I had three topics to write about. All were kind of negative towards some else in the poker realm. Nothing like cheating, not even dubious/shady practise or unethical. One person had a bad take trying to sell their course. From a second author the contibution was lazy. The last one delivered, in my opinin, low quality. Low quality when you take into consideration that the creator charged additional money. But I might not have been the target audience. I don't sell anything and nobody would gain anything after I convinced people to agree with me.
Instead go trough the book I borrowed. It begins with set theory.
There is a set that contains all river cards. {...}
We are holding A♥:K♥:
We could create the set of card needed to make top pair {A♦:A♣:A♠:}.
Or top pair with top kicker {K♦:K♣:K♠:}
When we think it's enough to hit a pair to counter opponent's hand we can add those two sets because they don't contain the same elements.
{A♦:A♣:A♠:} OR {K♦:K♣:K♠:} = {A♦:A♣:A♠:} + {K♦:K♣:K♠:} = {A♦:A♣:A♠:K♦:K♣:K♠:}
On the other hand if we think a flush or a straight is needed.
flush = {Q♥:T♥:9♥:8♥:6♥:5♥:4♥:3♥:2♥:}
straight = {Q♥:Q♦:Q♠:Q♣:}
We can't just add flush + straight because then there would be {Q♥:Q♥:} as a subset. We have to subtract {Q♥:} which is flush AND straight.
flush OR straight = flush + straight - flush AND straight.
{Q♥:T♥:9♥:8♥:6♥:5♥:4♥:3♥:2♥:} OR {Q♥:Q♦:Q♠:Q♣:} = {Q♥:T♥:9♥:8♥:6♥:5♥:4♥:3♥:2♥:} + {Q♥:Q♦:Q♠:Q♣:} - {Q♥:T♥:9♥:8♥:6♥:5♥:4♥:3♥:2♥:} AND {Q♥:Q♦:Q♠:Q♣:} = {Q♥:Q♦:Q♠:Q♣:T♥:9♥:8♥:6♥:5♥:4♥:3♥:2♥:}
In the first example the AND would have been {A♦:A♣:A♠:} AND {K♦:K♣:K♠:} = {}.
A or B = A + B - A and B works in both cases.
Afterwards (if all elements are as likely) we simply can divide the sizes of the sets. {A♦:A♣:A♠:K♦:K♣:K♠:}/{...}to get the probability.