# How can i find the combined probability of backdoor strd/fd?

• Bronze
Joined: 11.06.2014
Since backdoor strd and fd share same hands , i dont think the standar math type apply on them , for example equilab shows 17% backdoor strd and 17% backdoor fd , i cant simply multiple them and find it because they share same cards and i think this affects somehow the process , how am i supposed to find how often i will hit both?
• 3 replies
• Super Moderator
Super Moderator
Joined: 02.09.2010
Hi, Suboptimal88,
Can you provide a concrete example?

I'll have a stab at what I THINK you mean:

Hole cards:
7:s5

Flop:
6:sQ:d2

So you want to know the odds of hitting EITHER the straight OR the flush by the river.
Is that correct?

There are 47 unknown cards.
10 will get us one step close to a flush, and 8 will get us one step closer to a straight.
10/47=21.3%
8/47=17.0%

So the odds of getting one step closer are 18/47 or 38.3% or 1.61:1

So we hit one, and there are now 46 unknown cards.
If we hit one of the flush outs OTT we have 9 outs to hit a flush OTR
If we hit one of the str8 outs, OTT we still have 8 outs to hit the straight OTR

So:
Odds of hitting the flush OTR (assuming we now have a four-flush):
9/46=19.6% to hit a flush if we already have one.
8/46=17.4% to hit a straight if we already have one.

So to hit a runner-runner flush the odds on the flop are:
21.3% x 19.6% = 3.7% (multiply the odds of one by the odds of the other)

Odds to hit a runner-runner straight:
17.0% x 17.4% = 3.0%

Add the two together to get the odds for both paths:
6.7%

If you really wanted something different, please let me know.

@All math whizzes:
If I totally farked that calculation, please correct me!

Cheers,
--VS
• Bronze
Joined: 11.06.2014
No , i wanted to know how often i will i have a backdoor fd + strd on the flop.

Lets say for example i check a range on equilab and it says 18% backdoor fd + 19% backdoor strd , i want to combine them and find out how often i will have both hands on the flop. something like 7d6d on Ad5c2s , i dont want to find how often i will hit those hands by the river.

I want to use this to construct a bluffing range , a combination of both backdoors can be a good bluffing range but i dont know how often i will hit both together otf.
• Bronze
Joined: 28.01.2012
The example you gave won't work in equilab because on A25 the board has backdoor straight draw possibilities to run out as a wheel. So equilab will say 100% of your range has bdsd.

If you get 18% bdfd and 19% bdsd, try to combine them by ticking both things in equilab. Down the bottom you will get something like 25% "modified hand range contains:"

From there its simply (18+19)-25
=12% of hands are both bdsd and bdfd
= 6% of hands are bdfd
= 7% of hands are bdsd

Add these numbers up and you get 25% which is the same total number as above.