I was moaning in the previous post about the downloadable version and was asking this also in the support thread. It turned out that the results in the downloadable version are more accurate because the downloadable version uses unrestricted ranges. That might cause the little difference when I summed up the different equitys.
Good to know I didn't waste my money

Today I ran the first hand of "Simulation 1" with the future game simulation (FGS) of the HRC and the results are pretty much in line whith my anlysis.

For record:
In this exact situation the big stack gains EQ when the bubble goes on. Most of his EQ comes from the medium stack and the small stack looses just a little bit. Therefore we said ICM undervaluates the big stack, overvaluates the medium stack and is pretty acurate for the small stack.

Setup for the hand I'll analyse here:
BU: 4500
SB: 3000
BB: 1500

Blinds 150/300

With ICM HRC suggests the button to push 40,9%, the sb to defend 3,8% and the bb to defend 26,%

Now what happens if we simulate an entire round (Depth 3)?
The new suggestion is that the button pushes 37%, the sb defends 5,4% and the bb 24,7%

Interpretation:
Please take this with a grant of salt as it is my interpretation and doesn't have to be correct. If you think my thoughts on this are flawed please let me know.

FGS suggests that the medium stack in the sb expands his calling range by 42% from 3,8% to 5,4%. This is because he looses the most in this setup. So he wants to change stack sizes. (If he wins he will be the big stack and can abuse the bubble, if he looses he can't loose anymore future EQ)

The big stack on the button pushes less for 2 reasons:
a) the sb is calling wider
b) he is more risk averse than ICM suggests because he gains equity in this setup. A collusion with any of his opponents will diminish his future equity. On the other hand stealing the blinds is probably increasing his edge.

The short stack in the bb calls less since the button is pushing less.

Limitation
The suggestions with FGS Depth 3 seem to be more accurate to me, but HRC allows us to simulate only 1 entire round. The bubble is likely to be longer. So what would happen if we could solve the entire game or at least the entire bubble?
My guess is that the trend continues and the medium stack is defending even more. The others are obviously adjusting accordingly. But to which extand? We can only guess until one of you guys has solved the entire situation.

In "Kill Everyone" book authors presented so-called diffusion model and said it more accuratly represents equity of chip stacks. Probability of finishing for given position is based on the assumption that chips are moving randomly from one stack to another. Keep in mind this model also doesn't take into account skill level, stack order and blind posting.


I would like to hear your opinion or has anybody test it out against ICM?

Position is a pretty big factor when there is a short stack, especially in flatter payout structures. On the bubble of a 6 handed STT, if the chip leader has the short stack on his right and the second in chips on his left, his stack is worth a lot more than the other way around because he can shove super wide into the second stack who usually cannot call even when he's ahead of the chip leader's range. According to ICM, the big stack's chips are worth the same no matter where he is on the table.

I don't think modeling will work for tournaments if the objective is to get the most chips.

The goal is not, necessarily to accumulate more chips, the goal is to win the most money over the long haul. Therefore short stacks are often forced to play a negative CEV strategy in favor of a +$EV strategy.

This can be seen in the chip distribution in tournament play. The distribution curve will inevitably be skewed with the mode far to the left of the mean especially when nearing the bubble which is far more influenced by the payout table than the distribution of levels of skill.

Therefore the assumption that the odds for finishing in 1st are in direct proportion to the stacks are false. Otherwise we would see a more normal distribution curve for stacks which would only be influenced by the levels of skill.

So to answer the the OP, I think that the larger stacks should have a disproportionate advantage for finishing in 1st place over the smaller stacks who are sacrificing CEV along the way unless they happen to get a couple double ups and become a big stack, in which case they will then change strategies and start exploiting the smaller stacks.

Edit to add:
With regards to the issue of defining equally skilled, or with comparative strategies. This would be a very difficult thing to define because the goals of the short stack and the big stack will be far different as explained above.

Interesting, so Sinthoras1 has proven that in a winner-takes-all format where everyone is playing GTO, short stacks actually have more equity than their percentage of the chips in play? (Provided 3+ players)

I wondered the same thing.

forumserver.twoplustwo.com/showpost.php?p=43556043&postcount=729

ICM doesn't take position into account, it only looks at chip stacks and payout tables.

It doesn't take position into account because for MTTs that can change at any time. Also there's no way to quantify that advantage. It also can't take skill into account for the same reason.

Since ICM "base" model is wrong itself (with assumption of probability finishing) then models that trying to take future hands to account for equity changes (due to blind posting and stack changes) will be wrong too?
Where I can see such a curve or any data that prove your point?
I think order of the stacks would have impact on too, since having short stack on your left is advantage and opposite is also true.

ICM based on stack proportions is probably not that bad for small fields but I never played SnGs so I'm not sure.

Also ICM calculators aren't practical for large fields anyway but it's important to understand the principles involved.

I'm not aware of any such models for blinds/pos.

You can do plenty of your own simple calculations for ways to calculate for ICM. Not necessarily for adjusting CEV but many other useful stats.

One simple trick for roughly determining relative strength of ICM might be to plot the botom half/top half ratio.

(median stk-botom stk)/(Top stk - median stack) but I'm sure a probability expert could find a better way to measure distribution skew.

i.e. should go down sharply when approaching bubble and up after the bubble for a short time before going down again.

Also if you look at bottom payout, you can get a good idea of avg ICM on the bubble by converting bottom $ into the equivalent number of chips for an average:

Avg. value of surviving bubble in # of chips:
Bubble CEV = Strt-Stk * Bot $/$buy-in.

You can look at past results of similar buy-in, field size, structure For example, to get the following data.

Avg # hands at each level.
Avg Stk at bubble = #paid/chip tot.
#Tables@Bbl = #paid/(max-plyrs/tbl)
Orbits = number of orbits you expect to see before bubble.
BA1, BA2,... = Blinds+all antes for each level

Then if you are short when approaching the bubble you can estimate the min #blinds/orbit you need to win before the bubble.

I have other/better ways to estimate ICM in tournaments, using basic tourny info but these were what came to mind.

On-line, real-time tournament Avg stack should be displayed. Then match that number against the current list of player stacks, usually shown in the tournament window, You will see the average go above the Median (half of the field). As you get closer to the bubble, the average stk will be around the top third of the field.

For live play:
Avg chips = #entries * starting chips/# live plyrs.

Well as I said in a previous post, you need to be able to quantify that in order to add to any calculation. Also it's going to be changing in MTTs with table balancing and table break downs.