Calculating % odds with backdoor draws

dowzer

When calculating odds in Poker we assume 2.2% for each card which can help us hitting by the river - so if I am 4 to the flush on the flop then I have 9 "outs" giving me 39.6% of hitting my flush by the river.

However, what if I am 3 to the flush, for example, and need to hit runner runner to complete my hand? I know we shouldn't be chasing runner runner hands but I'm curious to know if there is a similar mathematical calculation in these scenarios?

NoseyBonk

In this case you'd be 23:1 

You'd need 10 out of 47 cards on the turn, and 9 out of 46 cars on the river - multiplied together = 90/2162 = 4% or 23:1.

Not as easy as the 2.2 or 4.4 rule though!

stokesyph

If you are 4 to the flush on the flop then you have a 34.96% chance of hitting it by the river not 39.6%. The chance of hitting a backdoor flush is 4.16%.

dowzer

In Response to Re: Calculating % odds with backdoor draws:

If you are 4 to the flush on the flop then you have a 34.96% chance of hitting it by the river not 39.6%. The chance of hitting a backdoor flush is 4.16%.
Posted by stokesyph

It would be 35.2% if you 8 cards left but with 9 cards left in the deck its 9 x 4.4% = 39.6%?

dowzer

In Response to Re: Calculating % odds with backdoor draws:

In this case you'd be 23:1  You'd need 10 out of 47 cards on the turn, and 9 out of 46 cars on the river - multiplied together = 90/2162 = 23:1. Not as easy as the 2.2 or 4.4 rule though!
Posted by NoseyBonk

Thanks Nosey - cant see me working that one out in 15 seconds

NoseyBonk

In Response to Re: Calculating % odds with backdoor draws:

In Response to Re: Calculating % odds with backdoor draws : Thanks Nosey - cant see me working that one out in 15 seconds
Posted by dowzer

Yeah It's just one of those stats you need to memorise ;-)

stokesyph

In Response to Re: Calculating % odds with backdoor draws:

In Response to Re: Calculating % odds with backdoor draws : It would be 35.2% if you 8 cards left but with 9 cards left in the deck its 9 x 4.4% = 39.6%?
Posted by dowzer

I don't know the exact maths of it but if you miss your flush on the turn then you have 9 cards to hit but with 1 card less in the deck so its not quite 9 x 4.4%. Hope that made sense.