Question about post-late reg add-ons (ICM)
So, this may be a long-winded post, but bear with me. My brother and I recently had a discussion about whether Add-ons were worth it - the one's where you can add-on after late registration is over - and we came up with some interesting findings.
We based our findings in math, but I'm definitely not sure we got the math right. I used my understanding of ICM, which I'm new to and very may well have gotten wrong. In fact, what I'm calculating might not even be related to ICM. It's very simplistic, but I'll explain more.
So, to start, let's assume a few things. Tournament buy-in is $5.50 (so $5 goes to the prizepool). Add-on is also $5.50, for 1.5x the original buy-in chips (5000 chips for buy-in, 7500 for add-on). You can also rebuy for $5.50 unlimited (5000 chips) until late reg ends.
For the purposes of a test case, we assumed 200 people registered, there were 200 rebuys, and we're at the end of late registration, so they'll be no more. That means there's 2,000,000 chips in play (200 x 5000) + (200 x 5000) and a total prize pool of $2000.
So, now we have to decide - are we going to add-on? Well, this is where things get interesting... I'm going to assume 4 different test cases, with all of the possible extremes:
- Nobody adds-on, and we have a short stack,
- Everybody adds-on (150 players including us), and we have a short stack,
- Nobody adds-on, and we have a huge stack,
- Everybody adds-on (150 players including us) when we have a huge stack.
(NOTE: This is where I'm really unsure of my logic/math - so if this is wrong, don't bother reading the rest, because I'm making the same calculations going forward. Feel free to correct!)
First test case:
We have 10000 chips, nobody adds-on, except potentially us. Add-on is 7500 chips. We go from 10000 / 2,000,000, or 0.005 of the total chip count, to 17500 / 2,007,500, or 0.00871 of the total chip count. Multiply by the prizepool, or 2000 before and 2005 after, and we get a "value" of our chips of $10 before, and $17.46 after. Given a $5.50 add-on, I'm viewing this as "profitable".
Second:
10000 chips, everybody adds on.
10000/(2,000,000 + (149 * 7500)) = 10000/3,117,500 = 0.0032
17500/(2,000,000 + (150 * 7500)) = 17500/3,125,000 = 0.0056
Value of chips (w/o addon) = 0.0032 * ($2000 + (149 * 5)) = 0.0032 * 2745 = $8.78 vs.
Value of chips (w/ addon) = 0.0056 * ($2000 + (150 * 5)) = 0.0056 * 2750 = $15.4
Again, "profitable" by this formula.
These make intuitive sense to me. We have a small stack, so whether a lot of people add-on or none do, we gain a significant portion of our stack and thus increase our value by enough to make it profitable.
What is strange to me, is how the numbers work out for a huge (even comically huge, which I'll show below) stack. I would assume that because the add-on is such a small percentage of our stack, it would no longer be profitable to add-on. But that doesn't seem to be the case.
Third:
Assuming a comically huge stack of 1,000,000 chips at the end of late reg.
1,000,000 chips, nobody adds on.
1,000,000/2,000,000 = 0.5
1,007,500/2,007,500 = 0.5019
Value of chips (w/o addon) = 0.5 * ($2000) = $1000 vs.
Value of chips (w/ addon) = 0.5019 * $2005 = $1006.3
Still profitable...
Fourth and final
1,000,000 chips, everybody adds-on
1,000,000/(2,000,000 + (149 * 7500)) = 1,000,000/3,117,500 = 0.3208
1,007,500/(2,000,000 + (150 * 7500)) = 1,007,500/3,125,000 = 0.3224
Value of chips (w/o addon) = 0.3208 * ($2000 + (149 * 5)) = 0.3208 * 2745 = $880.60 vs.
Value of chips (w/ addon) = 0.3224 * ($2000 + (150 * 5)) = 0.3224 * 2750 = $886.60
Still profitable?!
THE END. Somebody tell me why I'm stupid 😆 I know ICM is much more complicated than the above, but as far as I'm aware that's due to the calculations required when you've already made the money, and 1 chip has a significant value. If you haven't made the money, and you assume equal skill levels across the field, isn't what I've done above accurate for each scenario?
5 Replies
Have you ever encountered a hand so statistically improbable that it made you question the fairness of the game, or even consider if there might be some external influence at play? What was your reaction, and how did it affect your approach to future games?
Any chance to add chips at a ‘value’ price should be taken.
Yeah it's really as simple as this.
Per ICM the chip values have diminishing returns as your stack size increases, but you're getting 1.5x on your dollar and that's a deal you're going to want to take.
If you only got something like 1.05x what you were getting at the start then it would be a lot closer as to whether it's worth it for a big stack to take the add on. That's because additional chips are always worth less in ICM value. The effect is slight though early on in a tournament.
In practice these add-on tournaments almost always offer a great value for the add-on.
This isn't an ICM issue for me because we are not in or near the money yet. My guess is that in this example it would pay about 48 players and there are 150 players still in.
In these type of tournaments the only issue for me is how the extra chips affect my stack. At this point in the tournament assuming almost all of the 150 players do the add on, the average stack would be about 21,000 chips.
My theory (which never came up in practice because I didn't play a lot of add on tournaments) would be I would never do the add on if it meant adding less than 10% to my stack.
In this case doing it at 20% of my stack would mean I had 37,500 chips and adding the 7,500 would take me to over 2x the average stack. Even at around 60,000 chips adding the 7,500 chips would take me over 3x the average stack so I would consider it worth it.
With add-ons getting more than the starting stack size, I usually looked at these tournaments as having the buy in at twice the original amount (here it would be $10). I always did the add on when I played these tournaments except once and it wasn't because I had a huge chip stack. It was because I didn't realize we had to leave the money on the table when we went to the bathroom. When I got back to the table I had missed the Floor with the chips and when I went to ask I was told I was too late...
My approach is simpler. If the add-on increases my stack by 25% or more I will take it but I also look at what happens with the blinds coming up to see how much they devalue by m. In the rare instance I have 6x or more than starting stack, I may just mimic what the other big stacks do at the table.
When we played with add ons, it usually made sense to take it as the real tournament started after the rebuy period and plenty of players didn’t adjust their play.
