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I posted on this topic on the
wizard forum just recently. Basically edge is mostly theoretically unsound but used as a kind of hack which is supposed to help cover uncertainty on our opponents range.
Probably a more correct formulation than the type of thing you see in SNGWiz is one that doesn't say your opponent will call with 20+% of the hands is one where you give a range of what you predict your opponent's real calling range is. Maybe something like:
1% chance its: 5%
4% chance its: 8%
10% chance its: 14%
15% chance its: 18%
30% chance its: 20%
15% chance its: 25%
10% chance its: 30%
5% chance its: 40%
5% chance its: 50%
4% chance its: 60%
1% chance its: 75%
Or whatever. Because the truth may be that your push is marginally +$EV so long as his range is <22% but very -$EV once his rang is bigger. So to help protect you from having misestimated the range the edge can act like a hack to make sure you pass things that may be marginally +$EV when you have exactly nailed the opponents range.
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Interesting post. You could even move away from using top N% ranges and extend this to assign each of the 169 hands a separate probability of being played and thus play vs a probability distribution rather than a range.
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I've just been thinking about this again today and it occurred to me that so long as you can predict their "mean calling threshold", then at
worst you will be acting pessimistically and giving up some EV for those times they diverge from the mean and call much thinner/wider than the mean would suggest.
So being able to put them on a frequency distribution of hands rather than a range/threshold would actually let you find even more +EV pushes to play against them (rather than avoid the times they call much wider where your push is very -EV), and indicate the use of a -ve minimum edge to compensate for the pessimism we get vs the "top n%" results.
Juk [img]/images/graemlins/smile.gif[/img]