What's the equity % of a straight+flush draw vs a set?

[Anonymous]

This is at a $2/$2/$3 game (button also pays a blind of $2) – so it plays more like a $2/$5 game (I’d think).

UTG opens for $18; HJ calls,

I have 7♣9♣ in the CO, I call. Button goes all-in for $38. UTG calls, HJ calls, and I call on the CO.

4 players to the flop, $152 in the pot.

Flop is 8♣ 6♣ 3♦

UTG checks. HJ goes all-in for $313.

I have the open-ended straight flush draw. I’m getting about 1.5:1.

Question #1) IF I put HJ on a set, can someone help me calculate my equity % to win the pot at showdown? i.e. what are my chances to win the pot drawing to the flush & straight vs him drawing to a full house?

Question #2) Getting 1.5:1, was this the right call? Spoiler below..

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HJ actually flips over K♣T♣, and button had A♣J♣. Both of my hole cards were live as neither UTG nor button had a made hand.

However, obviously, my flush draw was dead as both HJ and button had higher flush draws. My hole cards were both live, and so was my straight.

Turn was a brick and river came a King, HJ took it down with a pair of King’s.

[Dave Thompson]

Against a set of 8s (and not removing any dead clubs from other hands) you would have 42% equity on the flop. Getting 1.5 to 1 you would need at least 40% equity to make a call profitable, so your equity is sufficient in that case. 3 ways against KTcc and AJcc (i.e. for the main pot) you have 39.5% equity on the flop, so again it’s about right. Heads up against KTcc with AJcc considered as dead cards (for the side pot), you have 43.5%. So your call was profitable long-term in either scenario. The best way to make these calculations, though, is to assign a range of possible hands that villain might have and calculate your equity against the whole range. If your range assessment was pretty much just sets and flush draws, then the numbers above would still be about right.

FYI I used an app called Poker Cruncher to make these calculations. It’s available for both iOS and Android.

• This reply was modified 6 years, 5 months ago by Dave Thompson.

[Anonymous]

Thank you!

I’m really surprised to hear that I made the right (very marginally) call, as played.

I guess what I had going for me was that both my cards were live, giving me 6 outs (drawing to any 7 or any 9). Then, any 5 or any 10 would’ve given me additional outs to the straight. That’s a total of 14 outs (never mind that UTG ended up having a 10 in his hand).

Actually…let me backtrack. I don’t think it’s 14 total outs. I’m counting any 7 or any 9 as outs, but what if a K,10,A, or J comes? Then my hole cards are dead. With that said, if we only count my straight draws (i.e. 8 outs), then I only have about 32% equity on the flop – then wouldn’t I need about 2:1 to make this a profitable call?

Could someone perhaps corroborate Dave Thompson’s analysis?

[John S]

Dave’s right. It gets kind of confusing when you’re working with two different types of numbers (ratios and percentages), but it’s extremely close here. Try This Calculator Your expected profit is 465 (the pot before you call), expected loss is 313 (what you are calling), and how often you expect to win is either 42% (against just a set), or 40% (against the two hands you posted). Against a set it’s a positive EV, against these hands it’s almost even (slightly negative).

As for our second questions about counting your outs if a A, K, or J comes (the 10 gives you a straight, so you can’t count this one), you are incorrect. You have to count all of your outs at the time you are making the decision. If they make a pair on the turn, you have less outs on the river, but your equity is calculated at the time of the call. So your 39.5% equity on the flop against these two hands includes the times you make a pair on the turn and they make a pair on the river, the times they make a pair on the turn and you make a straight on the river, and all other scenarios.

[Anonymous]

Thanks John, great contribution.

So, using the rule of 2 & 4 for approximate equity % calcs, you’re saying these % already factors in the fact that villain might make their pair, too?

So similarly, the 42% equity I had already factors in the fact that the villain might make their boat? And in spite of that fact, I still had 42% equity against that possibility?

I thought the rule of 2 & 4 only gives you the approximate % to MAKE your hand (in my case, straight or a flush) – but doesn’t factor in the scenario where your opponent might also make their hand (in this case, a set turning into a boat).

[John S]

The equity you have – whether you use the 4 & 2 rule or calculate the exact equity – changes on every street. So the equity you have is for that street only.

In the situation against the flopped set, you have 42% equity. That means if you dealt 1,000 (or 1,000,000) turns and rivers, you would win about 42% of them. Sometimes you will turn a straight flush and villain is drawing dead, and sometimes he will turn quads and you are drawing to 2 outs. But in the grand scheme of things, you will win 42% of the time and he will win 58% of the time.

Looking at another scenario, if you turn a flush draw, you gain equity (assuming your opponent doesn’t have a higher draw). If you were behind on the flop, you gain outs to win. If you were ahead on the flop, you reduce some of your opponents outs as some will give you a flush. That’s all in the math.

Similarly, look at a situation where one person needs runner runner to win the pot. Their equity on the flop will be below 5%. If they don’t pick up one of those cards they need for runner runner, they are drawing dead on the river. That’s why the equity is so low, because they need to hit on the turn to even stand a chance on the river.

[Author]

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