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Determining the Conversion Rate of VIP Program Points: The Turbo Takedown at PokerStars

On last week’s edition of Killer Poker Analysis, I covered the following topics:


1.) Open shoving distributions from the small blind in tournament situations when antes are around 12.5% of the big blind

2.) Knowing when to start playing in bigger games

3.) Heads-up play


I also announced that I won’t be doing a podcast today. I’ll miss everybody in the Rounder’s Radio chatroom, but I’m sure that you all will find a way to have a good time without me :)


If things go according to plan tonight, I’ll probably be playing poker at a poker room somewhere in Costa Rica this evening! My friends and I would occasionally play Mexican Poker at The Bike, so I fortunately have some experience playing poker in situations where the primary language spoken at the table is Spanish. Unfortunately, my Spanish is rustier than it was a few years ago, and Mandarin now seems to be my default non-English language. On more than one occasion, I’ve said some random stuff to people in Mandarin while here and have had to correct myself…aiya!


I’ve been working a lot this week, but all the time away from the online felt means that I should be well rested and ready for a big session this Sunday. This Sunday is the last Sunday of the month, so it’s Turbo Takedown time at PokerStars. This tournament costs 3,000 FPP to enter, so the big question is whether the Turbo Takedown is worth the 3,000 FPP. If you want to skip the math, you can skip to the end to get the result. However, following the math is a good idea if you want to learn how to do it for pretty much any tournament on any site that requires loyalty program points to enter.


The most effective conversion rate on FPP is about $0.016/FPP, you should enter the Turbo Takedown if your $EV is at least $48. The more entrants there are in a tournament with a fixed prizepool, the lower your $EV gets, so our goal is to figure out the maximum number of entrants that you’d want in the Turbo Takedown.


There are three components to your $EV:


1.) With a $1,000,000 prizepool and an Audi TT (or $40,000) added to first place, the effective prizepool of the tournament is $1,040,000.


2.) You get $100 for knocking out a pro. In a tournament that’s going to have around 20,000 people, the probability of being at a table with a pro is very low. Assume 40 pros are in the tournament. For your starting table, the probability that all 8 of your opponents aren’t pros is:


(19,959 nCr 8)/(19,999 nCr 8) = .9841


The probability that you have 1 pro at the table is:


(19,959 nCr 7)(40 nCr 1)/(19,999 nCr 8) = .0157


The probability that you have 2 or more pros at your table is .0001 (meaning that such cases are negligible). When you have 1 pro at the table, the probability that you eliminate that pro assuming no table changes and that everybody plays identically is (8/9)(1/8) = .11. 8/9 is the probability that the pro doesn’t finish in 1st at the table and 1/8 is your probability of knocking out the pro given that he doesn’t finish at 1st at your table. Given that table changes occur, the actual probability of eliminating a specific pro is less than .11. However, there are other adjustments that would be necessary to make this analysis exact, and given that the number of entrants in the tournament is unknown, the effort required to account for second and third order effects simply isn’t worth it. The amount of $EV added by the pro bounties is about (.0158)(.11)($100) = $0.17. If the field is larger, the $EV added by the pro bounties is even less. As a result, we can safely ignore the impact that the $100 pro bounties have.


3.) To make things more interesting, PokerStars is giving away cash bonuses based on number of consecutive cashes. Cash two months in a row and get a $100 bonus. Cash the following month, and get a $200 bonus. This trend continues, and if you can pull off 11 consecutive cashes, you get a $1,000 bonus. $1,000 + $900 + $800 + $700 + $600 + $500 + $400 + $300 + $200 + $100 = $5,500! The Turbo Takedown pays 5,000 spots regardless of the number of entrants. If the number of entrants is E, then the $EV of this promotion is:


((5000/E)^2)(100) + ((5000/E)^3)(200) + ((5000/E)^4)(300) + … + ((5000/E)^9)($800) + ((5000/E)^10)($900) + ((5000/E)^11)($1,000)


When E = 25,000 (maximum field size), $EV of the cumulative ITM bonus is $6.25, meaning that the cumulative ITM bonus is far from being negligible.


Let E denote the number of entrants. You want to enter the Turbo Takedown when the following equation is satisfied:


($1,040,000/E) + [((5000/E)^2)(100) + ((5000/E)^3)(200) + ((5000/E)^4)(300) + ... ((5000/E)^9)($800) + ((5000/E)^10)($900) + ((5000/E)^11)($1,000)] > $48


The result: you want to play in this month’s Turbo Takedown if there are 24,357 or fewer entrants.


May Your EV Always Be Positive!


Tony Guerrera



  



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One Response to “Determining the Conversion Rate of VIP Program Points: The Turbo Takedown at PokerStars”

  1. Gino Jacquelin says:

    Thank you for making the effort to line this all out for people like us. This posting ended up being really useful to me.

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