Dynamic edges based on skill differential *AND* fold equity
 

Consider these two common scenarios:

(a) You are in the SB and estimate that if you push into the BB he will call 10% of the time and when he does call you will be on the worse side of a 60/40. He has you covered so if you lose you will bust.

(b) You are in the BB and estimate that if you call the SB's push you will be on the best side of a 60/40. He has you covered so if you lose you will bust.

Now consider that you estimate that if you were to fold in either scenario you would on average be able to gain 1% of the prize-pool by playing better than your opponents from the next hand onwards.

In scenario (a) you will only bust 6% of the time so you are only risking 0.06% of your estimated future prize-pool share on the push, but in scenario (b) you will bust 40% of the time so you are risking 0.4% of your estimated future prize-pool share on the call (over 6.5x more!).

This indicates that if you have a significant advantage over your opponents then you should use a much larger edge depending on your fold equity (or more specifically the larger the chance of busting if you push/call). In general as your fold equity increases the lower the edge you can safely use. I agree though that it's not quite as simple as this in practice, as:

1. I'm assuming that the edge you choose is only to stop yourself from taking small +EV actions too early.

2. If you keep on passing up edge after edge to preserve your future prize-pool gain, then your overall ROI will decrease and thus your potential future prize-pool gain will start to decrease too.

3. In my example you busted in both scenarios if you lost, but in practice more subtle effects will come into play; such as leaving yourself short or gaining a huge dominating stack. So it is not purely based on your chance of busting but on the likely outcomes, their chances of occurring, and (most importantly) the edge you will have over your opponents after the outcome occurs.

I still think it's well worth considering though and goes to show that in the lower limit SNGs, where you are likely to be able to command a significant edge over your opponents, being a "good +EV pusher" is much more important than being a "good +EV caller" (aka: stop spite calling me! [img]/images/graemlins/tongue.gif[/img]).

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

Re: Dynamic edges based on skill differential *AND* fold equity
 

One could argue that ICM doesn't properly value a big stack that can punish a bubble. Making a marginally +EV call greatly increases the chances that a player will have a big stack on the bubble. I don't know how relevant this is to actual games but it's a decent argument for a devil's advocate.

Re: Dynamic edges based on skill differential *AND* fold equity
 

[ QUOTE ]
One could argue that ICM doesn't properly value a big stack that can punish a bubble. Making a marginally +EV call greatly increases the chances that a player will have a big stack on the bubble. I don't know how relevant this is to actual games but it's a decent argument for a devil's advocate.

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Imagine if you had another function that could be combined with the ICM output to account for these type of non-linear errors in the ICM model (including the effect I posted about in the OP), then what other reasons for using an edge would there be?

I'm thinking that you would use an edge to correct for errors in your estimated opponent ranges and also to not give off your true pushbot nature too early on and thus lose fold equity later, but perhaps if you factored in "loss of image" and could put people on perfect ranges there would be no need for an edge at all if you used the "corrected" ICM model?

Any other reasons left to use an edge?

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

Re: Dynamic edges based on skill differential *AND* fold equity
 

I may be missing your point, but don't you have to produce a call scenario with the same $EV as the push scenario if you want to build an argument here? Otherwise, it just collapses to "push loose, call tight".

It's not at all clear to me that b) will necessarily be a +$EV call in a lot of situations, let alone of the same value as a).

Re: Dynamic edges based on skill differential *AND* fold equity
 

[ QUOTE ]
I may be missing your point, but don't you have to produce a call scenario with the same $EV as the push scenario if you want to build an argument here? Otherwise, it just collapses to "push loose, call tight".

It's not at all clear to me that b) will necessarily be a +$EV call in a lot of situations, let alone of the same value as a).

[/ QUOTE ]
The example was just intended to show the effect of calling with no fold equity vs pushing with lots (iff you have a significant advantage over your opponents).

For example: suppose you expect to be able to make 1% of the prizepool in profit after passing on a +0.3% push/call, then using the 60/40 example from the OP:

Pushing: 0.3 - 0.06*1 = +0.24%
Calling: 0.3 - 0.4*1 = -0.1%

The push is still +EV and hardly changes because you are risking very little of your expected future profits, whereas the call becomes -EV because of the 40% chance of busting.

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

Re: Dynamic edges based on skill differential *AND* fold equity
 

I think you bring up a good point about the difference in the edge needed for a call compared to a push. The effect may be less than you state however since you double up 15x more often in situation (b) giving you a greater potential for future +EV. Situation A does pick up the blinds 90% which also adds to future +EV.

I think the problem is in trying to quantify how often +EV situations occur depending on your relative stack size. It seems like it would depend greatly on everyones relative stack sizes and the table dynamics, making it much too complex to generalize.


[ QUOTE ]
I may be missing your point, but don't you have to produce a call scenario with the same $EV as the push scenario if you want to build an argument here? Otherwise, it just collapses to "push loose, call tight".

It's not at all clear to me that b) will necessarily be a +$EV call in a lot of situations, let alone of the same value as a).

[/ QUOTE ]
Heres a quick example:
http://img340.imageshack.us/img340/1954/examplejs2.png

Not quite 60/40s but you get the idea. Assuming perfect reads which situation is better?

Re: Dynamic edges based on skill differential *AND* fold equity
 

OK - then I just don't get what you're saying. [img]/images/graemlins/crazy.gif[/img]

I may be a bit distracted by the way the OP is presented. I don't get the 1% thing at all. What you can win/lose after the push/call/fold is part of the original EV calc. It might need adjustment according to your relative skill with a huge/tiny stack and table dynamics, but that's not an arbitrary figure - it needs info about opponents, stack sizes and table dynamics.

As far as I know choosing a minimum edge is based on risk/reward considerations; edge over the field, confidence in your reads, likelihood of a better spot coming up soon, etc etc etc. All the same things that might lead you to take a negative edge in some (rare) spots.

I'd be more likely to pass up a marginal call than a marginal push - but that's because the risk-reward considerations are different. In particular, the read is a lot more critical for a call - but I incorporate that by making a slightly conservative read. Small differences in ranges can make huge differences in equity in some spots and very little in others, so I think minimum edge is too blunt a tool for that job.

Similarly for pushing into a loose opponent (ie with relatively little FE) - it's not so much about setting a higher minimum edge as being much less certain about their true calling range.

I also don't understand why at one point you seem to say you should use a higher edge for pushing - when the argument seems to lead to using a higher edge for calling?

Re: Dynamic edges based on skill differential *AND* fold equity
 

[ QUOTE ]
I may be missing your point, but don't you have to produce a call scenario with the same $EV as the push scenario if you want to build an argument here? Otherwise, it just collapses to "push loose, call tight".

It's not at all clear to me that b) will necessarily be a +$EV call in a lot of situations, let alone of the same value as a).

[/ QUOTE ]
Heres a quick example:


Not quite 60/40s but you get the idea. Assuming perfect reads which situation is better?

[/ QUOTE ]
Thanks. [img]/images/graemlins/smile.gif[/img] But it's not the calcs that bother me, it's the pertinence of the original scenario. I think it needs to be comparing like with like in order to be used to build an argument.

To answer your question, having a perfect read in both cases distorts the answer a bit - pushing is lower variance but calling might be better for the hourly rate. But you never have a perfect read, so I'll take the push, thanks. [img]/images/graemlins/wink.gif[/img]

Re: Dynamic edges based on skill differential *AND* fold equity
 

[ QUOTE ]
I may be a bit distracted by the way the OP is presented. I don't get the 1% thing at all. What you can win/lose after the push/call/fold is part of the original EV calc. It might need adjustment according to your relative skill with a huge/tiny stack and table dynamics, but that's not an arbitrary figure - it needs info about opponents, stack sizes and table dynamics.

[/ QUOTE ]
I used a fixed value of 1% to try to keep the example simple, but did try to point out that the value will depend on the different outcomes and the chance of each outcome occuring. From the OP:

[ QUOTE ]
3. In my example you busted in both scenarios if you lost, but in practice more subtle effects will come into play; such as leaving yourself short or gaining a huge dominating stack. So it is not purely based on your chance of busting but on the likely outcomes, their chances of occurring, and (most importantly) the edge you will have over your opponents after the outcome occurs.

[/ QUOTE ]

[ QUOTE ]
As far as I know choosing a minimum edge is based on risk/reward considerations; edge over the field, confidence in your reads, likelihood of a better spot coming up soon, etc etc etc. All the same things that might lead you to take a negative edge in some (rare) spots.
I'd be more likely to pass up a marginal call than a marginal push - but that's because the risk-reward considerations are different. In particular, the read is a lot more critical for a call - but I incorporate that by making a slightly conservative read. Small differences in ranges can make huge differences in equity in some spots and very little in others, so I think minimum edge is too blunt a tool for that job.

Similarly for pushing into a loose opponent (ie with relatively little FE) - it's not so much about setting a higher minimum edge as being much less certain about their true calling range.

[/ QUOTE ]
Again, I did point out that I was assuming the minimum egde was only being used for this reason to simplfy the example. From the OP:

[ QUOTE ]
1. I'm assuming that the edge you choose is only to stop yourself from taking small +EV actions too early.

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I also don't understand why at one point you seem to say you should use a higher edge for pushing - when the argument seems to lead to using a higher edge for calling?

[/ QUOTE ]
I have reread the OP a few times and can't see this?

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

Re: Dynamic edges based on skill differential *AND* fold equity
 

This bit.

[ QUOTE ]
This indicates that if you have a significant advantage over your opponents then you should use a much larger edge depending on your fold equity (or more specifically the larger the chance of busting if you push/call). In general as your fold equity increases the lower the edge you can safely use.

[/ QUOTE ]

You only have FE when pushing, and I can't see a reference to edges for calling until the concluding paragraph about not spite-calling.

Re: Dynamic edges based on skill differential *AND* fold equity
 

[ QUOTE ]
[ QUOTE ]
I think you bring up a good point about the difference in the edge needed for a call compared to a push. The effect may be less than you state however since you double up 15x more often in situation (b) giving you a greater potential for future +EV. Situation A does pick up the blinds 90% which also adds to future +EV.

I think the problem is in trying to quantify how often +EV situations occur depending on your relative stack size. It seems like it would depend greatly on everyones relative stack sizes and the table dynamics, making it much too complex to generalize.


[ QUOTE ]
I may be missing your point, but don't you have to produce a call scenario with the same $EV as the push scenario if you want to build an argument here? Otherwise, it just collapses to "push loose, call tight".

It's not at all clear to me that b) will necessarily be a +$EV call in a lot of situations, let alone of the same value as a).

[/ QUOTE ]
Heres a quick example:
http://img340.imageshack.us/img340/1954/examplejs2.png

Not quite 60/40s but you get the idea. Assuming perfect reads which situation is better?

[/ QUOTE ]
Thanks. [img]/images/graemlins/smile.gif[/img] But it's not the calcs that bother me, it's the pertinence of the original scenario. I think it needs to be comparing like with like in order to be used to build an argument.

[/ QUOTE ]
I think this example does a pretty good job of showing the abstract scenarios from the OP. As for "comparing like with like", then both have the same $EV of 0.14%, and this is the value to be compared against the edge threshold?

I agree that there is gonna be almost no chance to find a state where a SB push has the same state-transitions as a BB call and using an arbitrary value of +1% of prizepool advantage for all non-bust configurations isn't ideal, but I think "I will likely have an X% advantage over these opponents if I don't bust/cripple myself here" ('fudged' a bit based on doubling up, etc) is about all you are going to be able to consider while playing. [img]/images/graemlins/smile.gif[/img]

The important fact is that both have the same $EV output from the ICM model and in (a) you will bust 6.34% of the time and in (b) you will bust 38.5% of the time (not so far from the OP's abstract example).

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

Re: Dynamic edges based on skill differential *AND* fold equity
 

In the hypothetical scenario both moves have (hypothetically) the exact same $ value. It doesn't matter how often you bust out later.

If the $EV calc is done with perfect reads and an appropriately modified ICM model which takes into account the value of doubling more often when you call and short-stack skills etc etc, so that we truly are comparing like with like, then you should prefer to call because the only difference you can possibly make is in your hourly rate.

Re: Dynamic edges based on skill differential *AND* fold equity
 

[ QUOTE ]
This bit.

[ QUOTE ]
This indicates that if you have a significant advantage over your opponents then you should use a much larger edge depending on your fold equity (or more specifically the larger the chance of busting if you push/call). In general as your fold equity increases the lower the edge you can safely use.

[/ QUOTE ]

You only have FE when pushing, and I can't see a reference to edges for calling until the concluding paragraph about not spite-calling.

[/ QUOTE ]
Yep, and as your fold equity increases it increases from 0% to 100%, with 0% being no fold equity (hence calling).

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

Re: Dynamic edges based on skill differential *AND* fold equity
 

[ QUOTE ]
In the hypothetical scenario both moves have (hypothetically) the exact same $ value. It doesn't matter how often you bust out later.

If the $EV calc is done with perfect reads and an appropriately modified ICM model which takes into account the value of doubling more often when you call and short-stack skills etc etc, so that we truly are comparing like with like, then you should prefer to call because the only difference you can possibly make is in your hourly rate.

[/ QUOTE ]
Yes, I can see that, but how does this have any relevance to choosing edges? With a perfect $EV, from a perfectly corrected ICM model, with perfect reads then there would be no need for an edge in the first place as you would simply use a zero threshold for all cases.

The whole idea of the OP was that the ICM output is not perfect and the best you can do is estimate your likely future gains and use it together with your chance of busting (or if possible, consider the different outcomes as mentioned in point 3. of the OP) to help decide on a suitable edge to use (which can be viewed as a correction factor on the ICM model's output).

I think IFoldPktOnes example does a good job of showing a real world situation where the OP's ideas may be helpful in evaluating the non-perfect ICM model's output aided by an estimate(s) of your advantage over your opponents.

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

Re: Dynamic edges based on skill differential *AND* fold equity
 

[ QUOTE ]
[ QUOTE ]
In the hypothetical scenario both moves have (hypothetically) the exact same $ value. It doesn't matter how often you bust out later.

If the $EV calc is done with perfect reads and an appropriately modified ICM model which takes into account the value of doubling more often when you call and short-stack skills etc etc, so that we truly are comparing like with like, then you should prefer to call because the only difference you can possibly make is in your hourly rate.

[/ QUOTE ]
Yes, I can see that, but how does this have any relevance to choosing edges? With a perfect $EV, from a perfectly corrected ICM model, with perfect reads then there would be no need for an edge in the first place as you would simply use a zero threshold for all cases.

The whole idea of the OP was that the ICM output is not perfect and the best you can do is estimate your likely future gains and use it together with your chance of busting (or if possible, consider the different outcomes as mentioned in point 3. of the OP) to help decide on a suitable edge to use (which can be viewed as a correction factor on the ICM model's output).

I think IFoldPktOnes example does a good job of showing a real world situation where the OP's ideas may be helpful in evaluating the non-perfect ICM model's output aided by an estimate(s) of your advantage over your opponents.

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

[/ QUOTE ]
Sure, and if we're returning to the real world ... I already said that I think concerns over accuracy of reads are best dealt with by being sensibly conservative with said reads rather than relying on minimum edge to clean up after you.

The difference in edge from a slightly off read can be miniscule or enormous in different situations, so I'm not sure adding an arbitrary % to the minimum edge is going to be that helpful. It just means you'll miss a few more reasonably +EV spots and still take on a few that are hugely -EV.

Re: Dynamic edges based on skill differential *AND* fold equity
 

I agree with Juk that the skill advantage we are talking about isn't incorporated in ICM. Take the view that your ROI is just the sum of the EV of your plays. +EV opportunities occur throughout the tournament at rate determined by table dynamics. When you end your tournament life early you are giving up future +EV which contributes to your ROI, conversely by passing up too many marginal +EV spots you are also reducing your potential ROI. The edge we are talking about determines the balance between these 2 situations that will maximize your ROI.

For example, say you are playing a 10 player sng, there is no buy-in fee and your ROI is 20%. Someone goes all in on the 1st hand, you have an awesome read that he is holding AsKs, you hold JsJd and figure to be a 54.2% favorite if you call. According to ICM this is a break even call. You call because you love variance.

If you lose you have played a 0% ROI game since you made one break even decision, this happens 45.8% of the time. To make up for this you would need to average a 36.9% ROI when you double up the other 54.2% of the time to ensure you sustain your average 20% ROI. But how does your ROI scale with your stack size? Your larger stack allows you to play more hands profitably and increases your chances of pwning the bubble. But intuitively I wouldn't think that just because your stack is 1.844x its original value after you double up that you will have 1.844x more +EV opportunities and therefore a 36.9% ROI. If this intuition is correct then this call isn't really break even.

To put the question another way, what ROI would the 20% ROI player expect if he bought in for the value of a 2x stack (according to ICM) at the start of a 9 player tournament? As before there is no tournament fee.

Depending on your answer to the above question, here is the equity you would need to call an all in on the 1st hand and the corresponding %edge:

Answer - Equity Needed - %Edge
36.9% ROI - 54.2% equity - 0% edge
35% ROI - 55.1% equity - 0.16% edge
30% ROI - 57.7% equity - 0.64% edge
25% ROI - 60.8% equity - 1.22% edge
20% ROI - 65.0% equity - 2.00% edge

%Edge is the difference in equity between a call/fold required, expressed as a percentage of the total prize pool.

Hopefully I didn't screw up the maths or the logic. It's also a good point that I am ignoring the effect calling an early all in has on your hourly rate.

Re: Dynamic edges based on skill differential *AND* fold equity
 

Nice post, but I don't see the relationship to the argument in the OP. It starts off hypothesising out known problems with ICM and then acknowledges that these ignored factors make a difference.

I'm really struggling to see how the OP doesn't boil down to "push loose, call tight (and be careful with your EV calcs when you stand to lose a lot of $ if you get it wrong)". If it does boil down to this, I think there are more accurate ways to deal with the (being careful with EV calcs) bit than adding an arbitrary amount to the minimum edge when the actual effect on $EV varies hugely depending on the situation.

Re: Dynamic edges based on skill differential *AND* fold equity
 

It's easy to confuse what is being discussed with all the different factors that influence edge, since in the end all these factors are related. I think the OP was trying to concentrate solely on the difference in edge needed between calling/pushing due to skill factors.

When you push a large portion of your equity comes from stealing the blinds, so +EV pushes involve less all in confrontations then +EV calls. This means less danger to your tournament life and future +EV opportunities. In turn implying a higher edge is needed for calling than pushing if you are a skillful player.

The opposite is also true, a poor player should make marginal -EV calls in an effort to reduce the factor skill plays in the game. Oh, sorry Juk this actually means you will get spite called more often [img]/images/graemlins/tongue.gif[/img].

Re: Dynamic edges based on skill differential *AND* fold equity
 

I think I'm just confused about what the OP is trying to say. I think it's a range/reads issue, not an edge issue - but I'm also very likely to be dead wrong so I'll just shut up now. [img]/images/graemlins/blush.gif[/img]

Re: Dynamic edges based on skill differential *AND* fold equity
 

OK - I got it. And I think my objection was pointed out in the very first response - I was just being dim about the point being made in the OP. [img]/images/graemlins/blush.gif[/img]

1% is an arbitrary value - and typically a double up gives you a lot more unaccounted for $EV than a blind steal which is (usually) far and away the most likely outcome with a push, but impossible with a call.

If we could put sensible values on any additional edge over the field - for us - for each of the relative chip stacks we end up with - then this would be really useful. At the moment I think it's a little too arbitrary, but it looks like it would be amenable to a generalised formula.

So sorry Juk, and others. Thanks for your patience. [img]/images/graemlins/blush.gif[/img]