the essential probabilities to know

it is not necessary to know all the probabilities in poker but some remain essential.

for example:
When you have a pair in hand, you have a 1 in 9 chance of finding a set on the flop.

According to you, which ones to know imperatively ?

When we have JJ the chances of a bigger card appear on the board are 57% chance of TT of 69%. I find it very interesting because JJ causes a lot of discussion about how to play.

Soloman's Rule or The Rule of 2 and 4.

When you have a pocket pair you're actually about 1 in 8 (not 9) or 7 to 1 against to flop a set.
If you need one card for a flush you're about 4-1 against (1 in 5), that's a good one to know

If you want to get technical about the odds of you hitting a set on the flop with a pair in your hand is simple mathematics. The odds are 2/50 + 2/49 + 2/48 = .04 + .041 + .041 = .122 = 12.2%. 100/12.2 = 8.2 hands. Since we can't play 8.2 hands we say 1 in every 8 hands or 7 to 1 odds.

What are the odds of having a pair preflop? It's simple. You're going to get an A,2,3,4,5,6,7,8,9,10,J,Q,K for your first card. This is guaranteed. That mean you have 3 out of 51 cards to hit to make your pocket pair. 3/51 = .0588. We will round it up to .059 = 5.9% of the time. 100/5.88 = 17. One in every 17 hands you are dealt will be a pocket pair. The odds of you getting a pocket pair are 16 to 1.

If you have a J 10 Suited and Q, 9, 2 come on the flop and two of those cards are suited what are the odds of you hitting a flush? What are the odds of you hitting a straight? (Flush) There are 4 cards in your suit that you know have been already played, that means there are 9 kinds in your suit left that are still out there. 9/47 + 9/46 = .191 + .196 = .387 = 38.7%. 100/38.7 = 2.6. You will make your flush 1 in every 2.6 hands. To make your straight there are 8 cards to help you make that straight 4 K's and 4 8's. So 8/47 + 8/46 = .17 + .174 = .344 = 34.4%. 100/34.4 = 2.9. So you will make your straight once out of every 2.9 hands in this scenario.

What are the odds of you making a straight or a flush in this scenario? You have 8 cards to make the straight and you will have 9 cards to make the flush, that being said you will have to subtract 2 of these cards because 2 of them will help you make your straight and your flush therefore you will have 9 + 8 - 2 = 15. You have 15 cards to hit a straight or a flush. So, 15/47 +15/46 = .319 + .326 = .645 = 64.5%. 100/64.5 = 1.55. Hence, you will hit a straight or a flush in this scenario 1 out of 1.55 times. I like these odds. That being said, even if you hit your straight or flush still won't guarantee you the win. All it guarantees you is that you have a made hand. I still like those odds though.

I hope this information has been helpful.