True EV of PP Steps tournaments

[fnurt]

A number of people seem to be under the misapprehension that PartyPoker Steps tournaments offer good value because you can win big money for the cost of only a low initial rake. So I put pen to paper in order to determine the REAL house take on these tournaments.

Step Higher:
Step 5: $5000+300 (Advertised: $5000+300)
Step 4: $1940+210 (Advertised: $2000+150)
Step 3: $435+100 (Advertised: $500+35)
Step 2: $74+36 (Advertised: $100+10)
Step 1: $20+13 (Advertised: $30+3)

Original Steps (1-table):
Step 5: $1000+65 (Advertised: $1000+65)
Step 4: $461+74 (Advertised: $500+35)
Step 3: $167+48 (Advertised: $200+15)
Step 2: $38+17 (Advertised: $50+5)
Step 1: $7.60+4.40 (Advertised: $11+1)

Mini Steps:
Step 5: $400+30 (Advertised: $400+30)
Step 4: $127+38 (Advertised: $150+15)
Step 3: $36+19 (Advertised: $50+5)
Step 2: $11.70+10.30 (Advertised: $20+2)
Step 1: $2.60+3.40 (Advertised: $5+1)

All of this is derived through basic algebra. You can double-check any of my numbers, and I encourage you to do so, by simply looking at the possible outcomes from any step and seeing if my figures add up. For example, choosing one at random, Step Higher 2:

Rank 1(10%): Freeroll into Step 3
Rank 2-4(30%): Try again Step 2
Rank 5-8(40%): Loop back to Step 1
Rank 9(10%): $3 Cash

Thus, the total of all the outcomes is (10% * 435) + (30% * 74) + (40% * 20) + (10% * 3), which comes out to exactly 74. Sometimes, rounding error may cause a slight difference to appear.

The non-mathematical reason why there is such a difference between actual EV and advertised price is that the "freeroll" aspect of these tournaments obscures the fact that in effect, you pay the rake at each and every step. Because this is non-intuitive, and I can easily envision taking all day trying to persuade someone of it, I prefer to stick with the numbers, because numbers don't lie.

Hopefully, this information will help people make intelligent choices about whether these games are worth the investment.

[fnurt]

Bump in case someone is interested!

[maddog2030]

Nice work. I saw it the first time and bookmarked it. Just posting so you know there's people who are paying attention and like the results, but just don't have much to say on the subject.

[uphigh_downlow]

I am looking to invest some time in the steps, but I did not get the point of this post. Mostly because u left it open-ended.

Are u trying to say that the rake on each trny is incredibly high??

I cud be wrong, but the way I understand it is that its better to rise up the levels, than attempt a direct buy-in.

Its early here, so I cud be completely off. Do enlighten me.

Once you do, mebbe an hourly rate analysis could justify investing in a higher buy-in step directly.

Anyway looking for a reply.

[gildwulf]

bump, great post...all the more reason to buy in at the top

[uphigh_downlow]

[ QUOTE ]
I am looking to invest some time in the steps, but I did not get the point of this post. Mostly because u left it open-ended.

Are u trying to say that the rake on each trny is incredibly high??

I cud be wrong, but the way I understand it is that its better to rise up the levels, than attempt a direct buy-in.

Its early here, so I cud be completely off. Do enlighten me.

Once you do, mebbe an hourly rate analysis could justify investing in a higher buy-in step directly.

Anyway looking for a reply.

[/ QUOTE ]

Nvm I got it once i had my cofee.

The point is that only the step 5 offers value for money. The others are incredibly bad value for money given the vig, that you dont actually see.

Good analysis. Glad there are doubters like you that take the time to research seemingly trivial issues and come up with interesting results.

Thanks. Ther go my plans for steps

[Isura]

My head hurts. I don't get your math here. /images/graemlins/confused.gif

[ QUOTE ]
Thus, the total of all the outcomes is (10% * 435) + (30% * 74) + (40% * 20) + (10% * 3), which comes out to exactly 74. Sometimes, rounding error may cause a slight difference to appear.

[/ QUOTE ]

For example why is 10% * 435 used instead of 10% * 535, since $535 is the cash equivalent of buying into step 3? How did you calculate the whole thing, start from the buttom and work up? Please clue me in.

[fnurt]

[ QUOTE ]
My head hurts. I don't get your math here. /images/graemlins/confused.gif

[ QUOTE ]
Thus, the total of all the outcomes is (10% * 435) + (30% * 74) + (40% * 20) + (10% * 3), which comes out to exactly 74. Sometimes, rounding error may cause a slight difference to appear.

[/ QUOTE ]

For example why is 10% * 435 used instead of 10% * 535, since $535 is the cash equivalent of buying into step 3? How did you calculate the whole thing, start from the buttom and work up? Please clue me in.

[/ QUOTE ]

$435 is the correct number because it's the actual value of the buy-in that matters, not the displayed value. For example, the value of a free entry into a $500+100 event and a $500+200 event are exactly the same - either way your EV is $500. This is the phenomenon that makes many of these tournaments bad investments - not only do they take a rake up front, but a big chunk of the prize pool is already earmarked for the purpose of paying rake into your next tournament.

You're right that it's a circular result - the only reason I know the value is $435 is because I've done the math and found it to be $435. That's where algebra comes in; I expressed the EV of each step in terms of an equation, and then solved them all. For example, for Step Higher, you can easily calculate the EV for Steps 4 and 5. You can then express the EV for Steps 1-3 as X, Y, and Z, respectively, and create equations like Y = (10% * X) + (30% * Y) + (40% * Z) + (10% * 3). This is the exact same equation I used in my original post.

Once you have 3 equations using 3 variables, solving them for a numerical result is just basic algebra - by which I mean I probably would have been a lot faster at it 20 years ago!

[AleoMagus]

You should look at this excellent post by chaosuk:

Steps are not a rake trap (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=2325932&page=&view=&s b=5&o=)

I think it will show that while your analysis may be correct, it doesn't much matter, and it's really what we do everyday in ordinary SNG play, steps or not.

Regards
Brad S

[PrayingMantis]

Wow Brad, I was looking for this post by chaosuk for hours today (well not exactly hours), in order to link it here to this thread. I gave up when my search didn't get any results and I got tired of it.

Good job finding it. I also think it was a great post.

[curtains]

I didnt read it just now but isnt the idea in STEPS that if you are +EV that you build up EV in each step, that cancells out the rake effect. Despite that I always buyin at top step otherwise I won't play....too annoying otherwise.

[PrayingMantis]

I think this gets complicated because then it's a question of the time you put in order to "build up" EV from lower-steps. It's no wonder you buy in directly to a top step, because the EV you earn by winning seats at lower steps does not worth the time, and it might actually be -EV ($/H wise) in comparison.

But I don't think this has much to do with chaosuk post, which deals with the economics of SNGs' rake in general, and specifically the steps.

[fnurt]

[ QUOTE ]
You should look at this excellent post by chaosuk:

Steps are not a rake trap (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=2325932&page=&view=&s b=5&o=)

I think it will show that while your analysis may be correct, it doesn't much matter, and it's really what we do everyday in ordinary SNG play, steps or not.

Regards
Brad S

[/ QUOTE ]

That is a very good post and so is the one that inspired it. I think both sides have some valid points.

First, it's completely true that my calculations are based on the results for a hypothetical "average" player, one who has exactly a 10% chance of finishing in any given slot. That player would pay a lot of rake if they just sat there and played regular SnG's all day too. But even though the dynamic is the same in either case, it's still not clear to me that both are equal in terms of EV. Who knows, maybe Steps are the better deal for the average player because they may let him play all day for only minimal rake, even if he wins nothing.

But there is a second point, related to the flat structure of most of the steps. Imagine a ridiculously flat $50+5 where 1-9 places receive an entry into another $50+5, and 10th place receives $5 cash. Obviously, no one at all will beat this tournament. And looking at less ridiculous examples, it's clear that the flatter the payout, the harder a game is to beat.

I think I could probably develop some useful figures if instead of looking at the average player, I tried the same equations using a winning SnG player: let's say 15% first, 13% second, 12% third, which would be a robust 40% ITM for normal SnG's. Are those figures reasonable?

[chaosuk]

A belated thanks for the kind words guys; I'm planning on re-writing this article adding a little extra on the flatness and sticking it on my blog, which I haven't got up yet - it would be less of a blog more of place to store articles. But I would take issue with this statement:

'it's clear that the flatter the payout, the harder a game is to beat.'

hopefully I'll expand on it futher when I write it.

regards

chaos

Good job. But your computation have a major leak. You assume your "ROI" or your win chances are the same for all steps. It cannot be true - your chance of winning 500+50 SNG and 5+1 SNG are never 0.1 at the same time.

I would be very glad to you, if you take your time to make ajustments to your results. For example let's assume your are break-even Step 3 player. (0.1 for each 1-10 in Step 3). So you would have like 0.15,0.15,0.10,... and so on Step 2. And 0.2,0.2,0.15 ... on Step 1. But 0.08,0.08,0.1... on Step 4 and 0.05, 0.05, 0.08 ... on Step 5 (Certainly that are "dummy" probs, i have no information how good you might be on level up/down, if you were break-even on Level X.)

PS. That is not critic, i am really willing to research this more thoroughly.