Although it might seem to be an impossibly complex and daunting to the untrained observer, in reality poker essentially amounts to solving a big mathematics problem. There will always be a finite number of combinations, rules and options available to you in any round of poker, which means that if you can learn to understand and apply the mathematics underpinning of poker you have a far better chance of being the one who comes out on top.
Looking first at odds, maths can be applied both to odds and outs and pot odds in poker. In the case of the former, this is relevant if and when you see a flop, as you will want to be able to work out the odds that you or the other player can make a hand of cards better via an ‘out’ card.
A frequent circumstance during a game where this will apply is when you have two cards of the same suit in your hand and another two of that suit are on the flop. You have four of the cards for a flush and require one more from the same suit to complete it – with nine remaining. Thus in poker maths terms you have nine ‘outs’ available for completing your flush, from a ‘four-flush start.
Moving on to expected value, this means how much on average you can expect to lose or win during a hand. The aim is to use the strategy that offers the highest expected value and you work it out by multiplying what the results of each possible outcome will be by the likelihood of them happening, before adding them together.
Percentages is another aspect of poker where maths is extremely relevant. To use an example, if the pot on the table is currently worth $1 million and you hold a hand of cards that has a 20 percent chance of success, only for your opponent to bet $1 – in this situation should you fold or call his bet? The correct answer is that you should call, because you only stand to lose $1 while having a 20 percent chance of winning $1 million. The percentage is not that high in your favour, but high enough to be worth the bet due to the low betting amount. Maths can also be applied to improve your poker bluffing skills – although the common belief that a bluff must succeed more than 50 percent of the time is not strictly true. The correct equation is that the total pot percentage you invested equals the how often your bluff needs to work. Thus in a situation where there is a $100 pot and you are bluffing for $50, you need to be successful a third – or 33.3 percent – of the time.
Game Theory Optimal
Finally there is game theory optimal strategy, which can be applied to every single poker scenario to ensure can never end up the loser of the course of game and derives from the mathematics work of John Nash. A good example of it applied to poker would be if your opponent only called when he held pocket aces in Texas Hold’em. In this situation you would know that he had these cards every time he added money to the pot and would opt to fold in response. It is less likely than other situations described here, as people simply do not play poker according to GTO strategies.
The trick now is to go and sharpen up your maths skills so that you can in turn improve your skills at the poker table!