What is the truth behind recreational players losing faster at heads up vs 6 max, could some of the maths posters here maybe confirm the below quote which is from another thread where the standard comment in that thread was that recs do lose faster at hu than 6max, but than this poster explained that it wasn't true with the below reply.

There are a few issues with the calculation:

Win rates don't work that way. You can't just say a 2bb winner wins 2bb in any game from any position relative to the fish and that the fish is the only contributer to everyone's 2bb winrate. It's also difficult to directly compare wr between game formats (i.e. taking someones wr from one game format can't directly tell you what their wr is in another format).

Also the way the calculation was used is confusing. First the poster has 5*(6+2) and I can't decide if that means rake + wr or what because the poster adds another amount for rake on the end which doesn't make any sense to me. So the calculation seems off in some way even as a model estimation.

If I were to model it I would think you could start with looking at negative contributors to your winrate. So that would be composed of a percentage folded preflop forced bets (abbreviated later as FB; e.g. Blinds, antes, kills, straddles, etc) coupled with any -EV plays (which I am intentionally leaving loosely defined here).

So total losses looks something like:

F*(FB) + sum(-EV Plays)

If you look at this you can make some genralizations about 6 max vs hu play:

If F is the frequency you fold a force bet you see more forced bets in hu play so even if your same frequency holds in heads up as it does in 6 max you're likely still losing more money in hu because you are seeing more forced bets.

A simple example. Lets say you play 60 hands. In 6 max that's 10 orbits so you would pay the blinds roughly 10 times. So lets say you fold your small blind 80% of the time and your bb 70% of the time.

That means you will lose (.8*10*.5)+(.7*10*1) = 11 bb just from folding.

Now in heads up you would have played 30sb and 30bb. If you maintained those same frequencies you would end up losing (.8*30*.5)+(.7*30*1) = 12 + 21 = 33bb.

You lose 3 times more playing the same frequency of blinds (ignoring other factors) because you see the blinds much more frequently.

So let's say you adjust and don't fold as frequently. Well if you take the rest of the -EV plays those have to occur at some point in the hand. They are just aggregate of all the -EV plays a person makes. That means you will make these -EV decisions more frequently (because you're calling more and playing more postflop).

So in both scenarios it seems like players have more opportunity to lose money more quickly heads up than in 6 max.

The part I glossed over and may not necessarily be true is that all -EV plays are the same in 6 max vs hu or that players make the same mistakes at both which is why WR are hard to compare between formats.

The word faster sort of implies a time variable... Leaving all other things equal (and they aren't fwiw) you can play multiple HU hands per hands at 6m--the loss variable would need to be considerably larger at 6m to imply what he (Razilen) is saying is true.

Fish tend to lose faster at HU than at 6m

What about that fish would be less likely to fold at 6max and therefore play far too many hands and lose faster

First I would argue that it would be rare for a fish that can't fold in 6 max to then over fold in hu. I am sure anything is possible and it does happen but I would imagine it to be an exception not the rule.

Second you'll have to define what "too many hands" means. The fish is literally putting money into the pot for 100% of hu hands and hands likely get dealt faster in heads up so the fish would likely see more hands per unit time hu.

I would think a fish would find folding much easier in hu because he is not bored folding folding folding and can see the point of folding occasionally, while in 6 max he would be desperate to get involved and simply play too many hands where he/she should not be.

Regarding your second question, yeah he would play more hands hu, but if we use PLOHU as a example, playing nearly 95% of your hands heads up is not a mistake really, most of the best regs in huplo play close to that, so at least the fish would not be making -EV plays preflop, but this would be the total opposite in 6 max where he/she would be.

Also isn't it more fun for a fish where they can play more hands vs folding and folding over and over in 6 max, doesn't this have to be taken into account as in making the fish happy and enjoying themselves playing poker which is huplo say? while they would be bored af playing 6 max, ok this is a different topic to thread I know but just thought worth adding I thought.

So to define what is too many hands" well basically too many hands is playing too many hands preflop and getting involved in hands where they should not be, and if using PLOHU, they aren't making this mistake of playing too many hands while in 6 max they would be making a big mistakes preflop at least.

I don't understand. I mean the fish doesn't have to fold in 6 max or heads up so he doesn't have to get bored at either game. Not sure how boredom plays into it. Fish are going to play hands they want to play regardless of format, position, number of players, etc. In HU he simply gets to see more hands more frequently which is the point Brokenstars was trying to make.

I mean think of it this way 6 max probably plays something proprtional to 1/3 as slowly as heads up since 2 players can reasonably make decisions 3 times faster than 6 players.



Playing more hands didn't necessarily mean that he changes the frequency with which he plays post flop it meant that in the same amount of time the fish would have literally been dealt and played more hands in hu vs 6 max which means the fish gets more frequent opportunities to make mistakes AND those mistakes always cost him money since the fish is forced to pay a forced bet every hand in hu.

Also even if the fish does play a wider distribution of hands which the fish should hu, that doesn't automatically make their preflop decisions +EV. Just playing the correct frequency preflop doesn't mean the fish is making the correct play because EV is based on the entire hand and it's very likely if a fish was a loser with a tighter range adding more hands and likely more marginal hands is only going to make it worse because there are bigger leaks than just hand selection.


I think I covered all of this above but again what does too many hands mean?

Let's say I am a fish and play 30% more hands than I should in 6 max. How many hands "should" I play? Like what does that even mean?

So let's say by postion the percent of hands I should play are:

UTG - 17%
HJ - 22%
CO - 30%
BTN - 45%
SB - 35%
BB - 55%

So averaging that I "should" be playing about 34% of the time.

So a fish plays 30% more hands than he or she should so that is only .3*.34 = 10.2% more than he should so the fish is still only playing 44.2% of the time which is still 51% less than heads up.

Ok what if the fish plays 100% more hands? Still only 68% of the hands (looking at the average) which is still 27% less than 95% of hands.

Now I admit I am playing pretty fast and loose with these numbers and I hope that I am not missing something that totally invalidates my point (other than maybe the average isn't the best metric to use here) but you can see it still takes a fish making gigantic mistakes in 6 max to come close to playing the same frequency of hands as hu AND that's not even considering that we're talking about the absolute numer of hands seen and not the frequency with which villain sees postflop.

Why are we saying "recreational" = "fish"?

^ fair point.

The answer seems to be in the question itself, so hard to answer. Heads up he loses way faster. You can then add the number of tables, hands, the quality of players. The good player vs. one fish is, of course, winning way faster playing one table heads up vs. playing one table ring.

My quote was response to guy who said you just have to look winrates of hu players to see that recs lose more in hu. It's not that simple.
I don't actually know where they lose more, but everyone says hu so i guess it is hu. I assume someone did look at data to confirm that(You would have to look at how much recs are losing, not how much are pros winning).
By faster i meant winrates. There is good point above that you are playing more hands per hour in hu. Although on average even recs are playing more tables when playing ring games then hu.

Calculation goes like this
Lets say there are 6 players with exact same strategy. They are losing to rake 6bb/100(arbitrary number) . So their winrate is -6bb/100. This means every 100 hand in total they lose 6*6 36bb.
If you remove one player and put one much worse so that their winrate is 2bb/100 instead -6bb/100 he would have to lose 5*(6+2) 40bb/100 to them. As he also pays rake his winrate would be -46bb/100.
So just because pros have small winrates in ring games doesn't mean recs are not losing much.

Also the main reason why sites are so concerned with players losing too fast in hu is because as you see in calculation big percentage of recs loserate goes to site(I used arbitrary numbers but it's obvious that point still stand). While in hu much lower percentage of recs money goes to site.
They may be missing that despite hu pros are taking bigger percentage they will battle each other if there is reasonable number of tables(and there are no bots) so they will give more rake that way.

From a sites point of view.
They marketed and advertised and got a fish onto their site.

A fish shows up and play 100 hands and he busts.

If the fish plays heads up, they get 200 hands worth of play, 100 hands from fish and 100 hands from the HU reg.

If fish plays 6max, play against 5 regs, which creates 600 hands of play. The presence of the fish in the game, creates reg vs reg rake.


I think sites care less about how much money the regs win, and much more about how much volume of rake gets generated.

You know each hand only gets raked once right? 2 people in a hand does not mean "2 hands worth of rake" for the site

When you have a rec hold up 5 other players in a 6max game, rake is being generated once between 6 players, compared to that one rec playing a hu player, and then those other 5 regs would need to play more hands between themselves which would lead to more rake for the site. Sure a rec loses more bb/100 to a hu player but the same rec holds up 5 other 6max players from playing between themselves or vs playing someone else which overall means far less hands all together and far less rake to the site.

Does this have any merit?

I dunno, at least I'd rather face a 50/5 type who can't fold a hand postflop in 5/6 max rather than in heads up. Usually it's better to play rather tightly against such a player and if I play tight in heads up the opponent will win many blinds uncontested from me. Or I'll have to make some high variance light value bets, which I could avoid in 5/6 max and concentrate on betting good hands only against that particular player.

Depends a bit of course on the exact positions and what the other players on the 5/6 max table are like. If the table is otherwise full of good, aggressive players it can be hard to isolate the fish, but if the table is otherwise lucrative as well (due to nits to your left for example), then I'd rather play with many opponents.

And answering the actual question, I always thought that ie. calling with A2, then calling consequent bets after hitting an ace (ie. typical fish behaviour) is a smaller mistake in heads up. In 6 max it's very likely someone either beats him already or has nice equity with a draw, making his calls -EV. In heads up a crappy top pair is a much better hand. Which at least to me kinda makes fishy play a bit less fishy.

I have to admit this was a bit interesting and counter-intuitive.

My initial thought was that since winrates are much better HU, AND rake is higher (in terms of bb/100), then that must mean the fish MUST be losing more per hand not just hourly. But that's actually fallacious, since it doesn't account for the lower percentage rake at HU (site rake policy) and simple fact that there are less players paying.

Overall game rake (casino winrate) at HU is considerably less despite player per/100 rake being more (something like 10bb/100 instead of 6). Even if you if could beat up on a fish better HU than 5 regs could at six max it still might not make up for rake difference. With a 20bb HU winrate, and 20bb total game rake (10bb for each player), it gives the fish a 40bb loss rate which is less than the 46bb for 6max previously quoted.