Reading this article:

https://upswingpoker.com/vs-flop-raise/


Written by Ben Ward, about a hand played by Doug Polk, I'd like to discusse something about blockers.

It's about hand #1:

$2/$5 on WSOP.com. $467 Effective Stacks.

Doug is dealt K K in the big blind
Qualityfish1 limps on the button. Small blind completes. Doug raises to $35. Qualityfish1 calls. Small blind folds.

Flop ($73.50): J T T
Doug bets $22.50. Qualityfish1 raises to $111.37. Doug calls.

Turn ($296): 8
Qualityfish1 bets $222.18.

I don't care (not for this thread purposes) about decisions until here. Now, here Ben Ward writes:

"This is where the hand gets a bit trickier. Qualityfish1 continues for three-quarters pot, leaving him with just $99.79 behind. When our opponent bets a size like this that leaves them with such a small amount for the next street, we should treat it like a shove, and either fold or check-raise all-in."

Yeah, clearly we haven't got any fold equity, ok. He continues:

"The real question is how often we should be doing each when holding an overpair. The theoretically correct answer, as it often is, is some of the time. If we always go with all overpairs, our opponent can profit from under-bluffing. Likewise, if we always fold them, our opponents can profit from over-bluffing"

Ok, so, let's see how we decide if we fold or not:

"How do we decide which overpairs to go with? The best way is to pick ones which don’t block bluff combos. So, in this example, that would be overpairs which don’t contain a diamond, as our opponent’s most likely bluffing hands are diamond flush draws. An argument could be made that it is also better to go with aces than kings or queens, because (besides being a stronger hand) aces doesn’t block KQ, which is another one of our opponent’s conceivable bluffs.

That's my concern!
Do you think guys it is better to fold if we have the king of diamonds or is it better to fold if we do not?

It's better to fold if you have the Kd, you hold a blocker to his potential bluff hands

Yes, that's what Ben Ward suggests.

But when I thought about it, if you have one diamond, you also block one of his outs in case he has a semibluff.

So, I tried to run the numbers in flopzilla:

Villain Range when bets (mixing values and semibluffs):

JJ-99,AJo-ATo,KQo-KJo,QJo,JTo,AJs-A2s,KQs-K9s,QJs-Q9s,JTs-J8s,T9s-T8s,98s:a5b8a5b1a150:a10b1a5:a16:a16

https://imgur.com/a/BctApSg

If I don't put my hand, he has 30,8% semibluffs.

If I have KK with no diamond, he has 27,2% semibluffs.
If I have KK with , he has 26,4% semibluffs.

(So there's no much difference in his semibluffs whether or not I have the diamond, but, yes, there's more chance he has semibluff when I've got a diamond. Logical).

For informational purposes, we have something more difference when instead of KK we have AA:

AA with no diamond: 34% semibluffs.
AA with : 28,1% semibluffs.

This is because we would block the ace of diamonds, which blocks many more of its possible semibluffs...

Ok, BUT, that is when I think: what is really important when deciding whether to fold or not is our equity, right?

Let's see... Against villain range, If we have:

KK with no diamond: 59,4% equity
KK with : 61,1% equity

AA with no diamond: 64,5% equity
AA with : 66,1% equity

even QQ with no diamond: 57,5% equity
QQ with : 59,3% equity...

!!

imo, this means that it's better to fold when we do NOT have a diamond, isn't it?

Ok, we may have put an unrealistic range, so let's change it a bit to try to get closer to the point where it would be good for our equity not to have a diamond.

Let's remove from villain's range all the middle hands we put (AJ, KJ, QJ, 99 ...), those that which we would be ahead with our KK (or QQ, AA).

That is, we'll leave a range only with hands that beat us (Tx and JJ) and draws: oesd and flushdraws.

Now we have, when holding:

KK with no diamond: 37,5% equity
KK with : 39,3% equity

AA with no diamond: 46,8% equity
AA with diamond: 45,9% equity

Yep! Now we have a different situation, now it's slightly better to fold when we have diamond in the case we have aces (because A blocks a huge part of their flushdraws). But in the case of having KK, we still have more equity when we have a diamond.

So, imo, it's still better to fold when we DO NOT have a diamond in our KK.

Ok, let's change it more. Let's give him a lot of flushdraws, using K and Q :

https://imgur.com/a/FxAlxu9

now we have, when holding:

KK with no diamond: 45,1% equity
KK with : 46,0% equity

AA with no diamond: 50,3% equity
AA with 51,0% equity

Again, we have better equity when we have a diamond, so it's still (imo) better to fold when we DO NOT have .


What do you think?

Thanks!

I don't really study the game like I used to, So I don't know maybe you are right. But to me it seems like you are overthinking it.

Yes you will have more EQ with the Diamond in your hand but that is because you are taking the possible semi-bluff combos out of his range.

You can play with ranges and it can sway either way depends on how many bluff combos, value combos he has etc.

Range equity calculations already account for the change in combinations in ranges so it's pointless to compare those numbers with the change in semibluff frequency directly.

What you can do is use the semibluff frequency combinations as a rough approximation in your EV equations for the probability some event occurs. I don't believe that should be double counting but I could be mistaken. Been a long time since I flexed those specific math muscles.

amounts * equity = total equity

let’s say it is like x*y=z

when x goes down, y goes up, does z goes up or down?

it depends a lot on the specific number.

the graphic of this formula is a hypobolic paraboloid.

but what we do know, is that the equity thing(y), is pretty much fixed, it is always one combo out of 9 combos, so it is like 11% up or down.

the x is not so fixed, if he has 40 bluff combos, Kxdd has 5 combos, it is 1/8, 12.5% up and down. Howerever, if he has only 12 bluff combos, Kxdd has 3 combos, it is 25% up and down.

i only checked one of your pictures, it seems that you are giving villain too much bluff comcos, almost 40. in that way, the rate of x changing, is pretty low.

But ott, villain is almost all in, he shouldn’t have that many bluffs, 10 combos or less i would assume. So under my assumption, the changing rate of x would affect the fomula more.

The point of the article is that if you have a diamond, especially the Ad, it's much less likely V is bluffing a busted fd because it is much less likely he holds two diamonds. Most he would just fold. And in this case, if you held the Kd, you'd block the sfd. Those are by far the most likely busted draws. THAT is why you'd want to consider folding with the Ad or Kd - because you have one of the two most likely bluff cards, the likelihood he is bluffing is MUCH lower.

It has nothing to do with hand vs range equity really.