Re: Conjecture and Question
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One thing I hear a lot here is the whole "decreasing marginal value" of extra chips. But I think there's something that is being missed here:
If you are an excellent player, one of the best, then your ability to take advantage of a very large chiplead should be in your skillset. Players will know that you are less afraid of them than other players would be because if you lose a big pot to them you still have a nice stack.
Thus, I think for the very best players, having a relatively large stack for your table actually INCREASES your EV for the tournament because of the difficulty for you to go broke - example. Say in the very next hand after doubling up, you get allin with AA vs. KK. If you had not doubled up the previous hand, 20% of the time you will be out of the tournament. However, since you've doubled up, 20% of the time you will have an average stack for the tournament and the other 80% you will have an even bigger chip lead.
Thus by having a stack that's much larger than those around you greatly increases your EV because of the greatly decreased risk of gambler's ruin. Suddenly you can push small edges to the fullest because you know that even if you lose your small edge, you are not out.
Does this make sense? Here's a very contrived but alternate scenario. Say in the first few hands of the tournament, you and 8 other people double up. Then by some bizarre coincidence, within the next few hands all of you are moved to the same table. So now you have a table full of 20,000 chip stacks very early in a 10,000 starting stack tournament. In *this* situation I feel that your EV drops as per Mason's conjecture... now you no longer have an advantage over the rest of your table, you have to worry about any one of the stacks busting you out of the tournament in any one hand.
Note also that the initial premise specifies that Hero is one of the best players. I want to make clear that this is key for giving Hero the increased EV - he must be able to take full advantage of his big stack and not squander the extra chips making loose, speculative plays.
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But if you still have a huge skill advantage then wouldn't the deeper stacks favor you? Since you can therefore make all your chips work for you, and not just half your stack?
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