Is There Value in NLHU-MULTIS?

[Mr.November]

Is it really worth it to dish up 22 bucks to play the big NLHU-Multis on PS in the long run? Or is it better to just play NLHUSNG(1vs.1) one at a time for a better hourly-rate? Or how about the 4-man NLHUSNG?any data to back up responses?

[PrimordialAA]

I mean it's all really simple math... what do you think your win rate is in 1-1, the HU tourneys, and the 4 mans, for the limits your playing, give me some #s and I can do the math for you

[jay_shark]

Here is a post I wrote last year ( can't believe a year went by so fast ) about why choosing a 4 player tournament is often times more profitable .

http://forumserver.twoplustwo.com/sh...Number=7700993

[Indiana]

2+2ers like me have struggled with pages of math on this topic for years....the problem is figuring out what you win rate is in the 2nd match because bayesian statistics dictate that the 2nd opponent must be better than a random opponent after he has gotten past the first round.

I dont play 4mans because they take longer, make me more tired, and frustrate me when I have to wait for the 2nd match.

Indy

[TNixon]

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I have to wait for the 2nd match.

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Depending on how long the wait is, that right there can be a sufficient reason to avoid them.

But there's a bigger issue: after looking at that old thread, it seems that yet again, people are trying to make direct comparisons where those comparisons are impossible or irrelevant.

You can't compare profits from a $100 4 man directly to profits from two $100 2 player sngs. It's not the same thing at all. You're comparing apples and oranges.

If you want to make a valid comparison, you have to compare a $100 + 5 4 man to a $100 + 5 2 player and a $200 + 10 2 player, since that's basically what you're doing when you play a 4 man, playing double or nothing.

The average profit from a $100 4 man is $39 (using the very basic assumption of a 60% winrate for both games). If you were to play a $200 tournament *every* single time you won a $100, you'd end up with:

40% of the time lose the 100: -105
24% of the time win the 100 but lose the 200: -115
36% of the time win the 200: +290

Profit in this scenario is $34.80. Obviously, playing the $200 game for free is worth a fair amount. However, the skill of the players involved needs to be taken into account as well.

In the other thread, this was basically ignored by certain people (who seem to be fond of making incorrect comparisons, such as comparing a $100 4 man to 2 $100 2 mans), because the same thing can happen in individual matches. If you play a $100 followed by a $200, your first opponent might be a good player, giving you a smaller edge. If you beat the first opponent, your second one might be a good player.

However, there's a very important difference. In the series of 2 single tournaments, there are only 2 opponents in the player pool. But In the 4 man, you have one extra opponent. There are 3 potential opponent instead of 2. You only play 2 of them, but there's a very reasonable chance of playing the toughest 2 opponents out of the 3. For this reason, you can't simply ignore the fact that your second opponent won his first match. Yes, the better opponent in the other first game could lose, leaving the donk to you, but the fact of the matter is that there's going to be some amount of skew towards better opponents, just because the player pool is larger. Your first opponent in a 4 man is just as likely to be a good player as your first opponent in two individual games, but your second opponent in a 4 man is *more* likely to be a good player than your second opponent in the two individual games. More importantly, no matter what the initial arrangement is, you are more likely than not to end up playing the better 2 players out of the three, which is going to have some amount of impact on your overall winrate.

And it really doesn't take very much skew at all to erase the extra profit from the second rake-free game. A 1% difference in winrate in the second game (60% first game, 59% second game), cuts the advantage of the 4 man in half. A 2% difference (60% first game, 58% second game) erases it completely.

There's also another issue. The above math assumes that you play a $200 following *every* $100 that you win. If you consider them independently, the profit from a $100 game is $15, and the profit from a $200 is $30. Playing a mixture of $100s and $200s independently gives an average profit of $22.50 per game, or $45 for every 2 games, which is significantly higher than either number above.

Apparently just having the choice of whether to play the second game or not is worth quite a bit, which would seem to indicate that double-or-nothing is always a bad bet, although that seems extremely fuzzy and counter-intuitive to me.

[soop]

Nice explanation TNixon.

That last bit makes perfect sense to me. If you have a 60% win rate at both 100's and 200's (lucky you), then you are better off playing 200's. Waiting until you win a 100 means you only play 60% as many 200's as 100's and thus are worse off than if you played an equal amount of 100's and 200's.

[TNixon]

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Waiting until you win a 100 means you only play 60% as many 200's as 100's and thus are worse off than if you played an equal amount of 100's and 200's.

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Duh.

How was that not plainly obvious to me? [img]/images/graemlins/smile.gif[/img]

Of course, the normal caveat about assumptions. Your winrate at $200s will drop just as it would against playing the best 2 out of three opponents in a 4 man tournament.

The answer isn't really an obvious "4 mans are clearly more profitable", though. It depends on how the "best 2" opponents compare to the average opponent at the next level up. If the 2 best players out of 3 in a $100 4 man are worse than the average $200 single sng opponent, then the 4 mans are a clear win. If the reverse is true (which is entirely possible, I really don't know how much skew you would get from the bigger player pool, but a 50% larger pool has to make *some* amount of difference), then 4 mans are a loss.

So, as with almost everything else in poker, I guess the answer is "it depends".

Shocking, I know.

[img]/images/graemlins/smile.gif[/img]

[jay_shark]

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I have to wait for the 2nd match.

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Depending on how long the wait is, that right there can be a sufficient reason to avoid them.



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Almost everything you talked about was mentioned in great detail in the old thread . That's the problem with the 4 man tournies is that there is a waiting time which does cut into your hourly profits .

Your variance is obviously higher but there is a decent chance you may profit more from playing them .

[Indiana]

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but your second opponent in a 4 man is *more* likely to be a good player

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that's what i said above and i agree. this is the difficulty in this problem...the best way to figure out the "truth" to this problem is to gather a [censored] of data and examine ROIs and hourly rates from the data....There's just no way mathematically to calculate a posterior probability of winning the second match, GIVEN that you've won the first match, because the 2nd player has to be better on average than the first, in a bayesian framework.

Indy

[TNixon]

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Almost everything you talked about was mentioned in great detail in the old thread .

[/ QUOTE ]
If by "everything" you really mean "everything except for the fact that nobody actually tried to make a *correct* profit comparison, but there where a whole lot of correct ones", and you also exclude from "everything" the fact that although people did mention that the opponents would likely be tougher in the second round, there wasn't ever a clear enough explanation that you didn't attempt to wave your hands and dismiss the issue by saying "but you can end up playing those same opponents in a regular game", then...

er...wait...those were my two main points, and neither one of them was discussed in any sort of "great detail" at all.

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Your variance is obviously higher but there is a decent chance you may profit more from playing them .

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GJ drawing useless conclusions out of thin air. There's also a decent chance you may profit less from playing them. Your point?

In fact, here's one of your final quotes from the old thread, which shows exactly why there wasn't enough "detail" in the discussion.

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From personal experience and from what I've shown mathematically , it's more profitable playing the 4 way shootout .

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Because you drew that conclusion based on personal experience (which as you should know is completely useless unless you've actually recorded stats for comparison, and even then is subject to sample size issues), on math that was incorrect because you still don't seem to understand that you can't compare an apple directly to an orange, and on some hand-waving to simply ignore the fact that there are very real mathematical and logical reasons that the two opponents you play in a 4-man are likely to be tougher opponents than any two random players.

And then, of course, despite the shakiness of the foundation, you present it as an obvious, foregone conclusion, and when somebody makes statements saying that there's a good chance your conclusion was incorrect, you claim they're not saying anything new, and restate your original conclusion without any sort of refutation to anything that's been said.

Classic jay_shark forum activity

whee