Open ended straight draws

Here’s a hand that happened last night. I called two people’s all in bet and some people questioned the call. Here’s why I think they’re idiots.

I limped in preflop with 6,7 suited(hearts) then big time bumped it up to $4 preflop. Jimmy called and with the way preflop betting had been going I thought it was worth a risk with a suited connector to get a chance to break somebody. The flop came down 4, 8, 9 with one heart. I think I led out hoping to take down the pot right there. Big Time went all in for $14 and Jimmy called all in with $9. I had a decision to make. Here’s why I made the call.

I had an open ended straight draw against what I assumed to be two big over cards or an over pair. Open ended straight draw means I have 8 outs out of the 47 cards I haven’t seen. That makes 39 cards that won’t help me. So my odds against improving are 39:47 on the turn and then 38:46 on the river because one more cards has been shown. 39/47 * 38/46= 31.5% that I will make my straight on either the turn on the river. By calling the all in I’m automatically seeing the turn and the river. I prefers to calculate odds against winning rather than percent chance of winning because it’s much easier to compare that to the pot odds.

You can also just memorize that with an open ended straight draw and 2 cards to come the odds against improving to the straight are 2.2:1. But now don’t forget that I also have a back door flush draw and could catch runner runner for the flush. It’s not a great chance, but let’s look there are 13 hearts and three of them were out already leaving 10 cards that could give me my flush. So I actually have a bit better odds than that already. Now lets keep in mind that the 4,8,9 wasn’t very scary for the big cards I’m putting my opponents on so they could possibly just have overcards and no pair, so maybe I could pair up a 6 or a 7 and actually still win the hand. So the way I figure it I have a 2.2:1 shot of definitely winning the hand. There was like $15 preflop from the bets and the blinds and then there was $27 more from the all ins and my lead out bet making the post size $42 and I had to put in $14 to make the call. That’s 3 to 1 on my pot odds. And I think that I actually had better odds than 2.2:1 because of the backdoor flush possibility etc.

So it doesn’t matter the size of the bets in front of you, and it doesn’t matter whether or not you’re beat at that moment, it matters (especially in an all in situation) whether or not mathematically you have a positive expectation on that money that you put in the pot. So there.