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OSUAce · High Card Joined: 22 Nov 2005 Posts: 15

I don't know if its been written or brought up before, but my roommate and I came up with a pretty simple equation for determining how many double ups it takes to win a tournament. When I say double ups I don't mean on just one hand, but through the tournament, moving from 1500 chips to 3000, from 3000 to 6000....etc.

If you arn't familiar with the Ln function, just trust me

Number of Double-Ups required to win = Ln(Number of Entrants)/Ln(2)

So if 32 people buy into a tournament, then you must double up {Ln(32)/Ln(2)} times. This works out to be 5. (2^5=32)

So for the WSOP main event with a field of 5619 people, the winner had double up {Ln(5619)/Ln(2)} times, which works out to about 12.5

Note that if you need to double up 9 times to win a tournament, after 8 double ups you should own half the chips in play and probably be heads up or short-handed. After 7 double ups you should have 1/4 of the chips in play, which means if you have the average chip stack there are only 4 people left.

I like to use this equation to track my progress during a tournament to give perspective on how far I've come and how far I still have to go.
For instance, if I bought into a 500 person tournament, I know that I have to double up {Ln(500)/Ln(2)} times to win, which is about 9.
If I started with 1500 chips, and now I'm up to 8500, how far have I gotten?

Progress= {Ln(CurrentStack/OriginalStack)/Ln(2)}

So in this case I've doubled up {Ln(8500/1500)/Ln(2)} Times, which is 2.5

So out of the nine required double ups, I've gotten two and half of them out of the way.

2.5/9 = .277. So I can say after earning 8500 chips that I'm about 28% of the way to claiming #1

I pretty much winged this post, so if anyone has any comments/additions/critisisims, they're all welcome.

Ritter88 · High Card Joined: 23 Nov 2005 Posts: 3 Location: Chicago

It's kind of interesting and I can't argue with any of your math, but in my opinion it takes up some brain real estate that is best allocated elsewhere.

There's so very many things to be paying attention to that have practical implication to the play of hands as far as opps. tendancies and table dynamics, I just don't like spending much energy on things that are outside of my control.

Also, in your example, while I can't dispute the accuracy of your math, I have strong intuitive doubts that with 8500 chips you're anywhere near "28% of the way there". Things can change so quickly, and while you're calculating your Ln functions, you might miss a clue that could save your tournament life.

I do keep track of my Q as per Harrington, but as he says in Vol. 2, Q is the "weak force" implying that it's not nearly as relevent as the size of your stack in relation to the players at your table only. (for those who don't know, Q is the size of your stack divided by the average chip stack, so if the average is 2500 and you have 5000, your Q is 2).

Every now and then, I'll figure out the total chips in play and divide it by 9 to establish kind of a "final table target" and monitor my progress relative to that number, but again, it's pretty much just for entertainment value.

It does remind me how much I enjoyed algebra in school though...

copyright83 · Posted: Tue Nov 29, 2005 1:28 am Post subject: Other algebraic thoughts

I've been doing a little thinking on FTP's blind structure for these tourneys. I decided to put a thought I had to the test.

The key figure in these calculations is average orbits, or the number of laps around the table that the average stack could make. The cost per lap is figured as SB + BB + (9*Ante). Yes, this changes as tables get shorthanded, but my analysis goes only up to the money (in this tourney, which was a $10 tourney last night, I busted out 38th when 36 paid).

(Columts L to R: Level, average stack at start of level, cost per orbit, average orbits.)
Lv Avg. Cost AvgOrbit
1 1500 45 33.3
2 1644 60 27.4
3 1920 75 25.6
4 2209 90 24.6
5 2588 120 21.6
6 3105 150 20.7
7 3744 180 20.8
8 4363 240 18.2
9 5126 300 17.1
10 6211 585 10.6
11 7436 675 11.0
12 9263 1050 8.8
13 11478 1200 9.6
14 14270 1575 9.0

(and here I busted out)

Once the antes kick in at level 10, everyone suddenly becomes short stacked relative to the blinds.

Another observation: In general, at any point in the tourney, it takes 40-45 minutes to cut the field in half from its current size. This can be useful (i.e., there's 72 left, 36 cash, it will take 4-5 levels to reach the money) in planning long-range.

Just throwing it out there.

Mike (copyright1983)

If I were better at writing concluding sentences, then this one would be different. --Anonymous

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