Quote:
Originally Posted by NickMPK
This isn't true at this stage of the tournament. Daniel had about 2% of the chips in play, which gives him about 2% equity in the prize pool. If he doubled up, he would have about 4% of the chips in play, and about 4% equity in the prize pool. If he busted, he would have 0% equity in the prize pool. It's basically linear all the way including the point where you have 0 chips.
Now, if Daniel had 20% of the chips in play instead if 2%, this is a different story, since obviously having 40% of the chips doesn't give you 40% equity, as this is basically 1st place money, while 0 chips still gives you 0 equity.
It is true that someone with a very short stack may realistically have greater equity than their chip count would suggest merely because their shoves will almost always create protected pots with dead money in them. And this is not accounted for by ICM. But you actually have to shove your stack in to get this benefit.
I think your own explanation disproves your own conclusion about the 2% of chips in play stack.
I also think that 2% of chips in play has more than 2% of equity in the prize pool (ICM), due to some of the field having already busted.
If the ICM (growth) line as it moves to the right of the graph starts to flatten off in angle, as in the example you gave of 20% of the chips in play compared to 40% of the chips in play, then it must also be flattening off in some or many places at the lower percentage of the chips in play levels too, albeit only by a relatively small amount.
If DNegs wins the all in and increases his stack from ~3M to ~6.3M his new ICM value is not 2.1x what it was before he shoved, nor is his new ICM value 1.133x higher than pre shove if the villain folds and his stack has increased from ~3M pre shove to ~3.4M, it is less than 2.1x and 1.133x in each case respectively, whereas when he shoves, is called and loses his ICM obviously decreases by exactly 100%.
It is not much less than linear, but it is a little less.
If what I am saying is incorrect, which I don't rule out, then it could only be explained if the ICM line/curve is linear, linear, linear and then all of a sudden near to the money has a big spike or a variety of spikes that are in tune with the pay jumps etc. The graph may well in fact look something like this, but I still don't think that the rest of the graph is linear at the early and mid stages of a comp.
(some of it's non linear look might also be explained by the very sharp drop from a tiny stack down to no chips at all, but I think this only accounts for a small part of it)
Perhaps someone can post what the real ICM graph looks like?
One logical reason behind my belief of this is that if I was backing players, in say a 1000 runner field when it's early or mid stages and the average stack is 10,000 chips, I would instinctively prefer to have 4 players each with 2500 chips, than one player with 10000 chips. Again, I could be wrong about this.
Similarly, if a comp was a $10K buy in, 10K chips and I was given the option to instead buy in up to 4 times, into the very same comp, for $2.5K each time and get 2.5K chips, when the rest of the field all had to buy in for $10K, 10K chips, I would snap take the 4 x $2.5K option.
Fundamental to ICM not being linear is that smaller stacks have a disproportionate amount of leverage for their "cost", compared to bigger stacks, and, you can obviously have a small stack but still cash higher than a bigger stack than you. E.g. by laddering either deliberately or by just the natural way other players are knocking each other out.
Players are generally only thinking about and making decisions based on ICM when they are ITM or very close to it, which I think is a strategic oversight.
Last edited by SageDonkey; 07-18-2018 at 03:49 PM.