We all know 3B or Fold is a popular simplification for all positions except BB,
but I haven't heard much about simplifying to 4B or Fold.

Could this be a viable simplification, especially when OOP?

I ran some quick sims that seems to suggest it could be a pretty reasonable simpflication.

CO vs BTN 3B (BTN playing 3B or Fold)

EV with calls: 16.4bb/100



EV 4B or Fold: 16.4bb/100



Strategy changes: CO opens slightly tighter (28% vs 30%), BTN 3bets wider (15.7% vs 13.8%), CO 4bets wider (8.1% range vs 6.1% range)

What if we nodelock BTN to 3B the same range as vs normal GTO (13.8%)?



Strategy changes: Open our normal GTO range (30%) again, 4Bet 7.1%

**********************

SB vs BB

EV with calls: -25.7bb/100



EV 4B or Fold: -27bb/100



Strategy changes: Again we open tighter (39% vs 45%), BB calls tighter (34% vs 36%), BB 3bets wider (21% vs 19%), SB 4bets wider (12.9% range vs 9.7% range)

So here, in a wider formation, we are losing significant EV if BB max exploits us.

What if we node-lock BB to play normal GTO calling and 3b ranges?



We are still losing significant EV (-26.8bb/100)...

**********************

Conclusion: 4B/Fold is probably a fine simplification in all formations where we 4B OOP, except in SB vs BB where 4B/Fold would probably sacrifice too much EV to be a good strategy.

What do you think about about 4B/Fold as a simplification?

And what is the reason SB vs BB loses more EV when simplifying to 4B/Fold? Wider ranges? BB 3betting a more polarized range?

Interesting theory...

The "Outline" shown at the bottom doesn't show EV at that decision point, it shows the EV of that position over all possible preflop lines.

You've only locked one small part of the tree, so the EV losses are diluted by all the unlocked spots. The more decision points ahead, the less your simplification at that one node (e.g. CO vs BTN 3-bet) will change the global EV of that seat.

I recommend using the "Node Details" feature to zoom in on the EV of your simplification.

• Right Click node
• Node Details
• Line EV Sampling

The average value here tells you the EV at that decision point:

(CI = 8)

Total EV with calls after BTN has 3B and everyone else has folded: -108.6bb/100 (relative to starting stack)
We see that the EV of calling itself calling is not great anyway, basically just salvaging what little EV it can: -204.3bb/100 (relative to starting stack)



Total EV of 4B or Fold after BTN has 3B and everyone else has folded: -89.4bb/100
Somehow better EV?



Total EV of 4B or Fold if we nodelock BTN to 3B normal GTO range: -106.9bb/100
Still somehow better than with calls...



I guess there may be some solver innaccuricies here, but I think it at least shows we are not losing any significant EV from playing 4B or Fold as CO VS a BTN that plays 3B or Fold.

I realized that we are opening a tighter range when playing 4B or Fold, which I guess increases our EV in the node after BTN 3B.

To make things more "fair" I locked our opening range to normal GTO: -110bb/100



Still no huge EV loss compared to playing with calls..

Interesting! How much tighter does it want to open in the 4B/F scenario?

4b or fold is reasonable vs. larger 3bets and higher rake and specifically only when OOP

smaller 3b sizing
lower rake
tighter 3b ranges
higher stack depth

all above will make 4b or fold strategy worse

It depended on the exact settings, but something like 25-28% opening range.

Something else to consider is that this appears to be a lower-variance strategy. In finance, they use a metric called the Sharpe Ratio to determine the value of stuff,

Sharpe Ratio = EV/SD, where EV is typically measured relative to a risk-free strategy (folding, in this case).

Sharpe Ratio of Fold/Call/4-Bet = (98.914-97.5)/26.279 = 5.4%
Sharpe Ratio of Fold/4-Bet = (98.9-97.5)/24.988 = 5.6%

One could argue that your simplification is not only playable - but superior in terms of risk-adjusted returns.

That said, there are a few issues. For one, your sim isn't super accurate, CI 8 is still pretty messy in HRC. Secondly, risk-adjusted returns may not matter much in poker. Risk tolerance is kind of subjective, but the practical idea in finance is that a better Sharpe Ratio means you can delegate less of your bankroll to that investment, and more of your roll to other investments, increasing compound growth.

I'm gonna make a new thread to discuss this concept further.

I think the concept does make sense and is applicable to poker fwiw. I am looking forward to your post about this concept in the future.

Aside from simplifying ones strategy, I believe there is one more benefit to playing 3B/F and 4B/F: playing as PFR rather than PFC.

Based on experience and MDA I would say that the vast majority of players play better as PFR than as PFC; humans tend to overfold and underraise as PFC.

So by playing 3B/F we not only simplify our strategy, we also exploit the population tendency of overfolding and underraising as PFC, increasing the EV of playing 3B/F.

The same goes for playing 4B/F when OOP: we avoid playing as OOP PFC in 3B pot, putting our opponent in the spot of being PFC, making it more likely he is the one making postflop mistakes and not us.

In theory BU can 3bet with smaller size. I don't this it's losing ev BvB because ranges are wide but because BB has calling range and it can 3bet trashy hands, so 4bets deny less equity.

Idk if you run a sim where BTN can call.

To add to the list, 4b/fold performs worse when the 3bet range is polarised.

Bvb is a good example: when BB is 3betting hands like T3s, there are many hands in our range that perform well as a call. Playing 4b/fold takes away that option, which is why you noticed a big EV loss in your sim.

But for something like MP vs CO, the 3bet range is extremely linear. Facing this range, there are far fewer hands with EV(call) significantly above 0, so playing 4b/fold becomes more reasonable.

Absolutely, great addition.