Expectation
 

Let’s say you’re at 20/40 table and playing with 8 equally bad players. You make $40/hr at this game.

4 seats open up at the 40/80 table. 4 of the 20/40 players from your table move over and you follow. In the other 4 seats at the 40/80 table there are players who play just as well as you.

Would you make the same, more, or less at the 40/80 table per hour?

Re: Expectation
 

Less.

Re: Expectation
 

more

Re: Expectation
 

What happens to the 4 seats in the 20/40 game? Are they filled (presumably by more bad players) or do you get to play 5-handed?

Re: Expectation
 

the answer is: depends.

the problem with this question is that you have quantified each player's losses per hour in the 20/40 setting, but you cannot carry that number to the 40/80 tables as you have added a new variable to the mix. the bad players may lose more or less per hour when confronted with a table conformed of more solid players and less poor players. you cannot determine their winrates based on the information youve provided us.

Re: Expectation
 

if you make $40/hr, then you're opponents make that much in mistakes per hour against you. since they are equally bad, it is uniformly distrubuted amongst them. also, that is not to say that they EQUALLY contribute individually to your expectation as you are not in a pot with them all the time as they are in a pot with each other. but in the long run their mistakes are your gains...

now add other good players and now you HAVE to earn less from those other players WHEN you're in a pot all together. SOMETIMES those good players will get you out of a pot to play with those bad players. further, there are just fewer bad players so the cards are distrubited evenly among all 10 players...the good players will get good cards and play them WELl against you whereas you had bad players playing good cards against you before...

i think you'll earn less...but not by all that much in terms of relative BB/hr...but clearly more in terms of absolute $ figures...

-Barron

Re: Expectation
 

The thing is, you're going to be in pots with the bad players alot more than you're going to be in pots with the good players, assuming that one characteristic of the bad players is that they are too loose (a fair assumption). So while in the 20 game you were playing in 100% of the pots with bad players, it would probably drop to about 60-70% in the 40 game, as opposed to 50%, which makes up for the good players, against whom you have a long run expectation of 0 against.

Re: Expectation
 

where's your seat in the 40/80?

Re: Expectation
 

i think that you are trying to remedy the problem by saying that the players will play the same in the 40/80 game as they would in the 20/40 game, and therefore when a bad player enters a pot, he splits his negative expectation with the other good players in the pot equally. while that is the case, his negative expectation between entering the pot of a 20/40 game and a pot of a 40/80 game could be significantly different, because you dont know how he will change his game plan. he might tighten up a bit preflop with the increased aggression and decreased "pot odds" by the other loose players playing in every pot with him. he might raise more preflop, he might defend his blinds less, he might checkraise more often, etc etc. without even the littlest player traits defined, you cannot quantify precisely what his ev is between games.

in most situations, it would be logical to assume that your BB/100 would decrease when moving up in limits with better players, but that is not always the case is all that i am saying.

Re: Expectation
 

You would definately make more, there's no question about it. (Assuming nuetral seating.)

Re: Expectation
 

Yes, I was assuming that the bad players would play pretty much their same game/style, I think that was sort of a given.

Re: Expectation
 

I believe your BB/hr would decrease slightly but $/hr would increase significantly. Even though bad players now account for only 50% of your opponents pre-flop, since bad players are generally much looser, they will account for significantly more than 50% of your opponents post-flop.

Re: Expectation
 

[ QUOTE ]
You would definately make more, there's no question about it. (Assuming nuetral seating.)

[/ QUOTE ]

uh, more $/hr or bb/hr?

-Barron

Re: Expectation
 

Hi Gabe,

Scenario number one. Your opponents are losing 1/8 of a BB to one player(you) in theory. 8x5=40/hr. or $5/hour per player.

Scenario 2: 5 tough players and 4 bad players. The bad players are losing more than 1/8 of a BB/hr for the following reasons:

1)They are not getting as good a price to draw and hit the really big pots on the hands they play due to:

-more Isolation raises.
-less multiway pots.
-more aggressive play.

2) They will bleed their money away faster pre-flop to 5 tough opponents than just one, also due to insufficient odds.

3) They will never gain any value from poor bluff attempts as tougher players know better.

4) They will lose a few more bets as tougher players value bet them more.

They would now have to lose 200/hr combined ($50/hr each) to 5 players for you to net the same amount as the 20-40 game. The question now becomes, are the bad players really going to lose 5/8ths of a BB each in this game? It's pretty hard to quantify these numbers, but if you believe they will lose exactly this much then you would still have to play better than at least one of your other 4 good playing clones to make the 40-80 situation more profitable. If you chnaged one of the good clones to a break even player, you would now make $50/hr as there was $200/hr to split between the 4 good players. So in order to figure this properly, you need to really have a good idea of how much more the bad players are losing in the second scenario.

In real life, this is a good example of why bad players survive for long periods of time in weak games, so long as they can afford the stakes they are playing.

As a side note, it's my opinion that the reason good players hit a wall as they move up in limits is not only due to the fact that there are more good players, but that the definition of "bad player" changes dramatically.

Re: Expectation
 

hi gabe

you would make more, IMO, in the 20-40 game as described , for the simple reaswon that the bad players will play better in the higher stakes game. let's assume though that they don't. in that case, it looks like you make the same amount in either game. the main issue, of course, is how dividing up the proceeds between you and the good players, effects your ev. gabe, it's definately zero'ed out amongst the good players; the bads are losing twice as much but you must divide their losses between you and the good players.....hmmmm. you know gabe, you might be doing substantially better in the first game. and that second game....whew. for some reason, my experience is that the second game is more volatile than the first.

i'm going to say that while both games are definately profitable, the first game is at least modestly more profitable even if the bad players do not play better in the higher stakes game. the dividing up of the proceeds has got me in a math knot, but in the higher stakes game, you don't have the whole field to yourself. that just somehow seems less profitable.

Re: Expectation
 

You'd make more in the 40/80 IMHO, mainly because of the reduced effects of schooling. Certainly, I think schooling effects are overstated, but this question is set up in such a way that it's going to be very close and we're looking for tiebreakers, and that seems like a good one to me.

Re: Expectation
 

hey gabe, uncle ray has a great article this month in the 2+2 internet magazine concerning this exact topic...said article is likely what inspired your post but just in case you have missed it, check it out...

as to your specific example and question...if a guy is only beating the 20-40 against 8 weakies for ONLY one BB, i think he will struggle to make the same 40 hr.(one small bet/hr.) at twice the limit against with the harder lineup.

Re: Expectation
 

in the long run you make significantly less in the 40 because you have to now divide up what you make from the bad players with the other equally good players. it's a little more complicated (for instance what actually happens is the bad players will lose even more per hour in the tougher game), but the 20 is the clear favorite.

it will take sklansky to answer this sufficiently btw.

Re: Expectation
 

I'd expect to do better in the 40-80 as the bad players' bad plays are less bad in the 20-40 game because of the schooling effect Nate mentions. Subjectively, I think that's why the best games (for me) have a few bad players in them rather than all bad players.

Re: Expectation
 

[ QUOTE ]
Quote:
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You would definately make more, there's no question about it. (Assuming nuetral seating.)


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uh, more $/hr or bb/hr?

-Barron


[/ QUOTE ]

you're just pulling our legs with all your posts, right?

Re: Expectation
 

Usually I like your thinking, Nate, but in this case I must disagree.

You wrote: [ QUOTE ]
You'd make more in the 40/80 IMHO, mainly because of the reduced effects of schooling

[/ QUOTE ]

In the 40/80 game you will also have the other good players interfering with your desired strategies against the poorer players, and it seems to me this interference will cost you more than the effects of any schooling in the 20/40 game.

Anyway, the main reason I said the 40/80 game would be less profitable to you is that you will be divvying up the poorer players' losses amongst 5 winning players (instead of only one winning player), but the game is only twice the limit.

Hopefully for the sake of simplicity we can ignore such things as the house time charge and whether the losing players might play significantly better or worse in the higher game.

Re: Expectation
 

Do you think the bad players are so bad as to be doing much schooling in the game Gabe describes, Andy?

What about the effect of 4 other players as good as you in the 40/80 game? (when you say you like games with a few bad players and the rest good, I'll bet you are still better than most of the other "good" players you are sitting with. Not so in the 40/80 case Gabe posed, however).

Also, what about the fractions?

Re: Expectation
 

I guess we have to make some assumptions to proceed with our answer.

I will assume that the bad players play equally as bad in the 40 game (I think they would actually play worse because their plays become less bad, as it were, with more bad players playing with them in the 20).

Further, I will assume that the bad players equally contribute to the good players.

Finally, I will assume that you are playing 9-handed (sounds like it from the question).

So, at present, you are making $40/hr or 1BB/hr. Each of the bad players is contributing 1/8 BB/hr to you (the only good player). In the new game, you have 4 bad players contributing 1/8 BB/hr to the good players - of which there are now 5. So, your share is 1/8 BB/hr * 1/5 * 4 bad players = 1/10 BB/hr = $8hr.

Stay in the 20.

-Ash


[ QUOTE ]
Let’s say you’re at 20/40 table and playing with 8 equally bad players. You make $40/hr at this game.

4 seats open up at the 40/80 table. 4 of the 20/40 players from your table move over and you follow. In the other 4 seats at the 40/80 table there are players who play just as well as you.

Would you make the same, more, or less at the 40/80 table per hour?

[/ QUOTE ]

Re: Expectation
 

[ QUOTE ]
[ QUOTE ]
Quote:
--------------------------------------------------------------------------------

You would definately make more, there's no question about it. (Assuming nuetral seating.)


--------------------------------------------------------------------------------



uh, more $/hr or bb/hr?

-Barron


[/ QUOTE ]

you're just pulling our legs with all your posts, right?

[/ QUOTE ]

only some...el D doesn't seem to get that either...so dont sweat it

-Barron

Re: Expectation
 

I think the fractional analysis and the idea that a bunch of the money you were going to win is now going to other players is wrong. The fractional analysis that assumes that you can halve the amount you are winning from each player is definitely wrong.

There is actually enough PokerTracker data to figure out a close to definitive answer to this question.

-Michael

Turbo Texas Results
 

I simulated one million hands under each set of conditions using Turbo Texas Hold 'Em. I have my doubts about TTHE's capacity to do certain things well, but I think it's pretty well suited for this sort of macroscopic experiment.

Assumptions:

- The table is 9-handed.

- The blinds are $10/$20 in the $20/$40 game and $20/$40 in the $40/$80 game.

- There is a 10% rake up to $4. Pots are not raked if there is no flop. The players do not chop the blinds. There is a $1 tip on top of the rake on pots of $50 or more.

- 35 hands are played per hour.

Experiment #1 featured one good player (Bret Maverick) and eight fish, all of which used the same profile, Welcome Waldo. Welcome Waldo tends toward being loose aggressive before the flop and loose passive afterward - basically an ideal opponent, IMHO. The limit was $20/$40.

Bret Maverick made an average of $55.6/hour in this experiment. The Waldos lost an average of $28.4/hour. The house made $171.9/hour.

The good player made slightly more than the $40/hour that Gabe specified. I do not think this should matter all that much. I do think it might matter that all the fish were of the same profile, rather than a mix of various fishy profiles.

Note that I'd expect a 2+2er to do quite a bit better than Bret Maverick did against this lineup. The TTHE profiles are not as good as they could be at extracting the most from bad opponents after the flop.

Experiment #2 featured five good players, all using the Bret Maverick profile, and four fishy players, all using the Welcome Waldo profile. The good players are seated in seats #1, 3, 5, 7 and 9.

The Bret Mavericks made an average of $55.0/hour. The fishy players lost an average of $108.6/hour. The house made an average of $159.4/hour.

Seat position appeared to make some difference. The Bret Maverick profile in seat #7 did the worst, winning $46.9/hour. The profile in seat #9 did the best, winning $62.8/hour.

Some preliminary conclusions:

- At first glance, there appears to be almost no difference in the good player's expectation between the two experiments. That is, the money that you're making from the bad players appears to be commutative. You profit x/hand from each bad player, so if there are 4 bad players, you make 4x/hand, while if there are 8 players, you make 8x/hand. Doubling the betting limits should even this advantage back out. You are neither making nor losing money from the good players, since they have an identical profile to you.

- It's interesting that the house was actually making more per hour with the smaller betting limits (not just in terms of BB/hour, but also in terms of $$/hour). I suspect this is because, with the fishier game texture, more flops were seen, and more hands were played out to the point where the house was dragging the maximum rake.

- One thing that I did not consider is that you are likely to see more hands per hour when there are more good players in the game. For example, if we assume that 35 hands are played per hour at the table with 8 fishy opponents, but 40 hands are played per hour at the table with 4 fish and 4 good opponents, then you make about $7/hour extra in the later case.

- As some have alluded to here, it's worth mentioning that the fish are losing money a *lot* faster when there are several good opponents in the game - in fact, they're losing nearly 4x as much per hand in raw dollars, considering the increase in betting limits. If this induces them to play better, or to leave the table more quickly, whatever advantage you might gain from playing at the higher limits would evaporate quickly.

Re: Expectation
 

I would say 44.4%. Instead of eight seats of "dead" money, there are only four. And you must share a reduced pool with the other good players. That reduces your expectation by 5/9. It be reduced even more if the limits stayed the same, but since they doubled it's just a 56% reduction.

Re: Turbo Texas Results
 

see gabe i was right. im always right. im like some sort of genius.

Re: Expectation
 

Interesting point here.

Re: Expectation
 

"since bad players are generally much looser, they will account for significantly more than 50% of your opponents post-flop."

as opposed to in the first case where they make up 100% of your opponents pre and post flop... not a tough problem imo.

Re: Turbo Texas Results
 

Nice little test you ran, Nate, thanks.

Interesting that your sim results show about the same expectation in each game for the good player. Apparently the difference may not be as great as I had thought.

I best like being up against only fish, without good players interfering with my isolation plays, etc. I doubt if the sim could take into account the Mavericks playing differently against the other Mavericks and things like that. It should automatically include the schooling effect results to the extent that exists, though.

Re: Turbo Texas Results
 

Note that while the sim results are nearly identical (and I put a decent amount of stock in the sim in this situation), you'd prefer to stay in the 20-40 because the variance would be much, much lower for the same expectation.

Re: Turbo Texas Results
 

[ QUOTE ]
Note that while the sim results are nearly identical (and I put a decent amount of stock in the sim in this situation), you'd prefer to stay in the 20-40 because the variance would be much, much lower for the same expectation.

[/ QUOTE ]

Would it? I think the 20/40 game has a lot higher variance in terms of BB/hour with more players seeing bigger pots, etc. The 40/80 almost certainly has higher variance in terms of $/hour but I'd guess at we're looking at say a 1.5:1 ratio, rather than 2:1.

Re: Turbo Texas Results
 

[ QUOTE ]
Experiment #2 featured five good players, all using the Bret Maverick profile, and four fishy players, all using the Welcome Waldo profile. The good players are seated in seats #1, 3, 5, 7 and 9.

[snip]

Seat position appeared to make some difference. The Bret Maverick profile in seat #7 did the worst, winning $46.9/hour. The profile in seat #9 did the best, winning $62.8/hour.

[/ QUOTE ]

Interesting sim, thanks! Just want to point out that position shouldn't make any difference since you seated them symmetrically. The differences are just due to variance.

Re: Expectation
 

According to Gabe's set-up, you're making one BB/hour. So the players are apparently not horrifically bad, else you'd be making more.

Having said that though, the thing that makes the bad players bad is playing too many hands. They're therefore playing bad cards pre-flop. But when more of them limp the bad pre-flop limps become less bad.

The way I look at it, which game would I prefer: one where 4 players play worse than I do and four play just as well? or one where all 8 opponents play as well as I do? My expectation in the second game is to break even (disregarding rake and tips); in the first game, I have the power to choose my spots. Subjectively, I don't worry when I see a tough spot or two or three in a game I sit in if there is a soft spot or two or three.

Re: Turbo Texas Results
 

"Just want to point out that position shouldn't make any difference since you seated them symmetrically. The differences are just due to variance."

Seat 9 is the only player with an equally good player directly on his left in seat 1. All the other good players have a bad player directly to their left.

Re: Expectation
 

[ QUOTE ]

According to Gabe's set-up, you're making one BB/hour. So the players are apparently not horrifically bad, else you'd be making more.

[/ QUOTE ]

Agreed, which makes me think they aren't "schooling" to a tremendous extent, anyway.

[ QUOTE ]
Having said that though, the thing that makes the bad players bad is playing too many hands.

[/ QUOTE ]

Agreed that should be at least a large part of it.

[ QUOTE ]
They're therefore playing bad cards pre-flop. But when more of them limp the bad pre-flop limps become less bad.

[/ QUOTE ]

That is an oversimplification, I believe. A common exception would be unsuited mediocre hands which become worse when more players are in. Also, notice Nate's sim did not have them "limping in" a lot but rather fairly LAG preflop (which additionally hurts those mediocre hands which also don't play well multiway).

[ QUOTE ]
The way I look at it, which game would I prefer: one where 4 players play worse than I do and four play just as well? or one where all 8 opponents play as well as I do? My expectation in the second game is to break even (disregarding rake and tips); in the first game, I have the power to choose my spots. Subjectively, I don't worry when I see a tough spot or two or three in a game I sit in if there is a soft spot or two or three.

[/ QUOTE ]

I don't "worry" about it either. Still, I like to see as high a ratio of fish to good players as possible. Notice I am not saying I would like to see a bunch of maniacal fish in the game. We are specifying fish, not salmon rushing desperately upstream to spawn (and in Nate's sim case, the fishiness is more pronounced postflop).

Overall it appears a lot closer than I first thought, but I don't think it is as close as Nate's sim shows, for various reasons. And I rather doubt even Andy Fox would do better at a table only half of fish rather than wholly of fish at the same limit (again, not maniacal fish).

Most of the money won in poker flows from the fish to the good players, and the rest ends up going down the chute. And while I don't fear most good players, I do believe that they often interfere with the holy grail of picking on the fish. (Plus a lot of them are seat plugs).

This reminds me of a Tommy thread long ago where he described the other good players kind of avoiding confrontations with each other to a certain extent, there being fish in the game. He said something about how if (I forget specifcs) had occurred, that would have meant war. So now it occurrs to me that this tacit semi-truce with other good players could be quite beneficial in a way, stylistically speaking (if others are doing it too), in that it helps prevent you and others from interfering too much with the holy goal of picking on the fish.

Re: Expectation
 

[ QUOTE ]
Let’s say you’re at 20/40 table and playing with 8 equally bad players. You make $40/hr at this game.

4 seats open up at the 40/80 table. 4 of the 20/40 players from your table move over and you follow. In the other 4 seats at the 40/80 table there are players who play just as well as you.

Would you make the same, more, or less at the 40/80 table per hour?

[/ QUOTE ]

I saw Gabe this evening at HWP so he posed this question verbally. After a few minutes thought, I told Gabe that the $40/80 game has to be more profitable, assuming that the reason the opponents are bad is typical - that is they are too loose preflop and go too far with their hands post flop.

If the opponents were bad because they are all weak-tight nits, I'd rather have twice as many all to myself at the half size limit. But since you can't find a table full of weak-tight nits in Los Angeles (except perhaps in a bad low limit Omaha game), I felt the assumptions from the paragraph above are reasonable.

Essentially, with a table half full of loose opponents and the other half players who play as tough as you, the typical pots will feature two or three loose players with one or two of the tougher players. Often you will be one of or the only tough player. OTOH, when you are the only solid player in the game, you will all too often be waiting on the sidelines, watching the others play.

The other problem (not mentioned to Gabe) is that if you are in a super good loose game, a great player like Gabe does only slightly better than a very good player (like me), mostly because it's going to take the best hand to win and the decisions at the table are relatively simple.

Anyway, I thing the main thing Gabe was looking for was to see that mike l. was wrong again [img]/images/graemlins/smirk.gif[/img].

~ Rick

Re: Expectation
 

I thought about this one for a while today. the problem I have with your situation is that you only make $40/hr in the game with 8 bad players. if that is the case, you should prefer the 20-40 because the difference between your skill and theirs isn't great enough for you to make more in the 40-80.

I think a more realistic problem would be that you are making $60/hr in the 20-40, so could you expect to make more in the 40-80? I think at this win rate the games would be of equal expectation.

Re: Expectation
 

ok then, I'll bite. what's the difference between more $ and more bb/hr?