# Odds of runner runner

Say you are playing 5♥ 6♥

Flop comes up A♥ T⋄ 4♣

You have runner runner straight and flush draws. What is your chance of trips or better by the river?

This question made me curious. count outs

See a few mistakes in the above answer...

Correct: There are `combin(47;2) = 1081` two cards combination left.

But there are only 10 hearts remaining, so only 45 flush draws possible: `combin(10:2) = 45` flush draws

Correct:

``````7,8 = 15 (the flush combo does not count)
3,7 = 15 (the flush combo does not count)
2,3 = 15 (the flush combo does not count)
``````

Alas,

``````combin(3:2) = 3 not 6
5,5 = 3
6,6 = 3
``````

Ergo: total of 96 possible 2 card combo's that will give you trips or better.

Only 8.9% chance of getting trips or better

There are combin(47;2) = 1081 two cards combination left

combin(11;2) = 55 flush draws
7,8 = 15 (the flush combo does not count)
3,7 = 15
2,3 = 15
5,5 = 6
6,6 = 6

total = 112 = 10.36%

Statistically you cannot even call a small bet on the flop.

• "Statistically you cannot even call a small bet on the flop." It depends entirely on the stacks and the implied odds. It's true for short stack situations for sure. Due to how seldom you get there it's often good instead to add fold equity by pushing pressure when one had range advantage, i.e. raising. Commented Jul 23, 2019 at 15:32
• It's a bad draw in itself, but backdoors often add to other draws such as overcards (25% without BDFD, 29% with) or gutshots (16% eq without bdfd and 20% with), sometimes giving you that little extra that makes a call correct. For example KJhh here might be good enough to call a 1/3 bet while KJo is likely not. Using BDFD is also a great way to balance one's game by adding moderate bluffing frequencies on board that don't have any direct draws. Commented Jul 25, 2019 at 15:35