Dynamic edges based on skill differential *AND* fold equity

[jukofyork]

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]

[recondite7]

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.

[jukofyork]

[ 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]

[ymu]

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).

[jukofyork]

[ 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]

[IFoldPktOnes]

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:


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

[ymu]

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?

[ymu]

[ 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]

[jukofyork]

[ 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.

[/ QUOTE ]

[ QUOTE ]
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]

[ymu]

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.