The straights are tricky. I prefer to think of them in a certain way and I acknowledge that not everyone may think about them the same as I. A mental model that works well for me and simplifies the math is computing the chance of EXACTLY 1 of EACH of 3 ranks falling on the flop when you do not hold any of those ranks in the hole. There are a lot of ways to compute that number. I am going to stick with the method I have used throughout the other explanations.

If you want the flop to contain ranks X, Y, Z when your hole cards do not contain X, Y, or Z then:

You are looking for 1 of the 4 X. Then you are looking for 1 of the 4 Y. Then you are looking for 1 of the 4 Z. Then divide by the number of combinations. That gives you:

(4 * 4 * 4) / (50 * 49 * 48) = 0.054422%

That is the chance of EXACTLY flopping X, then Y, then Z. There are 5 other ways of flopping X, Y, Z that all have an equal chance:

X Z Y
Y X Z
Y Z X
Z X Y
Z Y X

So, the odds of flopping EXACTLY one each of ranks X, Y, and Z when you do not hold either X, Y, or Z on the hole are:

6 * 0.054422 = 0.3265%

We are going to call that number S, and we are going to be using it a lot.

Holding connectors 54 through JT and flopping a straight.

These connectors have room on both sides to form a number of straights. Graphically, if you are holding cards AB, then you could flop the following straights:

X Y Z A B - - -
- X Y A B Z - -
- - X A B Y Z -
- - - A B X Y Z

So there are 4 sets of X, Y, Z that will give you a straight. So you have a 4 times S chance of flopping a straight.

4 * 0.3265 = 1.306%

Holding one gapped connectors 53 through QT and flopping a straight.

These connectors have room on both sides to form a number of straights. Graphically, if you are holding cards AB, then you could flop the following straights:

X Y A Z B - -
- X A Y B Z -
- - A X B Y Z

So there are 3 sets of X, Y, Z that will give you a straight. So you have a 3 times S chance of flopping a straight.

3 * 0.3265 = 0.980%

Holding two gapped connectors 52 through KT and flopping a straight.

These connectors have room on both sides to form two straights. Graphically, if you are holding cards AB, then you could flop the following straights:

X A Y Z B -
- A X Y B Z

So there are 2 sets of X, Y, Z that will give you a straight. So you have a 2 times S chance of flopping a straight.

2 * 0.3265 = 0.653%

Holding three gapped connectors A5 through AT and flopping a straight.

These connectors can only flop one straight. Graphically, if you are holding cards AB, then you could flop the following straight:

A X Y Z B

So there are 1 set of X, Y, Z that will give you a straight. So you have a 1 times S chance of flopping a straight.

1 * 0.3265 = 0.327%