So in a sit and go, 10 players all equal skill level buy in for $10 (no rake). Payouts are $50, $30, $20

So starting with 1000 chips, we can definitively say that the value of 1000 chips with 10 people left is $10.

We can also say that the value of 10000 chips (with 1 person left) is $50.

Now if one person is knocked out, and another person doubles up to 2000. We know that the 2000 chip stack is not worth double the $ value. Its valued at somewhere between a bit higher than $10, and a bit lower than $20.

If we theoretically assume everyone is equal skill level at this point, what is the best method to determine the value of the 2000 chip stack at this point?

Also, since everyone's $ value of their 1000 chip stack goes up since one person is knocked out, doesn't this further justify never taking a 50/50 flip early in a tournament?

As far as I know ICM only cares about the payout structure and your chipstack relative to all of the chips in play.

I've never seen a calculation performed by hand, because it's quite tedious from what I've been told. I think it's because you have to evaluate what the likelihood of everyone's stack size getting them into a certain payout structure so with 9 participants there would be P(9,3) permutations for 1st, 2nd, and 3rd. That's 504 possible out comes each with it's own probability of occurence. You could knock that down a little if you only focused on the 2000 stack finishing in the money (I think that would be 3*P(8,2) so 168 outcomes).


It's best to use an ICM calculator for these things.

Carbon poker has extremely late registration up to 3 hours.

For example, for a $11 tournament, if you registered last minute, there would be about 70 people left with 38 places getting paid and about 240 total entries.

You would have to start off with a 5k stack at 500/1k blind levels.


Here, if you played perfect nash push bot, is this a +ev tournament to play based on ICM?

So when paying $11 for a 5k chip stack at that stage of the tournament, is that chip stack worth more or less than $11 given the amount of people who have been knocked out. I would assume more since from the SNG example, we can already see that even if a person's chip stack doesn't change, their $ value of their stack goes up as soon as a person is knocked out of the sng.

With 70 people left, the chip stack is still worth pretty close to exactly what you paid for it, which is the same as it was worth to someone who started at the beginning of the tourney.

ICM doesn't really matter until after the bubble, and even then not much until the final table.

Correcting my first sentence above - it's actually probably worth less now because you probably have less than the average stack. So when you enter a tournament late after a bunch of folks are eliminated you're likely overpaying for your chips.

My hunch is that based on ICM it would be. I don't have access to a way to verify that, but even so the real question shouldn't be whether ICM says its profitable, but whether it actually is profitable.

Remember ICM is not perfect.

http://www.pokerjunkie.com/icm-expla...ent-chip-model

Decent link behind the basic math of ICM and general conclusions from the basic case (caveat: did not read when the article was published).

But doesn't ICM take the (correct) assumption that each additional chip beyond the first has a dimishing $ value?

This is the reason why a 1000 chip stack is worth $10, but a 2000 chip stack could be worth say...$17, and a 10000 chip stack in the SNG example is worth $50.

So this also means a 500 chip stack is worth some amount more than $5.


Going back the the late entry MTT example of 240 entries, 70 left, $10 buy in,

the average stack (if we start with 1k chips) is 3428, and the value of that stack is $10 * 240 / 70 = $34

Now you late register for 1k chips, for $10. 1k chips is 29% of 3428 chips. and 29% of $34 is $9.86. But if we go back to the assumption that a smaller chip stack has a greater $ value, the 1k chips should be worth more than $10 making it automatically +ev (certainly more than 14 cents over the 9.86)

Not to mention with the blinds so high, its difficult not to find a decent spot to go all in where there are dead blinds in the pot to pick up so you can flip for a pretty good +chip ev situation within your first orbit.

Lemme know what you think of this.

I don't think so. The ICM adjustment with 70 players left and ITM not until 38, might be less than a penny. We can't even calculate it that early without a ton of computing power. But we generally assume the value is still linear, i.e. $9.86, until we are near the money.

I don't think an MTT structure exists where a late start conveys a positive stack value advantage.

ICM is really intended for single table tournaments, where it matters from the start.

I wouldn't consider 70 people left with 38 spots paying far from the money.

I think your ITM % will be significantly higher. Obviously, you will lose some money due to finishing in the higher spots less, but I believe that effect is much weaker than the increased ITM %.

Also, in a real world scenario I feel like I often have a pretty large edge against people short stacking.

You are using a straight chip value for your average stack but want to use ICM for your own stack to make it worth more. So you're comparing apples with oranges.

Yes, you probably make a small gain by buying in late because you take a share of the equity of every player who's been knocked out but it's only a quite small share (so small that as a previous poster said we generally ignore it in MTTs).

No you do not. That equity went to the players who won those chips. When you buy in late and pay the same but have less than an average stack, you now have less equity than the average of the field.

If you are close to the money ICM may give you a very slight bit of equity back but it will not make up for what you lost by buying in late.

Shouldn’t you take into account that if you bought in initially you might not be around before the end of the late registration? Then you would be comparing Expected Stack Early Buy-In to Initial Stack-Late Registration.

Let S = initial stack , Savg = average stack size of survivors at end of late registration and Pk = prob. of surviving by end of late registration.

Then assuming you are average, late buy-in is advantageous to you if

Ps*Savg > S,

or your survival probability has to be greater than the ratio of initial stack to average stack size. Also, there possibly are other advantages to late registration, e.g., less fatigue as tournament progresses and/or opportunity to make money or whatever during the initial stage before you register.

The above is admittedly simplistic. For example, it assume that you are an average player (but that is what ICM assumes.) This seems to be an area where one can look at his tournament history to determine a good buy-in strategy for this situation. I would also think this may have already been done.

Anyone?

I think the thing that many are overlooking are that the mechanism that drives ICM is proximity to the bubble.

While a wider distribution in chips may have a big impact on how imminent a bubble will burst later on, when blinds are still relatively small, this impact will be much smaller.

You can look at the strength of ICM as relative to the number of hands between now and the bubble and, I believe the effect falls off with the square of the distance. Therefore an early double up will have very little effect as long as the blinds are still small since the bubble will still burst at roughly the same level as normal.

Technically, registering late for a tournament is better than registering earlier if everyone is of equal skill level or slightly greater.

Personally, I think MTT's mainly come down to the endgame. You either get lucky or you don't, and as long as you play the endgame well you should be fairly profitable. Some people truly play the endgame horribly and they lose more from this from any good play they might make early on IMO.

"Technically" how? You're going to need to justify that with more than just you say so. I've explained why your statement is wrong. For pure tournament equity, starting late (meaning after some players are eliminated) is always a disadvantage in any kind of normal format MTT, because you then have less than an average stack.

And what do you mean by slightly greater? Than what?

Why is having less than an average stack bad?

Are you telling me that you wouldn't enter on the bubble with starting chips because you'd have less than average?

Its obviously very profitable to enter on the bubble with starting chips.

It doesn't work like this. If a player with a starting stack eliminates another player with a starting stack they don't double their equity in the tournament.

You can argue that ICM is flawed or wrong in some way, but its simply untrue that you get 100% of a players equity by eliminating them.

Some portion of that players equity is dispersed amongst the remaining players. There is a very simple reason for this:

You can only finish in one position. You can't finish in multiple paying positions no matter how many chips you have.

You're disputing lots of things I never said. The only point I made was that by entering late, your tournament equity is less than a person with an average stack size who is already in the tournament, since you have fewer chips than them. This is absolutely indisputable. And they paid the same fee you did.

Average stack doesn't matter. The question here is this:

If you pay $X to enter late do you get >$X in equity.

Assuming all players are of equal skill I believe the answer is yes in most situations.

I think Jacob's point of view is if you have average or below skill at those stages of the game that you are missing out on. Therefore you can expect no equity from playing. Given this, ICM will mean that the later you come in for the same entry fee and starting stack will be a force that can only benefit you if you are at average skill or below.

ICM calculators will tell you that you do not gain 100% equity from a double up although very early on, you will be gaining very close to 100% equity, according to the ICM model but as you approach the bubble, this impact will rapidly increase with what I believe to be around the square of the distance.

You can use magnets to see what I mean by how concentrated ICM effects are near the bubble, since the electromagnetic force is also related to the square of the distance.

However, one problem of only calculating ICM using Skalansky's model is that it's not the only force at play in tournament situations aside from skill. It doesn't take into account the accumulative cost of the blinds and antes to the average stack or more importantly the mode stack (where most players will be clustered). Therefore, ICM is only a partial solution and there's more to it than that.

The reason for this is that there are stacks that will be penalized for not playing since not playing 100% will mean that you will be blinded out before making the money. Such is the case for all starting stacks where payouts start at less than 50% ITM. This creates a force in opposition to ICM when you are far from the bubble which ICM doesn't account for with no blinds+ante component in it's algorithm.

Granted that, coming in late without taking a blind penalty will save you this cost and also the cost of the times you may get knocked out before your late registration. However it will also mean you will have a shorter stack and higher blinds and therefore require a greater win rate in order to survive to the bubble when compared to the average or perhaps more significantly the mode stack size (point at which most stacks will be clustered around). The mode will be lower than the average due to ICM.

Therefore the original statement of coming in late as an advantage for players of average skill or below is dependent on other factors which are not all aligned and is once again a issue of "it depends".

While this force is generally much weaker than the huge ICM force near the bubble, it is more widely distributed over the entire time before reaching the bubble. Therefore, ICM models will be less and less accurate as the distance from the bubble increases. It also over estimates the value of smaller chip stacks due to this effect.

I haven't seen much discussion over this effect although Harrington's series of books on tournaments hints of a strong force related to M (cost of 1 orbit in blinds+antes) and a weak force Q which is your stack relative to the average stack if memory serves and does seem to hint at two distinct forces at play.

Also some SnG calculators may take blinds and position into account however, they wouldn't apply to MTTs where this may change at any time due to table changes and also focus on the near term effects as opposed to the long term costs from what I understand.

Solving for this weak force is dependent on the blind structure and the payout table, number of players/table, and the distribution of starting hand strength relative to the stacks in play over time while also accounting for the dynamic structure you can expect to see before the bubble, making it a difficult problem to solve.

One hint that could allude to the quantitative effects of this weak force would be to look at a well established tournament and seeing what level the bubble tends to break on average. Count the number of hands you would expect to see over that time. Calculate the expected cost of blinds+antes over that time. Calculate the difference in this amount to your own stack size.

This would be the minimum amount that you would need to win in all of the hands you decide to play for some positive expectation. This would be your gross win-rate, not to be confused with your net win-rate as with cash games since we have already taken out the cost of the blinds+antes.

This is all before taking the effects of the ICM calculations into account, which could greatly skew the concentrations of when you should be playing hands depending on your stack size.

Respectfully, I’m fairly certain the statement above is incorrect.

For one, you will FOR SURE have less than the average stack. But ICM doesn’t weigh this linearly.

There are people who purposely max late reg and lollly gag in lines and try to get seated slowly at the WSOP so that by the time they sit down they are so close to the money that they might not even need to play a hand.

This is chicken **** behavior in my opinion but it is out there.

Consider this extreme example — registration is closing on a 100 person MTT. Only 13 players remain and 12 cash. Regardless of the payouts, if you know you are the only player that’s going to jump in at the last minute, you are printing money from an ICM perspective. Remember it doesn’t take into account blinds etc so ICM doesn’t know if you will have 1 blind and all in right away or 15 blinds with some playability. All it knows are the payouts and that you have roughly 1/8 of the average stack.

The $ ICM value of a starting stack goes up as players are eliminated. Oftentimes if you max late reg the $ value of your starting stack will be worth enough extra that it is worth how much you actually pay to buy in, rather than what you pay minus rake, which is what a starting stack is worth at the start of the tournament. So in terms of the dollar value of your stack you are practically getting in rake free if you max late reg.

That being said the early levels when all the worst players are still around is when a good player should have the largest edge, so in my estimation a good player is still better off registering earlier.

If I ever played like a really tough $50k where any edge anyone has is minimal, then I would definitely max late reg though.

Yea its funny to see a 10 year thread and see how far we have come with understanding ICM and poker generally. Turns out ICM applies to MTTs too, and way sooner than we thought back then.

Hahaha, I didn't notice that someone had bumped an old thread. I felt like I was in the twilight zone for a minute.

And still most regs are only really considering ICM preflop