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Example #2 "The straight draw"

You start with a Jack of Spades and a Ten of Spades. You get a rainbow flop with a Queen of Spades, a Three of Diamonds, and a Nine of Clubs. You've got a straight draw.

Lesson 1: What are my chances of hitting it on the next card?
Same as before, but with different outs. A King or an Eight will complete your hand. There are presumably four of each left in the deck. You've got 8 outs. The chance of getting one of them on the turn is 8 over 47, because there's 47 cards left in the deck. That comes out to about .170, or around 17%.

Lesson 2: I didn't get it on the turn! What are my chances now!?
There's still 8 cards left in the deck that'll help you, but 46 cards left in the deck. That's 8 over 46. It changes to .174. It's improved to a whopping 17.4%!

Lesson 3: I should of thought about my total chances first, I'm such an idiot. What are my chances of getting that card on the turn OR the river?
Once again we'll have to calculate the chances of a King or Eight NOT appearing, so we can do it like the last problem (in this case, {39/47} X {38/46}). Or, since we've already figured out our chances in the previous two lessons, we can just invert the probabilities and multiply 'em. You had a .170 chance on the turn, and a .174 on the river. By inverting, I mean subtracting them from one. Now we've got .830 and .826! Multiply and get .686! That's our chance of NOT hitting our card at all. So invert it again and get .314, or 31.4%.
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