Mathematicians look at poker in a very cold and hard calculating way which isn’t always an accurate representation of what is happening in reality. For example if someone had raised before the flop and you had called and the flop came 8-5-2 and you asked a mathematician to work out the probability that their opponent held a set then they would probably work it out like this. The odds of being dealt a pocket pair at all are 17.0 or 16/1 and the odds of being dealt a specific pocket pair are 221.0 or 220/1.
There are only three specific pocket pairs that can make a set and so dividing 220 by 3 gives us 73.33 which is just over 73/1. Now clearly this is not correct and the odds are too high for one simple reason. This is because the odds of being dealt a pocket pair or any specific pocket pair are derived from the entire spectrum of possible hands. But as poker players then we know that our opponent will not be holding many of those hands when they raise. This is why it is important to try and ascertain our opponents ranges because if we can do that or go some way towards doing that then this then turns into odds and probabilities of them holding certain types of hand.
Taking this to an extreme and let us say that our opponent only ever raised pre-flop with pairs (clearly not correct but keep with me). There are only 13 possible pairs and so the odds in this instance of flopping a set are only 4.33/1……much different than 73.33/1. However the true figure will be based on their likely range which will fall somewhere between only raising pairs to playing 100% of their range.
