I’ve worked with several students recently who were interested in furthering their understanding of some of the mathematical aspects of MTT poker. This is always something I like hearing, since I’m a firm believer that we as poker players should try to support our ideas about poker strategy with math as often as possible.
With this in mind, I’d like to present a few ideas and strategies I’ve developed which might help those of you struggling with certain mathematical elements of the game to put in place some specific training and studying processes that will push your game forward in this respect. They’re relatively simple and I can’t claim credit for any kind of revolutionary thinking here, but they’ve helped me throughout my career, and I hope they can do the same for you.
Equity training
This is probably the simplest form of math training – indeed, it’s so simple that more than one equity calculator available nowadays actually has an in-built function allowing you to do a version of this for yourself without any extra effort. However, a regular equity calculator is all you need for my version, which I think is a little more useful than simply knowing the equity of one hand versus another – after all, we never know what hand our opponent has, we only know their range.
In order to train yourself this way, first pick a random hand in the deck – it’s probably a little more productive if this is a hand that’s at least somewhat playable, since it’s not that useful to know exactly how trashy all your trashy hands are. Write the hand down somewhere. Now, use a random number generator (there are plenty available online) to generate a number between 1 and 100. Write that number down too, next to the hand you chose.
Once you’ve done that, load up your favourite equity calculator (I like HoldEq, an add-on for Flopzilla), and enter your chosen hand into player 1’s range. Then, for player 2’s range, take the random number you generated, and type it in as a percentage of hands. At this point, take a moment to write down your estimate for how much equity that hand has versus that range (note: you can also do this for range vs range calculations, if you pick two random numbers instead of a hand).
After that, all you have to do is run the equity calculation, and see how close you got. If you got within 1% either way (or 2% either way if you want to be generous), then give yourself a point. Run ten calculations, and see how many points you get out of 10. Train yourself this way before each session, and once you get to the point of being able to get 8 out of 10 or more consistently, you’ll be on your way to an excellent understanding of how different hands and ranges interact, especially if you’re able to do it in terms of range vs range.
Flop training
For this one (and for many other reasons) you’ll need to get yourself a copy of Flopzilla. It’s one of the most useful pieces of poker analysis software available out there, so I recommend getting hold of it regardless, but it’s particularly useful for this type of analysis. This will give you a solid grounding and understanding of how well certain hands and ranges hit the flop.
It’s very straightforward – make a list of ten random hands. You can click Flopzilla’s ‘Random’ button if you want to make it truly random, or you can pick hands you find difficult to play. Then write down your guess of how often each of those hands makes a pair or better, gutshot or better, flushdraw, or some combination of all of those, on the flop.
Next (and this part is important) make sure that the hand categories you’re checking for – top pair, middle pair, gutshot, pair+flushdraw, etc – all have ticks next to their names in Flopzilla’s list. Otherwise, they won’t be included in what constitutes ‘hitting the flop’. After that, all you need to do is choose each hand from the grid on the left, wait a few seconds, and Flopzilla will tell you how often this hand hits the flop.
Just like the previous exercise, you can give yourself points for how often you’re within 1-2%. You can also use a random number generator to choose a range (expressed as a % of overall hands from the top down) and judge how often that range hits the flop, for a more advanced version of the exercise. Developing your instincts for how well certain hands hit the flop is going to be pivotal in deciding which hands you should actually go to flops with – it’ll definitely help in flat-calling preflop and defending the big blind.
Nash preflop shove training
This requires a program capable of running Nash preflop shove calculations, such as CardRunnersEV, or my personal favourite, HoldemResources Calculator. All that’s required for this one is to pick a specific hand from your database where shoving all-in preflop was a realistic option for you, and take a guess at the Nash equilibrium shoving range that you could have shoved in that spot. Run it through the calculator, and see how close you got. Pick ten hands from your database, make ten guesses, and see how you got on – you know the drill by now.
You can also take this one step, or even two steps further if you do have HoldemResources Calculator – you can input your opponents’ perceived calling ranges and make guesses at how far from the Nash range you could deviate in that spot in order to exploit them. For the second step, you can run an ‘Advanced Hand’ as the program terms it, and figure out your Nash equilibrium or exploitative raise-folding or raise-calling ranges, and make estimates of those as well. You can also reverse the equation and make estimates of your calling ranges or 3-bet shoving ranges to create the opposite scenario.
The importance of the numbers
The bottom line is that basically any poker program that can do mathematical calculations can be turned into a way to help yourself become more familiar with the math on a rote basis. Obviously knowing this information offhand isn’t necessarily that useful during play, but you’ll find that your understanding of how well certain ranges play against others, how hard certain hands or ranges hit the flop on average, or how wide your Nash shoving range should be in any given spot begins to develop exponentially once you specifically train for it.
In the end, there’s no way to learn the solution to every spot in poker, obviously, and sometimes your instincts for what your opponents’ ranges actually are will be inaccurate. But your instincts are what drive your mathematical decision-making at the tables, and while you may not be able to work your way through complex calculations effortlessly just yet, spending time on improving your understanding of the mathematical side of the game will pay dividends in the long run, even if it’s just a case of making your ballpark estimates a little more accurate. Keep working at it – you’ll get there.
