Poker Homework: ICM Application

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Poker Homework: ICM Application
撲克作業：計算ICM

By grapsfan
Jan 30 2009, 09:59 AM
http://0rz.tw/2p2In


Independent Chip Modeling is a method of equating the expected value of a
tournament decision in terms of the # of chips you’ll win (cEV) and your
monetary equity associated with the decision’s outcome ($EV).  The
development of ICM theory was a key advancement in the “solving” of correct
SNG play…as we’ll demonstrate with a classic SNG problem.
ICM是一種計算你在比賽做出決策而贏得籌碼的期望值(cEV)，以及這個決策實際
贏得獎金數($EV)的方法。ICM理論是正確解決SNG打法的關鍵發展---我將會描述一個經典
的SNG問題。

There are four players left in a single-table 9-man SNG, with a traditional
4.5x-2.7x-1.8x payout table (where “x” is the buy-in).  The blinds are
200/400, and the chip stacks are as follows:
在一個9人的SNG牌局，現在還剩下4名玩家，獎金結構是傳統的4.5x-2.7x-1.8x
（這裡的"x"代表buy-in）。盲注為200／400，籌碼分別如下：

Seat #1: 800
Seat #2: 2100
SB: 5200
BB (You): 5400

Action folds to the SB, who shoves.  You have Ace-King.  What do you do?
Sounds like a no-brainer…but let’s take a closer look.
With ICM, we assign a $EV amount to each decision, based on the possibility
of payout percentages.  If we call with our Ace-King, we may win and be a
dominating chip leader, or lose and be out of the tournament.  So let’s
estimate we’re a 85% favorite to win the tournament if we with with
Ace-King, 10% to come in 2nd, and 5% to come in third.
這一局fold到SB，SB全推，你拿到AK。你會怎麼做？聽起來好像很無腦...但是
讓我們仔細檢視一下。
基於領獎比例的可能性，我們用ICM來確認每個決策的$EV。如果我們拿AK call，我們可
能會贏並且成為有壓倒性優勢的籌碼領先者，或者是輸掉而出局。所以讓我們估一下，如
果這手AK贏了，我們有85%機率第一名，10%機率第二，5%機率第三。

However, we also have to include our odds of winning the hand.  If the SB is
shoving with any two cards (and they should be), we’re a 65:35 favorite,
according to PokerStove.
然而，我們也要把贏這手牌的odds含括進來。假設SB推任何兩張牌（SB應該要這
樣做），根據pokerstove計算，我們有65:35的贏面。

The $EV of a call is the sum of the value of each decision:
這個決策的價值總和如下：
$EV(call) = $EV(win) + $EV(lose)
$EV(call) = (.85*4.5x + .10*2.7x + .05*1.8x) * .65 + 0
$EV(call) = 2.72x

We have to make similar outcome estimation if we fold.  Let’s say, based on
approximate chip equity, we’re 35% to win, 45% to come in second and 15% to
come in third.
我們也要做相同的計算在fold這手牌上。基於概略估算的籌碼equity，我們有
35%第一，45%第二，15%第三。

$EV(fold) = .35*4.5x + .45*2.7x + .15*1.8x
$EV(fold) = 3.06x

There is more value in a fold than a call with Ace-King, even though we’re a
big favorite from a chip equity perspective.
You can make similar calculations at key points in larger tournaments as well.
Let’s say you’re in a 180-man MTT on Stars.  Tenth through 18th pay out
2.2x the buy-in.  Seventh through 9th pay out an average of 4.7x the buy-in.
Fourth through 6th pay out an average of 11.7x the buy-in.  The top 3 spots
pay out an average of 37x the buy-in.
即使從chip equity的觀點來看我們有很高的勝算，fold AK還是比call更有價值
。在一些較大的比賽，關鍵時你可以做類似的計算。例如在180人的MTT。十到十八名的
獎金是2.2x。七到九名4.7x。四到六名11.7x。前三名平均拿到37x。

The blinds are 400/800 as the money bubble breaks.  You are 12th out of 18
remaining players with 8400 chips.  Doubling up will move you up to 4th.  A
fairly loose player, who has you covered, shoves from the cutoff.  You are in
the BB with J9s.  For the sake of this exercise, let’s assign the cutoff a
starting hand range of any two Broadway, any Ace, or any pair.  According to
PokerStove, your J9s is a 62:38 underdog to this range.
此時泡沫期已經過了，盲注為400／800。你有8400，在18名玩家中排第12。籌碼
加倍的話會晉升到第4名。一個相當loose的玩家，在CO全推。你在BB拿J9s，假設CO的範
圍是任何兩張人頭卡、任何A，任何對子。根據pokerstove計算，你的J9s在這種範圍下
是處於38：62的劣勢。

If you win this hand and are 4th in chips, let’s estimate you are 25% to
finish in the Top 3, 30% to finish 4-6, 30% to finish 7-9, and 15% to finish
10-18.
如果你贏了這一手，籌碼就變成第4多。讓我們估算你有25%前三名、30%四到
六名、30%七到九名、15%十到十八名。

$EV(call) = $EV(win) + $EV(lose)
$EV(call) = ((.25*37x + .30*11.7x + .30*4.7x + .15*2.2) * .38) + (.62*2.2x)
$EV(call) = 5.51x + 1.37x
$EV(call) = 6.88x

If we fold and give up almost one-tenth of our stack, let’s estimate you are
5% to finish in the top 3, 20% to finish 4-6, 35% to finish 7-9 and 40% to
finish 10-18.
如果我們fold並且放棄了幾乎十分之一的籌碼（big blind），讓我們估算你有
5%前三名、20%四到六名、35%七到九名、40%十到十八名。

$EV(fold) = .05*37x + .20*11.7x + .35*4.7x + .40*2.2x
$EV(fold) = 6.72x

With these results estimations, making a call with J9s, as a 3:2 underdog,
provides the best financial outcome.
根據計算結果，當處在2：3的劣勢時，拿J9s call仍然有最佳的利益。

有人問ICM是什麼，所以節錄這一段，翻完我也不太懂XD



ICM also provides some fuel to the “always take any slight advantage” fire
in MTT strategy.  Let’s say you’re a successful low-to-mid stakes tournament
player, with an expected ROI of 60%, so you should expect to make $15 (on a
long-term average) or so by participating in this tournament.  You’re in the
$24+2 32k guaranteed on Full Tilt, with 1500 players and 162 spots paying.
You raise on the first hand of the tournament from the cutoff with 99.  The
BB shoves, and tells you he has AKs…and you believe him.  Your 99 is a 52:48
favorite.  From the cEV perspective, this is an easy call.

From a $EV perspective, however, you need double your expectation to justify
the call.  To reach this point in the payout table, you’re passing almost
10% more of the field.  You have to double the likelihood of going deep,
reaching the Final Table, taking the whole thing down.  Is this reasonable,
just by adding less than .1% of the total chips in play, at Level 1 of the
tournament?  If the answer is “no” for you, then reconsider the “always
take a slight advantage” strategy.

I will grant you, this is a lot of math.  Performing ICM calculations takes
time.  Even when using an ICM Calculator from a poker site, it’s tough to
get the data you need to make a decision in the time bank available online.
Parts of the exercise, however, are a practicable skill.  You can spend a lot
of time going over tricky situations, running the numbers and seeing what the
right play is.  ICM takes practice, both in terms of figuring out what the
$EV play may be, and being willing to accept the likelihood of conflict
against traditional cEV pot odds.

I also HIGHLY recommend getting friendly with PokerStove and other card
calculator applications.  Running the numbers on $EV(call) and $EV(fold) may
be overwhelming, but there’s no reason why anyone can’t practice assigning
hand ranges, and spending time learning how typical hands play against each
range.  We all spent most of our youth doing homework for hours, with no
clear picture as to what we were getting out of it.

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