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.