harrington on pot odds

[Chrushinator]

i'm currently reading harrington's first tourney installment. in the "reading the table" section, he is outlining a situation and describing an easy call based on pot odds.

i thought that i understood the fairly straightforward concept, but this confuses me.

you're holding Qs4s. flop comes JsJc9s. it's going to cost you $200 to get into a $1000 pot. he says that "the odds of drawing a flush on the next card are about 4 to 1 against, and if you stay in for 4th and 5th street, the odds drop to 2 to 1 against."

i thought that 9 / 47 is roughly 5 to 1 odds against? did dan fuck up, or am i missing something?

[DaNutsInYoEye]

47 cards total. 9 help you, 38 don't. 38 to 9 = 4.2 to 1

[Staresy]

he says that "the odds of drawing a flush on the next card are about 4 to 1 against, and if you stay in for 4th and 5th street, the odds drop to 2 to 1 against."

What he means is that, your odds of hitting solely on the turn are 4:1. The 2:1 odds are you hitting your flush on either the turn or the river.

[arkana]

What DaNuts said.

Probabilities-> good outcomes / (bad outcomes + good outcomes)
Odds-> bad outcomes : good outcomes

So if 9 out of 47 cards help you, then you have 9 good outcomes and 38 bad ones. So your odds (of making the flush) is 38:9 and your probability is 9/47. Its just different representations of the same thing.

[Pelion]

i thought that 9 / 47 is roughly 5 to 1 odds against? did dan fuck up, or am i missing something?

i think you are confusing the chance to make the hand with the odds against making a hand.

there is a 1 in 5 chance of making the hand by the next card. so every time you play this situation 1 time will make a flush and 4 times will not (total = 1 + 4 = 5).
this means the odds are 4 to 1 against