Top 10 drills to improve your poker math skills

Mastering poker math is crucial for long-term success and gaining an advantage over your opponents.

From probabilities to expected values, ranges, and odds, we will cover the top 10 poker drills you can practice today to improve your math skills. Let’s jump right into it.

10. Mastering poker hand rankings
The recent controversy in the WSOP Circuit event where the losing hand was awarded the pot, and that player ended up winning the tournament should never happen. While this seems obvious, you are always responsible for identifying what you have and protecting your hand.

Therefore, knowing what beats what in poker is the first thing you need to master, and you should be able to identify it in the middle of the night.

While this is not an actual drill on its own, make sure to play around with hand rankings to be able to identify the winning hand in the blink of an eye. Whether it is flush vs a straight as in the infamous hand, or a kicker for the same combination, only you are responsible for knowing what you have.

Be able to count your outs quickly. (photo by Flickr)

9. Counting outs
Outs are cards that can turn your hand into a winning combination. Therefore, you need to be able to count them quickly and always know how many actual outs you have when you are behind.

For example, if you have a flush draw on the flop against a set, you have 9 outs to make your hand. If you are holding Ah7h on Kh9s4h, it means that from a total of 13 hearts in the deck, there are only 9 of them left, and since you know your opponent is holding a set, the only way you can win the hand is if you hit another heart.

To simplify the math, you can use the rule of 2 and 4 to get an approximation of how likely you are to improve. If one card remains to be dealt, your probability of hitting your draw is 18% (9 outs x 2), and if two cards remain to be dealt, it is around 36% (9 outs x 4).

While this is not an exact percentage to the letter, it is fairly close. Thus, you can use this shortcut to approximate when you are in the middle of the hand and learn how many outs you have in common hand matchups.

8. Drilling optimal pre-flop ranges
Pre-flop ranges are the easiest thing to master to perfection and will probably have the biggest impact on your overall win rate.

For this, you can study GTO pre-flop charts or download the solver and play unlimited drills for all possible situations until you know what hands to open from each position, how to play against 3-bets, and how to put pressure yourself.

Knowing your pre-flop ranges by heart will help you avoid many costly mistakes post flop and put you in many advantageous situations.

7. Understanding ICM implications
If you are playing tournaments, then understanding ICM (Independent chip model) is essential.

Since chips in tournaments do not have exact monetary value as in ring games, this model helps you determine the value of your stack based on the prize pool distribution at any given moment in the event.

Knowing your stack value will help you make better decisions near prize jumps or tournament bubbles and prevent you from making costly mistakes.

For example, if you are the second biggest stack with 50BB at the final table and face a shove from the chip leader while all other players have 5BB on average, you need to fold pretty much all of your hands, even if it is a +EV call chip wise.

This is because preserving your stack here and waiting until other short stacks bust is a priority since you will get the pay jumps, and risking getting eliminated here does not make any sense.

Unfortunately, there is no easy way to run these calculations while playing, so you will have to study it with dedicated software like ICIMIZER or other tools that allow you to input chip stacks and payout structure and then show your stack value based on ICM so you can make proper decisions.

6. Short hand strategy
Following up on the previous point about playing tournaments, mastering shower stack play is essential for being a successful tournament player.

The best way to do that is to study push fold charts extensively since almost all of your most important decisions will likely be made with a few chips behind.

When tournaments reach the late stages and the stacks get shorter, each decision can be crucial, so you better know for sure which hands to shove and when to call to maximize your EV.

5. Knowing your expected value
Expected value is the best way to determine the profitability of each specific play. Whether you decide to call, bet, raise, or fold, you can calculate the value of each of these actions based on your expected results.

For example, let’s say you are facing a $50 bet on the river in a $100 pot and estimate that you have a 30% chance of winning if you call. In this situation, your EV would be calculated by multiplying your chance of winning with the amount you stand to win and deducting the amount you lose by folding with a 70% chance in this case.

EV = (0.30 x $150) - (0.70 x $50) = 45 - 35 = $10

If the EV is positive, you are making money with this play. If it is negative, you are losing, and you should avoid it. The best way to train this is to get the solver and study the outputs yourself.

4. Pot odds calculations
Pot odds can help you determine whether calling a bet is profitable, and this is a concept you should know well to make math-based decisions.

You can use a poker odds calculator or do the math manually, for which you will need to calculate the ratio of the current pot size to the size of the bet you must call.

For example, let’s say the pot is $100, and your opponent bets $50, making the total pot $150. You must put in $50 to call and will take down $200 pot if you win, meaning you have 25% pot odds.

If you think you will win the hand more than 25% of the time, you need to call, and if you think you will win less often, folding is the preferred option.

3. Understanding implied pot odds
While implied odds calculations are a bit less math-based than others mentioned here just because there is no way to know exactly how much you can find in the future, it is still an extremely valuable concept to master.

To put it simply, implied odds are an estimation of how much money you can win on following streets if you improve your hand.

Let’s say the pot is $100, and your opponent bets $50, making the total pot $150. You have a flush draw, and you estimate that if you hit your flush, your opponent will call another $100 on the river when you move all-in.

To calculate this, you need to divide the amount you need to call by the total size of the pot based on your assumption that the player is going to call when you hit your hand. In this case, it would be $50 / $250 = 20%. If your hand has more than a 20% chance of improving, then calling here is justified based on the implied odds.

Work on post flop equity calculations. (photo by Flickr)

2. Hand equity calculations
Learn how to estimate hand equities by analyzing common situations. You can start pre-flop by seeing how much equity you would have with a pair against overcards, how suited hands change your equity, or look into common pre-flop all-in situations to see when it makes sense to commit all of your chips.

Many tools, such as various solvers or even simple Equilab programs, will help you learn this part fairly easily.

Once you have a good understanding of the pre-flop matchups, move to the post flop and start working on equity calculations on different boards and with various hands to grasp this concept.

1. Hand vs range equity
Arguably, the most important concept to master is being able to put your opponent on an actual range and understand where you stand against that range with your particular hands.

Since you have no chance to know what your opponent is actually holding in the real game, your best bet is to guess what hands he would play in that particular way and play against a combination of those hands.

If you are able to accurately assign ranges to your opponents, you will always know whether you should fold, call, or raise their bets based on your hand and perceived range.

To practice this skill, try to concentrate on the game and always guess what hands your opponent can have, even when you are not involved in an actual hand. Then just check whether you were right at the showdown and do it again in the next hand.

This practice will help you get much better fast, and you should start seeing results.