Open-Ended Straight Draw Odds Example

You start with a Jack of Spades and a Ten of Spades. The flop comes down...

Queen of Spades Three of Diamonds 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 are 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 are still 8 cards left in the deck that will help you, but 46 cards left in the deck. That's 8 over 46. It changes to .174. It has improved to a whopping 17.4%!

Lesson 3: I should have thought about my total chances first. What were my chances of getting that card on the turn OR the river?
Once again, we have to calculate the chances of a King or Eight NOT appearing, so we could 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 subtract the probabilities from 1 and multiply them. You had a .170 chance on the turn and .174 on the river. Now we've got .830 and .826! Multiply and get .686! That's our chance of NOT hitting our card at all. So subtract it from 1 again and get .314 or 31.4%.

Lesson 4: You expect me to figure that out at the table?
Not really. We're just trying to teach you the underlying math. It might be a good idea to memorize them so that you know though. There is an easier way to estimate odds though. It's generally called the 2-4 rule. The way it works is that if you are trying to figure your chances with one card to come, you multiply the number of outs you have by 2. If you are trying to estimate your chance for the turn and river combined, you multiply your outs by 4. The number won't be exact, but will serve as a rough estimation. So in this example, Lesson 1 says your chance is 17.0%. If you used the 2-4 rule, you'd come up with 16% (2 x 8). Lesson 3 says your chance for the turn and river combined is 31.4%. The 2-4 rule would estimate it at 32% (4 x 8).

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