Odds on a 3 Flush

[Still the Spank E]

I know this is pretty rudimentary, but is the formula for figuring out the odds of making one's three flush to multiply (10/37) by (9/36)=90/1332, giving you odds of 14.8-1? In other words, the odds of hitting one of your suit on the turn multiplied by the odds of then hitting one on the river? This seems the obvious solution to my largely unmathematical mind, but I thought I'd ask if this was right and, if not, what is? Thanks.

[Warik]

Just take the probability and then convert it into odds.

You have 3 spades, there are 10 left with 47 cards after the flop left.

10/47 * 9/46 = 90 / 2162 = 0.0416281

Now convert to odds..

(1 - 0.0416281) / (0.0416281) = ~23:1! Yikes.

[Still the Spank E]

I mistakenly subtracted the suited winners in the numerator from the total cards remaining in the denominator and THEN did the calculation. Thanks for the correction.

[Agrubbyone]

Im super new to this. See my other post. I was just reading and found your question/example here. Isn't it correct how you did it the first time by subtracting out the 10 cards that help? 10 cards that help over 37 that done = 10/37? To me that looked right. Why is it correct to have it 10/47?

[Bozeman]

While percentages can be combined, odds cannot be (so simply), so always best to leave expressing as odds to the end of the calculation.