but not everyone is like that. Perhaps you find it boring to fold. In that case, if you want to call with some hands even when the math says you should fold, I won't judge you.

Hit calculator

There is kind of a lot going on with the hit calculator, so let me explain it in steps.

Suppose that you want to know how often 76s flops a straight, a flush, a flush draw, etc. The hit calculator will answer all of those questions:

The results section (with all of the checkboxes) shows you that you'll flop a straight about 1.2% of the time, a flush 0.76% of the time, and a flush draw 10.96% of the time.

Suppose that you want to see how often 76s makes a straight by the turn, rather than on the flop. Easy:

Suppose that you want to see how often 7c6c makes a flush by the river when the flop comes Ac7h4d. Easy:

Analyzing whether to bluff the flop

Ok, that stuff was just a warm up. Now let's get in to the meat of the hit calculator.

Suppose that you have Qc3c. You raise preflop, and the BB calls. The flop comes 9d4s2h. The BB checks to you.

You could easily just check behind. You totally missed the flop. You have no made hands, and no draws. May as well check, right?

Well, what about bluffing? Let's explore whether that would be a good idea in this scenario.

The formula for figuring out how often a bluff needs to work for it to be immediately profitable is risk / (risk + reward). That was a big sentence, let me explain what it means.

Suppose the pot is $10. If you bet $5 into the pot, you're risking $5 in order to win $10, so the formula to see how often a bluff needs to work is $5 / ($5 + $10) = 33.3%.

Suppose you want to bluff $10 into the $10 pot. Now you're risking $10 to win $10, so the forumla becomes $10 / ($10 + $10) = 50%.

The insights section shows you how often various bluff sizes need to work so that you don't always have to be doing the math yourself, although you should get familiar with these numbers so that it is second nature to you when you're at the table.

Wait - what do you mean by immediately profitable? What's the difference between that and just regular profitable?

Great question. Let's go back to the situation we started with where we have Qc3c and are considering whether or not to make a $5 bluff into the $10 pot. If our bluff worked 34% of the time, it would be profitable play in the long run, even if we never got lucky on future streets.

Sometimes we may make our bluff and get called when we're losing to someone with, say, A9 for top pair top kicker. When that happens, we may sometimes get lucky and catch a queen on the turn or river, giving us a higher pair than the guy with A9. The immediately profitable calculation is saying, "Dude, even if you never got lucky, this bluff would still be profitable if it works just 33.3% of the time." Of course, you will get lucky sometimes, so in reality the bluff probably only needs to work like 25-30% of the time or so.

A good approach is usually to start off figuring out what the immediately profitable equation says, and then adjusting for other things. For example, we don't have too many outs with our Qc3c in this situation, but if we had a flush draw, we would have a much larger chance of getting lucky and outdrawing our opponent, and so our bluff might only need to work 20% of the time for it to be profitable in the long run, rather than the 33.3% that the immediately profitable equation told us. Also make sure that you adjust for things like implied odds and position.

Now let's return back to the question at hand of whether we should attempt a bluff with our Qc3c against our opponent who called our preflop bet and checked to us on the flop. Let's be a little bit conservative and say that a half pot bluff of $5 needs to work 30% of the time against our opponent. In reality, we have position on our opponent so I may go down to 25% personally, but let's play it safe for now. The obvious next question is how we can know how often this bluff will work.

First, let's set our opponents range. For someone who called preflop and checked the flop, I'd say something like the top 30% of hands except AA, KK, QQ and AKs (assuming they'd raise with those) is reasonable (if we wanted to be more precise, we could set some hand weights, but let's leave that for another day).

Next, let's set our cards (Qc3c):

Next, let's set the flop to 9d4s2h:

Now let's run a simulation and see how often our opponent's range flops various hands:

We're getting somewhere...

Next, let's ask ourselves what our opponent would call our $5 bet with. Middle pair? Top pair? Flush draws? Open ended straight draws? Gutshots? Overcards?

Alternatively, we can ask Premium Poker Tools what it thinks our opponent would call the bet with. Clicking "Set checkboxes to default" and then "Tight" is basically saying "Hey Premium Poker Tools, what do you think a tight opponent would call a bet with on this 9d4s2h flop?".

Premium Poker Tools is telling us that our opponent would "hit" this flop 79.01% of the time.

In other words, this is saying that our opponent would call or raise our bet 79.01% of the time. Which means that he'd only be folding 20.99% of the time, which really doesn't seem like enough to justify a bluff.

But maybe we don't agree with Premium Poker Tools' assumption that a tight player would call with two overcards on this board. If so, we can uncheck that checkbox and see that now the hit percentage is just 36.69%.

That means that our opponent would be folding 63.31% of the time, making a bluff totally worth it.

This is a great example of the fact that the hit calculator can't actually tell you what to do, and that it is just a tool to help you figure out what to do. You need to observe your opponents carefully and make educated guesses as to what they would be calling/raising with in different scenarios.

You also need to take other things in to consideration. For example, some players have a leak in their game where they call a lot of flop bets (called a cbet when the preflop raiser bets the flop when checked to), but fold on a lot of turn bets (betting the flop and then the turn is called "two barelling"). In that case, you're happy to see them call you on the flop. That's just more money in the pot for you to win when they give up frequently on the turn.

Analyzing whether to bluff the turn

Speaking of which, let's suppose that our opponent calls our flop bet and the turn comes Kd. Let's analyze whether we should try bluffing our opponent on this turn.

If our opponent calls the flop bet, that is information that we can use to narrow his range. For example, if we say that he wouldn't call flop bets with two overcards we can eliminate the hands like KTo from his range.

Doing so is really, really easy - just click the "Narrow range" button!

Next, let's set Kd as the turn card and simulate to the turn.

And let's redo the checkboxes now. We can't assume that he will continue with exactly the same stuff as he would on the flop.

Again, we can check off the checkboxes ourselves, or we can just ask Premium Poker Tools. Let's start off asking Premium Poker Tools what a tight opponent would continue with on the turn:

Wow, looks like only 17.86% of hands would continue. That would make bluffing immensely profitable. But what if our opponent isn't so tight, what if he is more straightforward. Let's ask Premium Poker Tools how that changes things:

Now 54.3% of hands hit. That's a big difference. So this is a scenario that really requires some skill to make a good educated guess as to what our opponent would continue with on this turn.

Analyzing whether to bluff the river

Let's suppose that we bet the turn, our opponent calls, and the river comes Jc. Should we try bluffing a third time on the river?

To analyze that question, we're going to take the same steps as before. First, let's narrow our opponents range. Since our opponent called the turn, we know that he doesn't have any hands that would have folded the turn.

Next, let's set Jc as the river card, and simulate to the river:

Now let's ask ourselves what we think our opponent would call, say, a half pot bet with. We can start off by asking Premium Poker Tools, and then adjusting it using our judgement if necessary.

This time the checks happened to have been already set to what Premium Poker Tools wanted to set them to.

Alright, so it looks like our opponent will only be calling or raising about 37.29% of the time, which means that he'll be folding 72.71% of the time, which is more than enough for bluffs to be immediately profitable.

Bluff raising

We have been analyzing "vanilla" situations where our opponent checks to us and we are considering whether or not to bluff. But what about situations where our opponent bets and we want to consider a reraising them as a bluff?

The math is the same. Let's go through an example. Suppose that the pot is $20. Your opponent bets $10. You are considering reraising to $40 as a bluff. How often would that bluff raise need to work?

Think about it like this: reraising to $40 is kinda the same thing as calling the $10 and then betting another $30 into what is now a $40 pot. Framed this way, we can use the risk / (risk + reward) equation to see that this bluff needs to work $30 / ($30 + $40) = 42.9% of the time in order to be immediately profitable.

Instead of doing this math yourself, you can just check out the "Bluff raising" tab in the insights section:

Again, you won't have this at the table with you so you should familiarize yourself with these numbers so that when you are at the table you can consider various bluff sizes and know how often they need to work to be immediately profitable.

Setting the flop according to a texture

If you have a hand that you played in real life, you can set the board cards and analyze the situation. But what if you are just studying poker, rather than analyzing a particular hand? The "Set flop" button is really useful for that.

This is what the set flop button and selector look like:

Let's take an example. By clicking the rainbow triple broadway option, it will set the flop to some random combination of three broadway cards (A, K, Q, J, and T in this case) that are all different suits. It won't set it to AsQdJh specifically every time, AsQdJh is just an example of a rainbow triple broadway board.

Suppose that you want to know how often to cbet a tight opponent. Well, your opponents play will vary a lot based on what the flop is, and so whether or not you should cbet will depend a lot on the flop. For example, coordinated middle boards tend to hit the preflop callers range pretty hard.

In studying the game, you can use the set flop button to quickly experiment with different flop textures.

Analyzing whether to call the river

Consider the following scenario. Your opponent raises from the button. You call from the BB with JhTd. Your opponent opens really widely from the button, so you put him on a range of the top 80% of hands.

The flop comes AcTs9s.

You check the flop, your opponent bets, and you call. Since this particular opponent would cbet almost anything, this only allows us to narrow his range slightly.

Next, the turn comes 3c.

You check, your opponent bets again, and you call. This particular opponent likes to two barell a lot, so we again can only narrow his range slightly.

Finally, the river comes 4d.

We check, and our opponent bets a third time. What do we do?

Well, the fact that he bet rather than checked is information that we can use to further narrow his range. Suppose that this opponent would only bet the river with top pair or better, and weak pairs as a bluff. With that assumption, we narrow his range, click simuate again, and see that 49.67% of the time he chooses to bet this river, he has us beat.

In this case, there aren't any ties to consider so the fact that our opponent has us beat 49.67% of the time means that we have about 50.33% equity against him, and we can use that knowledge along with the pot odds to determine whether we should call.