Why do your odds of hitting an out in Hold'em change when figuring the turn+river?

Question

I mean this:

If you have 9 outs after the flop, you have roughly a 19% chance of catching on the turn and 20% chance of catching on the river.

However, when figuring your chance of catching on the turn+river, you apparently only have a 35% chance of hitting one of your cards.

Why don't you have a 40% chance of catching?

Do you calculate something differently?

How does this all work?

Answer 1

the reason the percantage movesup from 19 to 20 percent is the fact that you have more knowledge of how many cards are out on the turn then the flop look its unimportant how it works ill simplify the process of figuring outs for you so you dont have to stress over exact numbers lon the flop count your outs times your outs by 2  then times that by 2 then add 2now lets go through a couple of examples on the flop lets say u have 4 outs now instead of looking at a chart just times that by 2 then by 2 again then add 2 it will look like the following

4(outs)x2=8

8(number from above)x2=16

16(the above answer)+2=18

turn the answer into a percent 18%

if your on the turn the percentage works like this

4(outs)x2=8

8+2=10

10%

these numbers arent exact but it puts u as close as u need to get so just focus on the other parts of your game now and leave the math to mathmaticians like david sklansky

Answer 2

When odds are calculated after the flop, they are counting the chances that you will catch your outs on the turn OR the river and any additional runner-runner combinations that may hit.  Your odds go down after the turn because you now only have one more chance to hit your outs if you haven't already and any runner-runner possibilities are now out of the equation.