Hi all,

I'd like to discuss a play detailed in Johnathan Little's new book "Excelling at Tough No-Limit Games". I've just started reading it and it's reasonable, although clearly aimed at beginner-level players.

The play comes from the first chapter, (written by Rob Tinnion) discussing EV calculations, and goes something like this:

It's a 500/1000-125 nine-handed game and UTG raises to 2500. Hero, in UTG+1, decides to bluff raise to 6,895. Everyone folds and UTG calls - the pot is now 16,415. UTG+1 flops a flush draw and jams for 26,264 under the assumption that UTG will fold 62% of the time and call 38% of the time. The EV calculations are given as follows:

When UTG folds, 16415 x 0.62 = 10,177.
When UTG calls and UTG+1 hits the flush: (16415 +26,264) x 0.38 x 0.36 = 5,838.
When UTG calls and UTG+1 misses the flush: 26264 x 0.38 x 0.64 = 6387.

Combined, the EV is 9,625 on the jam - all well and good; a pretty standard plus EV shove with a flush draw. It should be noted, too, that the author does make clear it is not wise to bluff-raise UTG very often, as they have a strong range and there are still seven players left after you who could wake up with a hand as well.

All that said, I think it's a little misleading, because the entire play makes several assumptions and overall has to be quite imbalanced.

What I mean is that this sequence only looks at one specific branch of the game tree - although of course it is the most likely, but you can't simply ignore the rest.

For example the remaining seven players will have a very small cold-calling range - let's say 1%, as well as a 4bet cold range, let's say 2%. So - the bluff-raise is only getting through the seven players left yet to act around 81% of the time.

When it comes to the UTG player, he will 4bet maybe 3% of the time, and call maybe 47% of the time, and fold the rest.

This means that we are only getting to the branch of the game tree that is detailed in the book about 41% of the time. 21% of the time an additional player will call or 4bet, meaning UTG+1 is most likely going into a 3-way hand with a weak holding and an inflated pot (more often than not out of position) or being forced to fold to additional action.

The remaining 38% of the time all players fold and UTG+1 wins a small pot for quite a substantial risk.

So:

41% of the time he goes heads-up against UTG with a weak holding.
38% of the time he wins the pot uncontested.
21% of the time, he is cold-called or raised and is either in a dicey spot or has to fold.

Is this really a desirable prospect?

In the brilliant book "Modern Poker Theory" by Michael Acevedo, UTG+1 has very few 3bet bluffs vs UTG - A8s, A7s, A5s, K9s, K6s, KQo - generally at a low frequency. We know already that in the situation above, UTG+1 is not drawing to the nut flush, so either he is bluffing with K9s, K6s or (most likely I suspect) he is deviating from GTO equilibrium and therefore opening himself up to exploitation.

We can give each outcome an approximate EV:

41% of the time he goes heads-up against UTG with a weak holding. The pot is 16,415. If he is shoving with a flush draw, how does he balance it? He would also have to shove for value with most, if not all, of his nutted hands on the occasions when he is 3betting for value. Of course, it's certainly not desirable for plays like this to force you into shoving top set on dry boards as well. So although the shove with the flush draw is plus EV in this case, it has to sacrifice a lot of EV in other spots in order to remain balanced. We've already seen that the flush draw jam has an EV of 9,625 - but you can be sure that at least as much is lost in other spots. Not only that, but some of the time UTG will have a bigger flush draw, or was intending to check raise a set etc. So let's say the overall EV here is 3000.

38% of the time he wins the pot uncontested, a profit of 5,125.

21% of the time, he is cold-called or raised and is either in a dicey spot or has to fold. Let's say the EV here is 2000 - sometimes he will get lucky after all.

So the actual (admittedly approximate) EV of the bluff-raise is:

(0.41 x 3000) + (0.38 x 5125) + (0.21 x 2000) = 3597.5 after risking 6,895 - a move that deviates from equilibrium, expects a considerable loss on average and results in huge imbalance in other ranges as well.

Sure, I get that this section of the book is about illustration and is not meant to be balanced etc - but still, I think these things should be more clearly clarified and I am certain that beginners out there reading the book will see this play and think that it's brilliant, only to eventually learn after multiple failed outings and a couple of successes that in fact it is almost never a smart move.