Join Date: Jan 2009
Posts: 4,987
Here is one way to think about it. There are many others, I'm sure.
In 6 hands, you get the top 50% 3 times on average. So getting it 6 times per round, gives you a 2 to 1 gain in frequency per round. You get the button only once so getting it 6 times gives you a 6 to 1 gain. So, unless top 50% benefit is worth 3 times the button benefit (6/2), I'll take the button.
Data I saw from thousands of hands showed that the EV for the button is about twice that of middle position. I showed the graph of EV versus position in another thread.
Poker Stove shows that in a 6-max game, having a top 50% hand against 5 opponents with random hands wins 21% of the time. But, it is not likely all 5 opponents will call but those that do call will likely have better hands. So, if we assume two opponents, one random and one at 30%, top 50% wins about 1/3 of the time.
Therefore, taking the button all the time gives you a doubling of EV. Getting top 50% all the time gives you a 1/3 win probability against the 1/6 you had before -- assuming all opponents have ability equal to yours. So, you get double benefit in each case. However, as stated earlier, you get the button benefit six times more than normal but the hand benefit only two times as often. Since the benefit of each is about equal, using the argument above, the frequency benefit of the button option makes that the preferred choice.
Admittedly, there is a lot of questionable aspects to this analysis, so I am not saying it is the absolute right answer, by any means.