-
ICM Math
This post is meant to demonstrate how to do calculations associated with ICM or Independent Chip Model. Please feel free to add your own examples or calculations to improve this post.
To do this, lets make some assumptions:
— 3 handed
— Prize Pool is ($10000, $4000, $1000)
— Stack Sizes are (8000, 3000, 1000)
— Total Chips = 8000 + 3000 + 1000 = 12000
_________________________________________________________
_________________________________________________________
BIG STACK
How often should the Big Stack get 1st place?
= (8000 / (8000 + 3000 + 1000))
= (8000 / 12000) = 2/3 or 66.67%
How often should the Big Stack get 2nd place?
medium stack gets 1st
= (3000/12000)) * (8000/12000-3000)
= (1/4) * (8/9) = 22.22%
small stack gets 1st
= (1000/(12000)) * (8000/(12000-1000)
= (1/12) * (8/11) = 6.06%
total chance
= 28.28%
_________________________________________________________
MEDIUM STACK
How often should the Medium Stack get 1st place?
= (3000 / (8000 + 3000 + 1000))
= (3000 / 12000) = 1/4 or 25.0%
How often should the Medium Stack get 2nd place?
big stack gets 1st
= (8000/12000)) * (3000/12000-8000)
= (2/3) * (3/4) = 50.0%
small stack gets 1st
= (1000/(12000)) * (3000/(12000-1000)
= (1/12) * (3/11) = 2.27%
total chance
= 52.27%
_________________________________________________________
SMALL STACK
<b style=”font-family: inherit; font-size: inherit;”>How often should the Small Stack get 1st place?
= (1000 / (8000 + 3000 + 1000))
= (1000 / 12000) = 1/12 or 8.3%
How often should the Small Stack get 2nd place?
big stack gets 1st
= (8000/12000)) * (1000/12000-8000)
= (2/3) * (1/4) = 16.67%
medium stack gets 1st
= (3000/(12000)) * (1000/(12000-3000)
= (1/4) * (1/9) = 2.77%
total chance
= 19.44%
_________________________________________________________
Chop Value
- Big Stack ICM is (66.67%)*($100) = <b style=”font-family: inherit; font-size: inherit;”>$66.67
- Medium Stack ICM is (25.0%)*($100) = $25.00
- Small Stack ICM is (8.3%)*($100) = $8.30
_________________________________________________________
Monetary Value of Chip
When heads-up,
- you’re playing to win an extra $10,000 – $4,000 = $6,000.
- There are 12,000 chips in play.
- The value is $6,000 / 12,000 chips = $0.50 / chip
When 3-ways,
- you’re playing to win an extra $4,000 – $1,000 = $3,000.
- There are 12,000 chips in play.
- The value is $3,000 / 12,000 chips = $0.25 / chip
-
6 Replies
-
One thing I love about @ARW posts is that you can apply them to every situation. Maybe we can use this post to break down a hand from the final table of the Tournament of Champions – we’re posting it tomorrow at noon, so if anyone sees some hands where ICM is a factor, we can break them down here in the forums! We’ll also be reviewing that final table in real time with the panel in the monthly Strat Chat on the fourth Wednesday of every month – if you played on the final table and fell victim to @Raisy_Daisy (like me) but you’re not a premium member, why not try the 7-day free trial of the premium membership that week so you can join the panel and review your play?
-
The tableplay from the ToC Final Table has been released, so I’d encourage everyone to pick a hand with ICM considerations and we can review it here with @ARW – hey @PokerGeekMN is there an easy way to find the payout structure from the lobby? Of course with a silver pin on the line, this plays like a winner-takes-all-battle-to-the-death-there-can-be-only-one kind of situation, but for the sake of theory, we can approximate the payout values for ICM.
-
The payouts are listed in the results of the TOC post.
1: Frogman-Rick (United States), 161,500 (50%)
2: EANDERSON85 (United States), 96,900 (30%)
3: RecPokerSteve (United States), 64,600 (20%)https://rec.poker/announcements/online-home-game-results/nightly-series-toc-june-2020/
-
-
Is the section labeled “Chop Value” supposed to be a chop based on ICM? If so, the calculation for each stack should be the sum of the probability of finishing in a particular spot multiplied by the prize for that spot?
Like this:
-
Big Stack: 0.6667 * $10000 + 0.2828 * $4000 + 0.0505 * $1000 = $7848.70
-
Medium Stack: 0.25 * $10000 + 0.5227 * $4000 + 0.2273 * $1000 = $4818.10
-
Small Stack: 0.0833 * $10000 + 0.1944 * $4000 + 0.7226 * $1000 = $2333.20
-
Chop value is such an interesting dynamic isn’t it @tvstensby @ARW ? particularly when in the moment of negotiating splits. What factors other than ICM have you considered or heard other people consider? What proportion of the tables you’ve chopped have been ICM payouts vs modified by these factors? Do more skilled players benefit from chopping or playing it out?
-
I am a “low volume” player and have only chopped once. We simply shared a part of the remaining prize pool equally between us (2 players), and then played for the rest. We had similar stacks and we were the only two left, so ICM calculations were not relevant.
In the tournament that I chopped a three way split was also proposed earlier by the most experienced player at the table. He wanted an extra cut, which I and the other player did not accept.
Unless the stacks are relatively deep (>25 bb?) or several players remain I think that skill advantage is not significant enough to accept uneven chops. As long as the less experienced players have a rough idea how a push/fold charts looks like the advantage of the skilled player will be small amounts of value that adds up over time. No reason to let them “cash out” without a fight.
-
-
Log in to reply.