Equity value of a 3-straight on the flop

I didn't realize this before, but a 3-straight on the flop is worth just under 5% equity, surprisingly high.

I found this when analysing the following match-up:

Flop: 3♦10♦4♣

Me: 5♥5♣ - 14.04%
Villain: 3♥3♠ - 85.96%

But remove the 3-straight

Flop 3♦10♦K♣

Me: 5♥5♣ - 9.19%
Villain: 3♥3♠ - 90.81%

Definitely something to consider when you're weighing up an all-in call, as I faced on this hand.

Doesn't that % also include our outs for hitting our set?

5% sounds about right. You'll find that it's the same for a backdoor flush draw.

Backdoors are considered roughly 1, or 1 and a half outs i think.

ya backdoor flush is around 4% so that sounds right.

ChuckTs said:

Doesn't that % also include our outs for hitting our set?

Click to expand...

The %ages given in the post are the win %ages... so if you look at the second example without the 3-straight, presumably our entire equity comes from the two Five outs (plus a very small amount for runner-runner Tens or Fours), which is about 9%.

BTW there's no reason I can think of why the odds for a backdoor flush should be the same or similar to the odds for a backdoor straight...

I'm not sure if there's a "reason" per se, it's just convenient that the likelyhood of the two possible backdoor draws happen to be roughly the same.

I think its because you could make many straights: 5432A, 65432, 76543, and not just one, so you have many combinations for runner straight after the turn.

Maybe thats why flush and backdoor straight have same %

ChuckTs said:

Doesn't that % also include our outs for hitting our set?

Click to expand...

Not sure what I was thinking when I wrote this