Understanding Turn equities against made hands

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Understanding Turn equities against made hands

Hi Everyone

I've been trying to compile a spreadsheet of equity comparisons for some contentious spots by analysing them with propokertools. In doing so, I've come across a number of spots which I had previously thought that I had a grasp on, but am now seeing that I may have misunderstood or misapplied them. Some of the problems I think are NLHM legacy issues whereas some are just misunderstanding or lack of knowledge on my part. My question is a bit long-winded and I apologize in advance for that. Any help, as always, is appreciated.

Below is an example:

[Please note that the example will, for the most part, focus on equities as face up and not so much on player characteristics and ranges.]

$2/4, 4 handed $622 eff stacks.
SB posts $2
BB posts $4
UTG limps $4
Hero ($622) is the BTN (AsKdTh3c) and raises to $16
SB folds
BB calls $12
UTG calls $12

POT $50

Flop: QsJs2c

SB checks
UTG Bets pot ($50)
Hero Calls ($50)
SB Calls (50$)

Pot $200

Turn: Td

SB bets pot ($200)
UTG calls ($200)

Note on Hero's thoughts: At this point it is very likely that UTG has a set and that SB (for simplicity's sake) either has the AK straight or air. I discount naked flush draws as I'm holding the Ace of Spades and I'm blocking combo draws to some extent.

Hero Shoves for $556 into $600
SB folds
UTG Calls $356 and shows (JJxx).

The river is irrelevant for our purposes

When I saw this call, naturally I was quite happy because I thought that UTG was making a mistake by calling because on the turn, I'm ahead and, he would not have enough equity to justify the call. I then ran some numbers and found out that both my assumptions were incorrect- at least the way that I'm calculating it (which may be incorrect cause I suck at math... like really... even the most basic shit).

I have SB calling 356 to win 1512 which is equal to ($556 shove + $600 pot+ his $356 call). That being the case, he only needs 24% on the turn to break even. Propokertools has his equity on 36% on this hand. In fact any bare set vs any bare nut straight on the turn = 36%.

That got me thinking, and this is where I would like some help, In any given moment in PLO we need 33.3% equity to break even because calling a pot sized bet leads us to commit 33.3% to win 100%. (Eg: (200 pot) + (200 bet) + (200 call) = 600. Therefore our 200 call nets 600 and that ratio is 1:3 or 33.3%.

That being the case, does that mean that whenever we're in a similar spot as SB above, but are facing a perfect pot bet for our stack, we should be happy to stack off knowing that Villain has a straight because we are netting 2-3%? Previously, I have been snap-folding sets on similar turns and feeling really good about it. However, I'm not so sure anymore...

Although mathematically this makes sense (If all we're worried about is breaking even or pushing thin equities against a tough field), It seems so wrong to be constantly calling when we're behind on the turn. Especially since this game is already so full of that "Oh-So-Sweet-Variance"!

So in a nutshell, is anyone ever happy to get it in like this? If so, I fear I may be approaching this game wrong (which is worrisome because I've been playing it for a while now :/).

6 Comments

Loading 6 Comments...

gael67 8 years, 8 months ago

On the turn a set has 10 outs to beat a straight. There is 42 unknown cards (since we see 8 cards and we know that the straight hand has a minimum of 2 cards which are not blockers to the outs improving the set). So the set has 10/42 = 23% chance to improve. Certainly not 36%. In this situation and in absence of implied odds, it the right play to fold the set hand.
By the way the 36% are the chances for a set to beat a straight when you are all in on the flop.

This_noob 8 years, 8 months ago

Ah shieeet.... I must have messed up the inputs on PPT :/ Ladies and Gents, these are the effects of sleep deprivation!

Gael, thanks for setting me straight- really appreciate it :)

Tom Chambers 8 years, 8 months ago

In this case you are blocking him once with the ten so it is 9/42 = 21.4% if you are sure he has a set. Of course from his perspective what matters is whether he's blocking himself, and whether he puts you explicitly on AK (or any two non-blocking cards). In practice when you have a AK here you mostly either have nut spades or AKT. So he'd have to weight those and account for them.

Regardless, it's low 20s, max of 25% if no one has a blocker.

MaxVieuxlieu 8 years, 8 months ago

You also need to consider when you have the second set that your opponent can you have dominated with the bigger set. Those situations where you feel like Villain always has the nut straight, well sometimes he has the top set instead or in addition to the straight and you are virtually drawing dead. Top set with a flush draw will look like the nut straight many times, especially if there's a gut shot to go with it.

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