ICM - Calculation Minimum Edge

[Dirk72]

If you use the ICM to make a push/fold decision, you need a minimum edge between push equity and fold equity before pushing.

SNGWiz is using this formula to calculate the minimum edge :
Edge = EM * S * (P - 1) / (100 * BB);
where:
EM = an edge multiplier you can define
S = the smaller of your stack size and the biggest potential opponent stack size.
P = the number of players in the hand.
BB = the size of the big blind.

Does anyone has experience in calculating this Edge and what do you use as Edge Multiplier?

[K䲰䮥n]

lol capital Edge

[Onyyn]

I'm not completely sure if I'm on the right track with this, but isn't this equivalent to the prize pool "minimum edge" that SNGPT uses? They use a 0.5% gap between fold ev and push ev to determine a statistical "wash," and the point at which you'd generally fold rather than shove.

It's early, and I was drunk and playing Wii Bowling last night, so I should probably go back and sit in the corner now.

Also, in a completely mundane, unimportant moment, I think this is my "member" post [img]/images/graemlins/blush.gif[/img]

[SumZero]

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.

[jukofyork]

[ QUOTE ]
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.

[/ QUOTE ]
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.


[ QUOTE ]
"The idea behind the edge formula is that you don’t want to risk your entire stack early in a tournament when the blinds are small. You should be playing tight and let other players bust out."

To me, this doesn't make any sense. EV is EV. If we are talking about Eq% or $EV then we should do whatever we can to maximize our $EV. The only reasons I can think of to include an edge value is as a hack because one (or more) of the following is going on:

1. We are miscalculating $EV based on our valid information. Giving it is the wizard doing this, I think it is safe to say this isn't true.

2. We are incorrectly estimating our opponents calling ranges as too tight and this helps us not get surprising calls. If this were the case though the right fix would be to change the opponents calling ranges, not add an edge factor.

3. We are trying to account for some kind of metagame. I.e., if we push every edge we will push more and potentially cause our opponents to play more correctly in the future and will not be able to get away with future steals. But if this were the case I'd almost expect it to be a bigger deal late in the tourney than early as early it may be only once every ~25 hands that you get a decision that is within the margins of the edge so even if you always pushed then you'd have only minor metagame effects. But late in the game every couple of hands may be within the margin and this is where the metagame aspects come into play the most.

4. You are better than everyone else so you want to wait for even better later plays. But isn't the reason you are better is because you can identify and make the +$EV moves? Wouldn't you be even better if you played identically but also took this one +$EV move. And if this were the reason the edge formula would have to change based on the players ROI/skill.

Can anyone provide a proper sound theoretical argument for why you should have an edge threshold and why it should change the way the SNGWiz one does?

[/ QUOTE ]
I think you could also add a 5th reason in that you might want to pass small +EV edges to let the other players make mistakes vs each other (eg: spite calls) which result in you yourself gaining some EV from their mistakes.

Juk [img]/images/graemlins/smile.gif[/img]

[jukofyork]

[ QUOTE ]
[ QUOTE ]
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.

[/ QUOTE ]
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.

[/ QUOTE ]
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]