Corrections to incorrect thinking

After doing some more thinking, I realize I need to correct two mistakes in my recent thinking. Thinker, heal thyself! :-) The first mistaken thought process I want to address is the hpe formula I came up with last night. I knew at the time I devised it that it had a flaw, but couldn't quite put my finger on what that flaw was. Now I can. At a six player table, only five players can be eliminated; once the fifth player is eliminated, you have a winner and the tournament is over. The sixth player can never be eliminated. My original formula had the winner eliminating himself, which is a logical impossibility. The formula worked fine for places 2 through 6, but failed for first place finishes; the hpe value came out too low in those cases. The hpe for the first place finisher should be identical to the hpe for the second place finisher, since they both played the same number of hands and both saw the same number of players eliminated (the 2nd place finisher sees himself being eliminated on his way out). The corrected formula is therefore as follows:

hpe = num_hands / (num_players + 1 - max(place,2))

The other thought process I want to correct is my recent theory about second place finishes. The golden 2 is untenable. The golden one-two is tenable, and must be the goal. To achieve a profit, both first and second place finishes are equally important. Without the first place finishes, you have no realistic chance of making a profit. Without the second place finishes, you need more first place finishes than you otherwise would; this also ends up meaning you have no realistic chance of making a profit. I'll amend my golden one-two definition slightly. To achieve the golden one-two, you must average just a hair better than one first place finish and one second place finish every six tournaments. Where that hair falls is up to you!

buy_in entry_fee num_players num_hands place winnings

 50000       800           6        71     2   105000
 50000       800           6        31     5        0

delta: $3,400
tournament balance: $1,255,090
balance: $6,385,821