Multiplayer vs Heads Up odds: Which one is better?

In another tread it was claimed that you are more likely to lose in a heads-up tournament. The argument is that you need to win 55% of your HU tourneys to recover a 10% rake.

Suppose the blind structure is the same (e.g, 10%) irrespective of the number of players in the tourney. Do you prefer more or fewer players? What is the "optimal size" of a tourney to maximize your expected value from playing the tourney?

Ok I looked up a couple things and here is what I have found out about myself. (Note: My sample sizes are all way too small and may be inaccurate due to the small sample size.)

bodog is the site I have the most stats about my MTT play. From playing 44 tracked MTTs I have cashed in 10, or 22.73%. I have 1 win (2.27%) 1 third place finish (2.27%) and 7 final tables (15.91%). Average field size being 168 players.

Analysis:
In a 168 player MTT top 18 get paid. Pay structure is as follows:
18-10th = 1.2%
9th= 1.7%
8th= 2.6%
7th= 3.5%
6th= 5.0%
5th= 6.5%
4th= 8.0%
3rd= 11.9%
2nd= 20.0%
1st= 30.0%

Now I need some help with the math

Ok so lets say you are playing $5 MTTS with average of 170 players, that means prize pool is $850. If you played 100 5+.50 Mtts you are in for $550. A min cash in one of these games is 1.2% of $850 or $10.20. To recoop the $550 of buy ins you need to cash 53.92 out of 100, ($550/$10.20). So we can clearly see that if you are only min cashing in MTTs you are not going to be a winning player.

Look right so far nuts?

jordanbillie said:

Ok so lets say you are playing $5 MTTS with average of 170 players, that means prize pool is $850. If you played 100 5+.50 Mtts you are in for $550. A min cash in one of these games is 1.2% of $850 or $10.20. To recoop the $550 of buy ins you need to cash 53.92 out of 100, ($550/$10.20). So we can clearly see that if you are only min cashing in MTTs you are not going to be a winning player.

Look right so far nuts?

Click to expand...

No. You don't need to cash that often to be profitable because you will win more than the min cash (on average) when you make the money.

nuts422 said:

No. You don't need to cash that often to be profitable because you will win more than the min cash (on average) when you make the money.

Click to expand...

Yes I know that, that is why I said if you are just min cashing you won't be profitable. Of course I am not just min cashing as you can see from my stats.

So going on with some analysis:

My 15.91% final tables is nice because that would be almost 16/100 tournament that I get at least 1.7%, so thats a guaranteed $230 over the course of 100 $5 mtts (1.7% of $850 times 15.91). Out of those 7 FT's only 2 were 9th place and the other 5 were better (8,7,7,3,1). If we take a look at my 2 7th place finishes (4.54%) they would make me an extra 1.8% on top of the $230 or another $69.46 lets say $70 (1.8% of $850 times 4.54). So now we are up to $300...OH CRAP I FORGOT ABOUT MY MIN CASHES. So that is 10 cashes, 7 being final tables so 3 min cashes or 6.81%. A min cash gets us $10.2 so times 6.81 equals $69.46 over 100 MTTs. So we are at $370 or -$180 if we pretend that my stats do not include that one very important win and the third place finish, they were both just a minimum cash instead.

From looking at this data I can conclude one thing: The more entrants a tournament has, the harder it is to make a profit in the long run. You have the chance at the big payday for a win, but without it you won't be making much.