What Value To Bluff Ratio Do We Need When Check-Raising Flop?

[LondonImp]

Quick x/r question I hope someone can answer for me.

When we are cbetting the flop with a polarised range we should be looking for a ratio of approximately 2 bluffs for every 1 value hand.

Is this the same ration we should be using when we are check-raising the flop versus a cbet? And what if we are check-raising the flop as the preflop aggressor to protect our checking range?

[AJH914]

I just watched the Lexi Gavin check raising class. She noted a 1:1 ratio of value to bluffs. I’d refer you to that video for more details.

[kkep]

That's a good question. I generally ask myself how many nutted hands hit my range and are there enough draws to raise with my best hands and draws.
3-bet flops may only need straight draws where as 2-bet pots usually need some sort of flush draw too. I never really tried to count combos before deciding
to c/r or not. I think how the hand played pre-flop, position and how the board texture interacts with the ranges is enough information.

[LondonImp]

tl;dr - Yeah 1:1 does seem to work as a ratio.

I just watched the Lexi Gavin check raising class. She noted a 1:1 ratio of value to bluffs. I’d refer you to that video for more details.

Thanks for this, I've now watched the video.

Clearly Lexi is a great player, she wouldn't be a pro otherwise, but I have very little confidence in her classes.

At one point she refers to opening from MP and the BB defending. The flop is then favourable for the BB's range and so she said it's not a spot she'd be looking to x/r. Well you clearly can't x/r in position... She also got hand rankings wrong in the last video I watched. Two pair 77s over 55s beating QQs over 22s apparently (or something very similar).

My problem with this particular spot is that if we balance our ratio of value to bluffs at 1:1 then our opponent can easily exploit us by over-folding.

In short, the pot odds that we would be setting our opponents would be too steep in comparison to the equity of their range (assuming a "standard" x/r size) and so it would make it easy for them to play against us. We want to make them indifferent to calling to put them in the very toughest spots and induce mistakes.

If we are looking to exploit our opponents then this completely changes, but in order to exploit we first need a very solid starting point.


[EDIT: Or maybe I'm talking nonsense (highly likely)... Let's take a look at an example:

Pot = 100
Cbet = 33
X/R = 123 [~3.75 * cbet size]

Equity required for breakeven call: 26%

That's actually quite a bit lower than I thought it would be off the top of my head.

How should the cbetter defend?

Here is their equity matrix:



The cbettor needs to defend with everything that has over 26% equity. Which is their entire range apparently.

The assumptions here are:

- BTN v BB 6-max ranges used
- Flop: 6d 5d 3c
- BTN cbets range 33% pot
- BB x/r for value with 2p+ and bluffs with 84s,98o,87o for a ratio of 27 value to 28 bluffs.

Maybe 1:1 is idea then... Although this does seem to imply that we actually should be using more value than bluffs to stop our opponent being able to simply call with their entire range.

Maybe I've gone wrong here.

Anyone?]

[LondonImp]

Here seems to be more proof that we need more value than bluffs in our range.

Pot = 100
Cbet = 33
X/R = 123 [~3.75 * cbet size]

Equity required for breakeven call: 26%

- BTN v BB 6-max ranges used
- Flop: 7s 5d 3c
- BB x/r for value with 2p+ and bluffs with OESD (no Ace) for a ratio of 19 value to 12 bluffs (roughly 3:2)

Here is the new equity matrix for the BTN:



Now this is much harder to defend correctly. A fold with a hand >26% or a defend with a hand <26% is now a mistake. Surely this is going to induce far more mistakes?

EDIT: Actually no, it's quite intuitive. Although I'm not sure everyone would correctly defend their T high gutshots and bottom pairs.

[LondonImp]

Okay, I think I've got to the bottom of this myself.

The 2:1 value to bluff rule of thumb is based on a 75% pot size bet. This was suggested, and mathematically proven, by Matthew Janda in his book "Applications of No Limit Hold'em".

A 75% pot size raise is actually substantially bigger than 3.75x the cbet.

Assuming a pot size of 100 and a cbet of 33 then a 3.75x raise (more or less as suggested by Jonthan Jaffe and Lexi Gavin) would be: 33 * 3.75 = 123.75.

But a 75% pot size raise, assuming the same starting stack and cbet size would be: (0.75 * [100 + 33 + 33]) + 33 = 157.5.

So a 75% pot size raise is roughly 27% greater than a 3.75x raise. That's a big difference.

As we know, as our bet/raise size decreases, the number of bluffs in our range compared to the number of value hands must also come down.

So 2:1 is simply too high to be balanced based on the recommended raise size and we need to go closes to 1:1.

I'd estimate based on all of this that on average we'd need between 1.3 and 1.5 bluff combos for every value hand.