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This is a very important lesson and can also be quite intimidating to a lot of people as we are going to discuss Poker Math!

Texas Hold'em Introduction Rules. A single 52-card deck is used. All cards count as its poker value. Aces may be high or low. One player is designated as the dealer, usually with a laminated marker. How to calculate odds. Our betting odds calculator takes a step further and calculates the percentage probability of winning and losing.The team would win 5 out of 6 games and lose 1 of them. By converting fraction to percent, we can say that the chances of winning are 5/6 = 83.33%, and of losing 1/6 = 16.67%. Do you understand how we calculated this percentage?

But there is no need for you to be intimidated, Poker Maths is very simple and we will show you a very simple method in this lesson.

You won’t need to carry a calculator around with you or perform any complex mathematical calculations.

What is Poker Math?

As daunting as it sounds, it is simply a tool that we use during the decision making process to calculate the Pot Odds in Poker and the chances of us winning the pot.

Remember, Poker is not based on pure luck, it is a game of probabilities, there are a certain number of cards in the deck and a certain probability that outcomes will occur. So we can use this in our decision making process.

Every time we make a decision in Poker it is a mathematical gamble, what we have to make sure is that we only take the gamble when the odds are on in our favour. As long as we do this, in the long term we will always come out on top.

When to Use Poker Maths

Poker Maths is mainly used when we need to hit a card in order to make our hand into a winning hand, and we have to decide whether it is worth carrying on and chasing that card.

To make this decision we consider two elements:

1. How many “Outs” we have (Cards that will make us a winning hand) and how likely it is that an Out will be dealt.
2. What are our “Pot Odds” – How much money will we win in return for us taking the gamble that our Out will be dealt

We then compare the likelihood of us hitting one of our Outs against the Pot Odds we are getting for our bet and see if mathematically it is a good bet.

The best way to understand and explain this is by using a hand walk through, looking at each element individually first, then we’ll bring it all together in order to make a decision on whether we should call the bet.

Consider the following situation where you hold A 8 in the big blind. Before the flop everyone folds round to the small blind who calls the extra 5c, to make the Total pot before the Flop 20c (2 players x 10c). The flop comes down K 9 4 and your opponent bets 10c. Let’s use Poker Math to make the decision on whether to call or not.

Poker Outs

When we are counting the number of “Outs” we have, we are looking at how many cards still remain in the deck that could come on the turn or river which we think will make our hand into the winning hand.

In our example hand you have a flush draw needing only one more Club to make the Nut Flush (highest possible). You also hold an overcard, meaning that if you pair your Ace then you would beat anyone who has already hit a single pair on the flop.

From the looks of that flop we can confidently assume that if you complete your Flush or Pair your Ace then you will hold the leading hand. So how many cards are left in the deck that can turn our hand into the leading hand?

• Flush – There are a total of 13 clubs in the deck, of which we can see 4 clubs already (2 in our hand and 2 on the flop) that means there are a further 9 club cards that we cannot see, so we have 9 Outs here.
• Ace Pair – There are 4 Ace’s in the deck of which we are holding one in our hand, so that leaves a further 3 Aces that we haven’t seen yet, so this creates a further 3 Outs.

So we have 9 outs that will give us a flush and a further 3 outs that will give us Top Pair, so we have a total of 12 outs that we think will give us the winning hand.

So what is the likelihood of one of those 12 outs coming on the Turn or River?

Professor’s Rule of 4 and 2

An easy and quick way to calculate this is by using the Professor’s rule of 4 and 2. This way we can forget about complex calculations and quickly calculate the probability of hitting one of our outs.

The Professor’s Rule of 4 and 2

• After the Flop (2 cards still to come… Turn + River)
  Probability we will hit our Outs = Number of Outs x 4
• After the Turn (1 card to come.. River)
  Probability we will hit our Outs – Number of Outs x 2

So after the flop we have 12 outs which using the Rule of 4 and 2 we can calculate very quickly that the probability of hitting one of our outs is 12 x 4 = 48%. The exact % actually works out to 46.7%, but the rule of 4 and 2 gives us a close enough answer for the purposes we need it for.

If we don’t hit one of our Outs on the Turn then with only the River left to come the probability that we will hit one of our 12 Outs drops to 12 x 2 = 24% (again the exact % works out at 27.3%)

To compare this to the exact percentages lets take a look at our poker outs chart:

As you can see the Rule of 4 and 2 does not give us the exact %, but it is pretty close and a nice quick and easy way to do the math in your head.

Now lets summarise what we have calculated so far:

• We estimate that to win the hand you have 12 Outs
• We have calculated that after the flop with 2 cards still to come there is approximately a 48% chance you will hit one of your outs.

Now we know the Odds of us winning, we need to look at the return we will get for our gamble, or in other words the Pot Odds.

Pot Odds

When we calculate the Pot Odds we are simply looking to see how much money we will win in return for our bet. Again it’s a very simple calculation…

Pot Odds Formula

Pot Odds = Total Pot divided by the Bet I would have to call

What are the pot odds after the flop with our opponent having bet 10c?

• Total Pot = 20c + 10c bet = 30 cents
• Total Bet I would have to make = 10 cents
• Therefore the pot odds are 30 cents divided by 10 cents or 3 to 1.

What does this mean? It means that in order to break even we would need to win once for every 3 times we lose. The amount we would win would be the Total Pot + the bet we make = 30 cents + 10 cents = 40 cents.

Break Even Percentage

Now that we have worked out the Pot Odds we need to convert this into a Break Even Percentage so that we can use it to make our decision. Again it’s another simple calculation that you can do in your head.

Break Even Percentage

Break Even Percentage = 100% divided by (Pot odds added together)

Let me explain a bit further. Pot Odds added together means replace the “to” with a plus sign eg: 3 to 1 becomes 3+1 = 4. So in the example above our pot odds are 3 to 1 so our Break Even Percentage = 100% divided by 4 = 25%

Note – This only works if you express your pot odds against a factor of 1 eg: “3 to 1” or “5 to 1” etc. It will not work if you express the pot odds as any other factor eg: 3 to 2 etc.

So… Should You call?

So lets bring the two elements together in our example hand and see how we can use the new poker math techniques you have learned to arrive at a decision of whether to continue in the hand or whether to fold.

To do this we compare the percentage probability that we are going to hit one of our Outs and win the hand, with the Break Even Percentage.

Should I Call?

• Call if…… Probability of Hitting an Out is greater than Pot Odds Break Even Percentage
• Fold if…… Probability of Hitting an Out is less than Pot Odds Break Even Percentage

Our calculations above were as follows:

• Probability of Hitting an Out = 48%
• Break Even Percentage = 25%

If our Probability of hitting an out is higher than the Break Even percentage then this represents a good bet – the odds are in our favour. Why? Because what we are saying above is that we are going to get the winning hand 48% of the time, yet in order to break even we only need to hit the winning hand 25% of the time, so over the long run making this bet will be profitable because we will win the hand more times that we need to in order to just break even.

Hand Walk Through #2

Lets look at another hand example to see poker mathematics in action again.

Before the Flop:

• Blinds: 5 cents / 10 cents
• Your Position: Big Blind
• Your Hand: K 10
• Before Flop Action: Everyone folds to the dealer who calls and the small blind calls, you check.

Two people have called and per the Starting hand chart you should just check here, so the Total Pot before the flop = 30 cents.

Flop comes down Q J 6 and the Dealer bets 10c, the small blind folds.

Do we call? Lets go through the thought process:

How has the Flop helped my hand?
It hasn’t but we do have some draws as we have an open ended straight draw (any Ace or 9 will give us a straight) We also have an overcard with the King.

How has the Flop helped my opponent?
The Dealer did not raise before the flop so it is unlikely he is holding a really strong hand. He may have limped in with high cards or suited connectors. At this stage our best guess is to assume that he has hit top pair and holds a pair of Queens. It’s possible that he hit 2 pair with Q J or he holds a small pair like 6’s and now has a set, but we come to the conclusion that this is unlikely.

How many Outs do we have?
So we conclude that we are facing top pair, in which case we need to hit our straight or a King to make top pair to hold the winning hand.

• Open Ended Straight Draw = 8 Outs (4 Aces and 4 Nines)
• King Top Pair = 3 Outs (4 Kings less the King in our hand)
• Total Outs = 11 Probability of Winning = 11 x 4 = 44%

What are the Pot Odds?
Total Pot is now 40 cents and we are asked to call 10 cents so our Pot odds are 4 to 1 and our break even % = 100% divided by 5 = 20%.

Decision
So now we have quickly run the numbers it is clear that this is a good bet for us (44% vs 20%), and we make the call – Total Pot now equals 50 cents.

Turn Card

Turn Card = 3 and our opponent makes a bet of 25 cents.

After the Turn Card
This card has not helped us and it is unlikely that it has helped our opponent, so at this point we still estimate that our opponent is still in the lead with top pair.

Outs
We still need to hit one of our 11 Outs and now with only the River card to come our Probability of Winning has reduced and is now = 11 x 2 = 22%

Pot Odds
The Total Pot is now 75 cents and our Pot odds are 75 divided by 25 = 3 to 1. This makes our Break Even percentage = 100% divided by 4 = 25%

Decision
So now we have the situation where our probability of winning is less than the break even percentage and so at this point we would fold, even though it is a close call.

Summary

Well that was a very heavy lesson, but I hope you can see how Poker Maths doesn’t have to be intimidating, and really they are just some simple calculations that you can do in your head. The numbers never lie, and you can use them to make decisions very easy in Poker.

You’ve learnt some important new skills and it’s time to practise them and get back to the tables with the next stage of the Poker Bankroll Challenge.

Poker Bankroll Challenge: Stage 3

• Stakes: $0.02/$0.04
• Buy In: $3 (75 x BB)
• Starting Bankroll: $34
• Target: $9 (3 x Buy In)
• Finishing Bankroll: $43
• Estimated Sessions: 3

Use this exercise to start to consider your Outs and Pot Odds in your decision making process, and add this tool to the other tools you have already put into practice such as the starting hands chart.

Everyday players are sitting down at the tables and consistently making fundamental mistakes because of lack of knowledge, misinformation or failing to maintain focus.

Even just a small strategical adjustment in poker can potentially save you a huge amount in the long run.

In this article we will point out some of the best live and online poker tournament strategy tips you can use to improve your game as quickly as possible.

Tip 1: Play The Right Starting Hands

Whether it be lack of patience, or an unfamiliarity with opening ranges, many tournament poker players still open too wide. This is especially true when it comes to early and middle position opens, where there are still many opponents left to act behind who can be dealt a strong hand.

The problem is when called, wide openers are often at a range disadvantage. Often being dominated by their opponents, they are vulnerable to 3 bets since they frequently won't have a holding strong enough to continue under pressure.

Furthermore, although opening a hand like 7 ♠ 5♠ might at times not be a terrible strategy from early or middle position, speculative hands like suited connectors and gappers, as well as small pairs, work best with deep stacks behind.

These speculative hand types infrequently connect strongly with the flop, so those times they do you want to have deep stakes behind to have the potential to win a huge pot. Modern day tournament structures often only see deep stack play occur during the first few levels of play. This leads us into the next tournament poker tip, being stack size aware.

Learn which hands to open raise in MTT's - Watch lesson 6.1 from the Road to Success MTT Course. A power-packed 50 minute video below, just use one of the button options to unlock it and get instant access.

Tip 2: Be Stack Size Aware

Effective stack size plays a critical role in a tournament players success.

Having a deep stack, and therefore expanding an opening range to include a lot of speculative suited hands and small pairs is a tournament strategy that is going to be punished if a number of short stacks are yet to act behind. This most notably occurs in turbo tournaments where the average stack size is quite short.

Short stacks will be in push-or-fold mode. Being short, they don't have time to wait and will be looking to take any opportunity they can to move all-in. This high rate of all-ins will leave wide openers frequently being forced to relinquish their hands, without even having the opportunity to try to hit a nice flop. Problematic hands often include; J8s , KTo and weak Ax hands.

It's not just short-stacks that can cause a problem, aggressive players will be looking to attack wide-openers. This is especially true when a player opens with a vulnerable M8-M14 (20bb-35bb) stack. 3 bets get good leverage against this stack size, since continuing in the pot represents committing a significant portion of a players stack.

Wide openers would be wise not to commit a large percentage of their stack with marginal holdings, and so will be forced to fold, or face being in a high-risk situation. Staying aware of your own stacks utility, as well as anticipating how opponents will utilize their stacks, is an important tournament poker tip to keep in mind.

POKER TIP: If you are currently using BB to calculate stack size, here's a look at why using 'M' is a better MTT strategy.

Tip 3: Be Careful Overplaying In The Early Stages

As a stack gets deeper, the less willing a competent player will be to put their entire stack at risk since they have more to lose. It's rare to see good players all-in during the early stages of a tournament with hands like AKo or JJ preflop.

Smart players recognize that their counterparts aren't going to be risking their entire stack with weaker hands like AQo . Therefore, even a strong hand like AK could be at a significant equity disadvantage facing a deep stacked opponents all-in range. Could you fold QQ here?

Rather than putting in an extra raise, often times just calling with even very strong hands in the early stage of a poker tournament has great benefits.

• Allows your opponents to continue with hands they were folding to a re-raise that you have crushed.
• Disguises the strength of your hand and keeps you unpredictable.
• Prevents you from getting all-in facing a super strong range where often times you're crushed.

Tip 4: Continuation Bet Aggressively But Not Always

Players have learnt the value of c-betting, but it's a strategy that is often misapplied. Being the preflop aggressor shouldn't lead to a mandatory c-bet and double barrels.

This is especially true in multi-way pots yet players continue to make fruitless c-bets with weak holdings into multiple opponents.

Even in heads-up situations, key factors to consider include;

• How does the flop texture interact with players ranges?
• Who has the strongest range?
• Who has nut advantage (the biggest share of super strong hands)?
• How passive or aggressive is the opponent we're facing?
• How does the stack size/SPR allow us to operate on the flop and future streets?

The following hand illustrates the effect nut advantage can have on profitable continuation betting and how it applies to this tournament poker tip:

Tip 5: Be ICM Aware

The Independent Chip Model or ICM, is a great model players use to make more profitable decisions when deep in a tournament and especially at a final table.

Unlike in cash games, chip values fluctuate depending on the stage of the tournament and the competing opponents stack sizes. At it's most extreme, ICM strategy can make A♠A♣: an easy fold preflop.

Imagine a situation in a satellite where 9 players get a World Series of Poker entry and there's 10 remaining. The action folds around to a player with 100,000 in tournament chips who moves all in from the small blind. You're sitting in the big blind with A♠A♣: and also 100,000 in chips. You look around and see a few opponents with only 1000 chips left, which is the size of the current big blind. Obviously one of these short stacks is likely to bust very soon.

Obviously one of these short stacks is likely to bust very soon. Moreover the chance that they collectively out survive your 100,000 stack is extremely remote. You'd likely be a 99% chance to get a WSOP entry, so why would you call with your A♠A♣ and risk busting next around 20% of the time?

Aside from calling too wide in spots when the most profitable strategy is to proceed tightly, the opposite can also be true when it comes to pressuring your opponents. ICM allows players when they have the opportunity to assert pressure on there opponents stacks, to go ahead and do so liberally, since thinking opponents counter-strategy is to play a tight range of hands.

Here's an example of how drastically a hand range can change when the opportunity to assert pressure at a final table exists. 5 of the 6 remaining players at the Pokerstars Sunday Millions have 15bb's, whilst the UTG player has a short 2bb stack. Since the 15bb stacks wants to avoid busting out next and missing out on a large pay jump before the immanent bust out of the 2bb stack, the small blind can adjust their all-in range. Instead of the profitably 57% all-in range in normal play, they can move all-in with 100% of hands to apply pressure on the big blind.

Whilst the big blind should adjust their calling range from the regular 36% to just 10% of hands to account for the ICM effect in play.

The PokerNerve Road to Success course teaches players how to master ICM situations, which is key to tournament poker success since ICM comes into play as the prizes become significant. If there was only one tournament poker tip that you take away from this article, it's that you need to know ICM!

Tip 6: Bet The Appropriate Size

Strong players are capitalizing on their opponents tendencies to bet too big or too small in a number of different situations. With some similar considerations to that of continuation betting, when selecting a bet size important aspects include;

• Which player's range does the board texture favor?
• Who has the greatest nut saturation?
• How does SPR influence our betting strategy

There are many great articles online about bet sizing. You should be sure to check out ThePokerBank's and the Pokerology's to learn more about this tournament tip.

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Tip 7: Take Equity Realization Into Account

Poker Tournaments Online

Possibly due to the popularity growth of Twitch, many poker players approach to big blind play has evolved. The current trend is to defend the big blind with virtually any 2 cards, as some top pros elect to do, and the justification for this is taking advantage of the excellent pot odds being offered.

While the inclusion of antes combined with commonly seeing a small open raise size does offer the big blind generous pot odds, this has led to a fundamental flaw in the way many players approach big blind play in poker tournaments. The key concept overlooked, is equity realization.

Equity realization reflects a players ability to take a certain hand, and win their share of the pot, frequently enough, to make it profitable in the long-term. Although some top pros have the ability to win their equity share of the pot even out of position, less skilled players rarely do. This leads to a large chip loss in the long run.

It is quite difficult to realize of your equity when out of position, with no initiative and a weak range. This means them glorious odds you are being offered aren't quite as good as you think!

The following article explains this crucial tournament poker tip in more detail; Equity Realization.

Tip 8: Don't Miss Double And Triple Barrel Opportunities

'One and done' is the plight of many aspiring tournament poker players. Everyday at the tables I see players missing profitable opportunities to double, or even triple barrel. Understanding what turn and river cards are advantageous to a players range, along with opponent tendencies, are crucial parts of a winning barreling formula.

The most common scenario at the table, is a heads-up pot where the big blind calls an open-raise. And this happens to be a great spot to barrel. Big blind defenders have a wide range, and it's important to pressure this wide range, especially on only partially connected board textures with one or multiple high cards.

RedChipPoker has a great article on spotting profitable double barrel opportunities which you can read here: THE +EV DOUBLE BARREL GUIDE

Tip 9: Check-Raise More Flops

The biggest difference between the current tournament population, and the future generation, will likely be their approach to check-raising the flop. This opportunity typically occurs in a heads-up pot, after defending the big blind verse an opponents raise.

Currently, MTT players only check-raise the flop in this situation around 7-8% of the time, when closer to 20% is a more optimal strategy. On certain flop textures, check-raising close to 25% of the time is an extremely profitable strategy. And if players are getting out of line with their c-bets, then check-raising at an even higher frequency could be a profitable exploit.

By giving up too easily on a wide range of board textures, or taking a more passive approach and simply calling, c-betting can be done with reckless abandon. However, by selecting a nice mix of check-raising hands, combining some strong hands with some good semi-bluffing candidates, a check-raiser can become tricky to play against and exploit the average players tendency to over c-bet.

POKER TIP: Applied correctly and check-raising becomes a super powerful weapon in your arsenal leading to more profitable poker results. But also think beyond the flop, there's plenty of check-raising opportunities you may be missing. This video demonstrates an interesting turn check-raise situation.

We discuss check raising strategy in more detail in our post over on unfeltedpoker.com.

Tip 10: Develop A Good 3betting Strategy

Whilst 3 betting aggressively is a strategy many players employ, especially in online poker circles, failure to apply optimal 3 betting strategies has certainly led to a lot of spewy poker. Simply attacking opponents who are suspected of opening wide doesn't cut it in the modern poker world.

Players have learnt to deal with 3 bets more profitably, by mixing in some calls with timely 4 bets. Moreover, the role stack size plays when it comes to 3 betting it still largely misunderstood by much of the poker community.

Sure there are certain stack sizes where 3 bets gain a lot of leverage, but how about the role blockers play? And when is 9♦7♦ a better 3 bet candidate than K♦T♠ ? These are just some of the considerations when it comes to a profitable 3 betting strategy. See how to design strong 3betting ranges in this article by Donkr.

Bonus Poker Strategy Tip: Avoid and Deal with Downswings

As a poker player you want to earn your money as easily and as stress-free as possible right? Well, understanding ROI, variance and bankroll management can help (see TopPokerValue's article on bankroll management).

All poker players at some point experience downswings. In some cases, this can affect their play, volume or state of mind.

You'll be miserable, hating poker, playing less and earning less per tournament as your play will suffer.

Along with finding ways that work for you to keep a positive mindset, taking pro-active steps can help keep you confident by knowing you are dealing with the situation like a professional whilst at the same time taking positive action to get back on track and winning.

What is ROI and variance?

Every tournament you enter has an EV associated with it. So if you enter a $10 tourney, as a good player maybe you have a 30% ROI, so you make $3. So it doesn't matter whether you brick that tourney or win it for $5000, you make $3 in the long run.

Now, of course, you don't make $3 each time. 80-85% of the time you lose that $10, some percentage of the time you win a little bit, and some very small percentage of the time you win a lot. How small those ‘small percentages’ are primarily depends on not only your skill edge, but also the field size which is an extremely important concept that is often ignored.

Variance is a factor of two things:

1) Your edge

2) The field size

Example 1)

You play the Hot $55 which has $30K guaranteed, every day for a year on Pokerstars. It has 1600 runners and you have a 5% ROI, because turbo ROIs are small. Your average yearly profit is $605 however you will lose money on the year 55% of the time.

Example 2)

You play a $20 tourney with $3K guaranteed on a softer site every day for a year. It has 200 runners and you have a 30% ROI, because it's a normal speed tourney and you’re against an easier field. Your average yearly profit is $2400 and in this case you lose money only 12% of the time.

A lot of people would look at those two tournaments and make a decision based on the buy-in and 1st place prize money as to which was better to play, and it would be grossly wrong. Once you accept all the above, you realise that the 'up top' number is largely meaningless.

Yes, on the same site bigger fields may mean a lot of fish have registered to play, but you'll find a lot of small field, soft, non-peak hour tournaments have a great pro-to-fish ratio and hence are great value. Of course once you consider other sites that have smaller fields, you'll often find they are a better choice than what might be running on Pokerstars.

So what can you do?

Chances Of Winning Poker Tournaments

When players start losing money and along with that, confidence, not only does their game deteriorate but they often compound that problem by failing to make rational decisions. Often losing players, or players on a downswing, go 'bink chasing' and decide to take a shot to win all their money back in one tourney. Or load up some quick $82 hyper-turbos to try to turn it all around quickly.

People get overly fixated on what's 'up top' and wanting to score big in one tournament. That’s a sure-fire strategy to fuel a down swing. If your house got knocked down would you try to slap it back up in a week? Take that opportunity to rebuild a better, stronger house.

Make sure you're adding in some study and keep focused (see Sky's Matsuhashi How To Study Poker series), and stay fresh and positive as you approach each session. Be smart and get back into profit quicker instead of enduring a 6-12 month variance rollercoaster!

Closing Words On Tournament Poker Tips

Poker is a multi-faceted game which makes it fun but challenging. Challenge yourself to factor in the relevant concepts, and make more profitable decisions. Tighten up from the big blind, and in general around the table. This tip often quickly improves a new players results, or those that have a got a little sloppy with their play.

Calculate stack size using 'M'. Always be aware of your own, and your opponents stack sizes so you don't get yourself caught in awkward situations. One awkward situation that often comes up is when you hold an overpair to the board and an opponent puts the heat on you. Don't be afraid to make big lay downs to preserve your stack, especially in the early levels.

Be aware of your cbetting frequency. There's no need to waste tournament poker chips cbetting every time, especially when the pot is multi-way. Pick your spots to make profitable plays. Remember when it comes to the final table, regularly profitable playing ranges might alter due to the payouts. ICM is the key when it comes to those final big decisions.

Another key to success is knowing when to fire multiple bullets at your opponents. Barreling, especially against a wide big blind range can really help increase your non-showdown winnings. Finding ways to accumulate chips without always having the best hand is what top players do. This is why check-raising and having a good 3 betting strategy is so important. Correct use of these strategical concepts and the other tips outlines will get you winning more at the tables.

Now that you've acquired some great holdem tournament strategy tips to help you achieve MTT success, go out there an implement them!

One of the quickest way to improve your poker game is to take on a poker coaching, a course or join a poker training site; if that is something that interests you be sure to check out the PokerNerve road to Success Course for some advanced poker tournament strategy or you can check out HowToPlayPokerInfo's guide on poker training & poker courses to find the right option for you.

Any other poker tournament strategy tips? Leave them below in the comments, we would love to hear them!