[AleoMagus]

[ QUOTE ]
when you have no FE and a coinflip gives you FE if you double up

[/ QUOTE ]

This is outside the strict mathematical aspects of this single hand, but actually, yeah, good example.

This hits to the heart of some issues that I have with SNG mathematical methods, especially concerning the conversion of chip values to their dollar equivalent. ICM.

On the one hand, we can say 'that's not fair, you are introducing other factors which do not really fit into the model which we are assuming is correct'

Lets face it though, Chips do NOT have a dollar equivalent in tournaments, even if that is what ICM tries to approximate for us.

The reason is simple - You don't get paid until the tourney is over, and so what happens on the next hand really matters. If your chip stack grants you less mathematically describable advantages (like FE) then these things cannot be ignored.

On that same line of thinking, even a very very big stack might have slightly more value than we suppose because it may actually tighten the calling ranges of opponents we have covered. This matters in future hands, and so despite how ICM may approximate our momentary equity, we cannot ignore hands that are yet to come in which our equity will be modified for the better by tighter calling ranges.

Now, this is not original and many people have been saying these kinds of things for a while, but still, I find myself more intrigued with these issues lately. In the past, I have implied that ICM doesn't ignore future hands, because it is based on probability calculations about what those future hands will result in.

Let me make clear, that I am happy with the ICM. I think it does what it is supposed to. It gives us a reasonable and functionally accurate estimate of what our equity in a tourney prize pool is, based on each player's respective chip position. nothing more.

What matters, I think, is that we get better able to recognize where future hands will modify what ICM calculations (when extended to hand analysis) are telling us, because there are factors outside the scope of the model.

Fold equity is a good example. Table image is another good example, and already mentioned in this thread. A well timed, slightly -$EV play when you are big stack can reap long term rewards (not considered in the usual ICM hand analysis) if it tightens up the range of hands that opponents will push into you with. Another example is having a shortstack at the table, and our occasional desire to keep a bubble going if the presence of the shortstack reduces the number of hands that our own all-ins will be called with.

I do not think that we need to modify ICM to account for these things. I have thought in the past about 'weighted' models which slightly overvalued/undervalued stacks, but I think this is a bad approach.

What we need to do is change the extension of our reasoning when we use the results of the model in hand analysis. For example, even if we find a situation where we can push with 74o for a slight gain in equity, this slight gain may not be worth the future ramifications of (possibly) having to show a 74o push.

To make what I mean clear, consider good old fashioned pot odds calculations. Nobody ever felt the need to alter our value of money when implied odds were brought into the picture. We simply realized that the potential for winning future bets meant that those pot odds calculations were incomplete, and that we could go against these calculations when we took this into account. We know we can call with a flush draw even if we aren't immediately getting proper odds, so long as we suspect that we have the potential to win future bets which make the play profitable.

In the same respect, I think ICM only provides us with immediate equity estimates, and can be overriden by future +$EV opportunities in certain situations. Rather than having this equity come from future bets in the hand, it now comes from future hands within the tournament. I think this was once suggested as 'implied equity'.

I am just thinking out loud here, and as I say, I'm sure this isn't news to many of you. This is especially obvious to me now that I am looking over this thread another time. Oh well...

Any other thoughts?

Regards
Brad S