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So the following I think is clearly true.
Consider the following chipstacks.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=146><TBODY><TR><TD height=0 vAlign=bottom width="50%">Player
</TD><TD height=0 vAlign=bottom width="50%">Chips
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Villian 1
</TD><TD height=0 vAlign=bottom width="50%">15000
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Villian 2
</TD><TD height=0 vAlign=bottom width="50%">18000
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Villian 3
</TD><TD height=0 vAlign=bottom width="50%">12000
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Villian 4
</TD><TD height=0 vAlign=bottom width="50%">5750
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Villian 5
</TD><TD height=0 vAlign=bottom width="50%">10000
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Hero
</TD><TD height=0 vAlign=bottom width="50%">6750
</TD></TR></TBODY></TABLE>
ICM can determine how often each player finishes in each place. It looks like this.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=584><TBODY><TR><TD height=0 vAlign=bottom width="13%">Player
</TD><TD height=0 vAlign=bottom width="13%">Chips
</TD><TD height=0 vAlign=bottom width="13%">1st
</TD><TD height=0 vAlign=bottom width="13%">2nd
</TD><TD height=0 vAlign=bottom width="13%">3rd
</TD><TD height=0 vAlign=bottom width="13%">4th
</TD><TD height=0 vAlign=bottom width="13%">5th
</TD><TD height=0 vAlign=bottom width="13%">6th
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 1
</TD><TD height=0 vAlign=bottom width="13%">15000
</TD><TD height=0 vAlign=bottom width="13%">22.22%
</TD><TD height=0 vAlign=bottom width="13%">21.29%
</TD><TD height=0 vAlign=bottom width="13%">19.67%
</TD><TD height=0 vAlign=bottom width="13%">17.04%
</TD><TD height=0 vAlign=bottom width="13%">12.89%
</TD><TD height=0 vAlign=bottom width="13%">6.88%
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 2
</TD><TD height=0 vAlign=bottom width="13%">18000
</TD><TD height=0 vAlign=bottom width="13%">26.67%
</TD><TD height=0 vAlign=bottom width="13%">23.47%
</TD><TD height=0 vAlign=bottom width="13%">19.75%
</TD><TD height=0 vAlign=bottom width="13%">15.36%
</TD><TD height=0 vAlign=bottom width="13%">10.19%
</TD><TD height=0 vAlign=bottom width="13%">4.57%
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 3
</TD><TD height=0 vAlign=bottom width="13%">12000
</TD><TD height=0 vAlign=bottom width="13%">17.78%
</TD><TD height=0 vAlign=bottom width="13%">18.27%
</TD><TD height=0 vAlign=bottom width="13%">18.60%
</TD><TD height=0 vAlign=bottom width="13%">18.29%
</TD><TD height=0 vAlign=bottom width="13%">16.24%
</TD><TD height=0 vAlign=bottom width="13%">10.82%
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 4
</TD><TD height=0 vAlign=bottom width="13%">5750
</TD><TD height=0 vAlign=bottom width="13%">8.52%
</TD><TD height=0 vAlign=bottom width="13%">9.80%
</TD><TD height=0 vAlign=bottom width="13%">11.67%
</TD><TD height=0 vAlign=bottom width="13%">14.71%
</TD><TD height=0 vAlign=bottom width="13%">20.59%
</TD><TD height=0 vAlign=bottom width="13%">34.71%
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 5
</TD><TD height=0 vAlign=bottom width="13%">10000
</TD><TD height=0 vAlign=bottom width="13%">14.81%
</TD><TD height=0 vAlign=bottom width="13%">15.85%
</TD><TD height=0 vAlign=bottom width="13%">17.09%
</TD><TD height=0 vAlign=bottom width="13%">18.45%
</TD><TD height=0 vAlign=bottom width="13%">18.72%
</TD><TD height=0 vAlign=bottom width="13%">15.08%
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Hero
</TD><TD height=0 vAlign=bottom width="13%">6750
</TD><TD height=0 vAlign=bottom width="13%">10.00%
</TD><TD height=0 vAlign=bottom width="13%">11.33%
</TD><TD height=0 vAlign=bottom width="13%">13.21%
</TD><TD height=0 vAlign=bottom width="13%">16.14%
</TD><TD height=0 vAlign=bottom width="13%">21.37%
</TD><TD height=0 vAlign=bottom width="13%">27.95%
</TD></TR></TBODY></TABLE> -
So you open this wondering what kind of nonsense I would be going on about.
I thought I would start slow.
So how does ICM determine the above?? -
One simple way to explain it is that ICM conducts a drawing for the prizes. Each player gets one ticket for each of his chips. The first ticket drawn is awarded first place. The second ticket drawn is awarded second place and etc. Only one prize per player please.
There are other ways to explain it, but I thinks this one works pretty well. -
OK we haven't talked about prizes yet. ICM did not need to know them. It already knows the answers. See above.
Originally Posted by Cashweekly
So the following I think is clearly true.
Consider the following chipstacks.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=146><TBODY><TR><TD height=0 vAlign=bottom width="50%">Player
</TD><TD height=0 vAlign=bottom width="50%">Chips
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Villian 1
</TD><TD height=0 vAlign=bottom width="50%">15000
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Villian 2
</TD><TD height=0 vAlign=bottom width="50%">18000
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Villian 3
</TD><TD height=0 vAlign=bottom width="50%">12000
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Villian 4
</TD><TD height=0 vAlign=bottom width="50%">5750
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Villian 5
</TD><TD height=0 vAlign=bottom width="50%">10000
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">Hero
</TD><TD height=0 vAlign=bottom width="50%">6750
</TD></TR></TBODY></TABLE>
ICM can determine how often each player finishes in each place. It looks like this.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=584><TBODY><TR><TD height=0 vAlign=bottom width="13%">Player
</TD><TD height=0 vAlign=bottom width="13%">Chips
</TD><TD height=0 vAlign=bottom width="13%">1st
</TD><TD height=0 vAlign=bottom width="13%">2nd
</TD><TD height=0 vAlign=bottom width="13%">3rd
</TD><TD height=0 vAlign=bottom width="13%">4th
</TD><TD height=0 vAlign=bottom width="13%">5th
</TD><TD height=0 vAlign=bottom width="13%">6th
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 1
</TD><TD height=0 vAlign=bottom width="13%">15000
</TD><TD height=0 vAlign=bottom width="13%">22.22%
</TD><TD height=0 vAlign=bottom width="13%">21.29%
</TD><TD height=0 vAlign=bottom width="13%">19.67%
</TD><TD height=0 vAlign=bottom width="13%">17.04%
</TD><TD height=0 vAlign=bottom width="13%">12.89%
</TD><TD height=0 vAlign=bottom width="13%">6.88%
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 2
</TD><TD height=0 vAlign=bottom width="13%">18000
</TD><TD height=0 vAlign=bottom width="13%">26.67%
</TD><TD height=0 vAlign=bottom width="13%">23.47%
</TD><TD height=0 vAlign=bottom width="13%">19.75%
</TD><TD height=0 vAlign=bottom width="13%">15.36%
</TD><TD height=0 vAlign=bottom width="13%">10.19%
</TD><TD height=0 vAlign=bottom width="13%">4.57%
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 3
</TD><TD height=0 vAlign=bottom width="13%">12000
</TD><TD height=0 vAlign=bottom width="13%">17.78%
</TD><TD height=0 vAlign=bottom width="13%">18.27%
</TD><TD height=0 vAlign=bottom width="13%">18.60%
</TD><TD height=0 vAlign=bottom width="13%">18.29%
</TD><TD height=0 vAlign=bottom width="13%">16.24%
</TD><TD height=0 vAlign=bottom width="13%">10.82%
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 4
</TD><TD height=0 vAlign=bottom width="13%">5750
</TD><TD height=0 vAlign=bottom width="13%">8.52%
</TD><TD height=0 vAlign=bottom width="13%">9.80%
</TD><TD height=0 vAlign=bottom width="13%">11.67%
</TD><TD height=0 vAlign=bottom width="13%">14.71%
</TD><TD height=0 vAlign=bottom width="13%">20.59%
</TD><TD height=0 vAlign=bottom width="13%">34.71%
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 5
</TD><TD height=0 vAlign=bottom width="13%">10000
</TD><TD height=0 vAlign=bottom width="13%">14.81%
</TD><TD height=0 vAlign=bottom width="13%">15.85%
</TD><TD height=0 vAlign=bottom width="13%">17.09%
</TD><TD height=0 vAlign=bottom width="13%">18.45%
</TD><TD height=0 vAlign=bottom width="13%">18.72%
</TD><TD height=0 vAlign=bottom width="13%">15.08%
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Hero
</TD><TD height=0 vAlign=bottom width="13%">6750
</TD><TD height=0 vAlign=bottom width="13%">10.00%
</TD><TD height=0 vAlign=bottom width="13%">11.33%
</TD><TD height=0 vAlign=bottom width="13%">13.21%
</TD><TD height=0 vAlign=bottom width="13%">16.14%
</TD><TD height=0 vAlign=bottom width="13%">21.37%
</TD><TD height=0 vAlign=bottom width="13%">27.95%
</TD></TR></TBODY></TABLE>
Anyway lets add some prizes. The quick among you already see there are 67500 chips in total, and yes this is a stars $12/45.
Since we are all guaranteed $33 we can subtract this form each prize and get the following prizes.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=188><TBODY><TR><TD height=0 vAlign=bottom width="50%">1st
</TD><TD height=0 vAlign=bottom width="50%">121
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">2nd
</TD><TD height=0 vAlign=bottom width="50%">77
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">3rd
</TD><TD height=0 vAlign=bottom width="50%">44
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">4th
</TD><TD height=0 vAlign=bottom width="50%">22
</TD></TR><TR><TD height=0 vAlign=bottom width="50%">5th
</TD><TD height=0 vAlign=bottom width="50%">11
</TD></TR></TBODY></TABLE>
And multiply the chart above by the prizepool chart and get.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=584><TBODY><TR><TD height=0 vAlign=bottom width="13%">Player
</TD><TD height=0 vAlign=bottom width="13%">Chips
</TD><TD height=0 vAlign=bottom width="13%">1st
</TD><TD height=0 vAlign=bottom width="13%">2nd
</TD><TD height=0 vAlign=bottom width="13%">3rd
</TD><TD height=0 vAlign=bottom width="13%">4th
</TD><TD height=0 vAlign=bottom width="13%">5th
</TD><TD height=0 vAlign=bottom width="13%">total
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 1
</TD><TD height=0 vAlign=bottom width="13%">15000
</TD><TD height=0 vAlign=bottom width="13%">$26.89
</TD><TD height=0 vAlign=bottom width="13%">$16.39
</TD><TD height=0 vAlign=bottom width="13%">$8.66
</TD><TD height=0 vAlign=bottom width="13%">$3.75
</TD><TD height=0 vAlign=bottom width="13%">$1.42
</TD><TD height=0 vAlign=bottom width="13%">$57.10
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 2
</TD><TD height=0 vAlign=bottom width="13%">18000
</TD><TD height=0 vAlign=bottom width="13%">$32.27
</TD><TD height=0 vAlign=bottom width="13%">$18.07
</TD><TD height=0 vAlign=bottom width="13%">$8.69
</TD><TD height=0 vAlign=bottom width="13%">$3.38
</TD><TD height=0 vAlign=bottom width="13%">$1.12
</TD><TD height=0 vAlign=bottom width="13%">$63.53
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 3
</TD><TD height=0 vAlign=bottom width="13%">12000
</TD><TD height=0 vAlign=bottom width="13%">$21.51
</TD><TD height=0 vAlign=bottom width="13%">$14.07
</TD><TD height=0 vAlign=bottom width="13%">$8.19
</TD><TD height=0 vAlign=bottom width="13%">$4.03
</TD><TD height=0 vAlign=bottom width="13%">$1.79
</TD><TD height=0 vAlign=bottom width="13%">$49.57
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 4
</TD><TD height=0 vAlign=bottom width="13%">5750
</TD><TD height=0 vAlign=bottom width="13%">$10.31
</TD><TD height=0 vAlign=bottom width="13%">$7.55
</TD><TD height=0 vAlign=bottom width="13%">$5.14
</TD><TD height=0 vAlign=bottom width="13%">$3.24
</TD><TD height=0 vAlign=bottom width="13%">$2.27
</TD><TD height=0 vAlign=bottom width="13%">$28.49
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Villian 5
</TD><TD height=0 vAlign=bottom width="13%">10000
</TD><TD height=0 vAlign=bottom width="13%">$17.93
</TD><TD height=0 vAlign=bottom width="13%">$12.20
</TD><TD height=0 vAlign=bottom width="13%">$7.52
</TD><TD height=0 vAlign=bottom width="13%">$4.06
</TD><TD height=0 vAlign=bottom width="13%">$2.06
</TD><TD height=0 vAlign=bottom width="13%">$43.77
</TD></TR><TR><TD height=0 vAlign=bottom width="13%">Hero
</TD><TD height=0 vAlign=bottom width="13%">6750
</TD><TD height=0 vAlign=bottom width="13%">$12.10
</TD><TD height=0 vAlign=bottom width="13%">$8.72
</TD><TD height=0 vAlign=bottom width="13%">$5.81
</TD><TD height=0 vAlign=bottom width="13%">$3.55
</TD><TD height=0 vAlign=bottom width="13%">$2.35
</TD><TD height=0 vAlign=bottom width="13%">$32.54
</TD></TR><TR><TD height=0 vAlign=bottom width="13%"></TD><TD height=0 vAlign=bottom width="13%"></TD><TD height=0 vAlign=bottom width="13%">$121.00
</TD><TD height=0 vAlign=bottom width="13%">$77.00
</TD><TD height=0 vAlign=bottom width="13%">$44.00
</TD><TD height=0 vAlign=bottom width="13%">$22.00
</TD><TD height=0 vAlign=bottom width="13%">$11.00
</TD><TD height=0 vAlign=bottom width="13%">$275.00
</TD></TR></TBODY></TABLE> -
You can put the above into an ICM calculator and see I am not making this stuff up.
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OK so you are still wondering, "When is he going to start saying stupid s***"?
Well just for reference let's throw up a different chart.
This one has a different prizepool. It is winner take all, and the prize is $121.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=219><TBODY><TR><TD height=0 vAlign=bottom width="33%">Player
</TD><TD height=0 vAlign=bottom width="33%">Chips
</TD><TD height=0 vAlign=bottom width="33%">1st
</TD></TR><TR><TD height=0 vAlign=bottom width="33%">Villian 1
</TD><TD height=0 vAlign=bottom width="33%">15000
</TD><TD height=0 vAlign=bottom width="33%">$26.89
</TD></TR><TR><TD height=0 vAlign=bottom width="33%">Villian 2
</TD><TD height=0 vAlign=bottom width="33%">18000
</TD><TD height=0 vAlign=bottom width="33%">$32.27
</TD></TR><TR><TD height=0 vAlign=bottom width="33%">Villian 3
</TD><TD height=0 vAlign=bottom width="33%">12000
</TD><TD height=0 vAlign=bottom width="33%">$21.51
</TD></TR><TR><TD height=0 vAlign=bottom width="33%">Villian 4
</TD><TD height=0 vAlign=bottom width="33%">5750
</TD><TD height=0 vAlign=bottom width="33%">$10.31
</TD></TR><TR><TD height=0 vAlign=bottom width="33%">Villian 5
</TD><TD height=0 vAlign=bottom width="33%">10000
</TD><TD height=0 vAlign=bottom width="33%">$17.93
</TD></TR><TR><TD height=0 vAlign=bottom width="33%">Hero
</TD><TD height=0 vAlign=bottom width="33%">6750
</TD><TD height=0 vAlign=bottom width="33%">$12.10
</TD></TR><TR><TD height=0 vAlign=bottom width="33%"></TD><TD height=0 vAlign=bottom width="33%"></TD><TD height=0 vAlign=bottom width="33%">$121.00
</TD></TR></TBODY></TABLE>
Of course this is just the first few columns from the chart above. We will come back to this later. -
This is all interesting and you equity in the prize pool is important information but it changes on every hand, with every movement of the button. ICM is far more useful as guide for your final table actions. Used to determine opening, calling and overcalling ranges it will allow you to crush players that don't understand it.....
Level: 600.0/1200.0/75.0
Structure: 0.44/0.28/0.16/0.08/0.04
Players: 6
Runtime: 692ms [300 Iterations]
<TABLE class=simple border=1 cellSpacing=2 cellPadding=3><TBODY><TR><TH>Player</TH><TH>Stack</TH><TH>Push%</TH><TH>EQPre</TH><TH>EQPost</TH><TH>EQDiff</TH></TR><TR><TD>UTG</TD><TD>15000.0</TD><TD>24.9%</TD><TD>0.2077</TD><TD>0.2108</TD><TD>0.00313</TD></TR><TR><TD>UTG+1</TD><TD>18000.0</TD><TD>43.3%</TD><TD>0.231</TD><TD>0.2342</TD><TD>0.00322</TD></TR><TR><TD>CO</TD><TD>12000.0</TD><TD>43.9%</TD><TD>0.1803</TD><TD>0.184</TD><TD>0.00378</TD></TR><TR><TD>BU</TD><TD>5750.0</TD><TD>34.2%</TD><TD>0.1036</TD><TD>0.1084</TD><TD>0.00483</TD></TR><TR><TD>SB</TD><TD>10000.0</TD><TD>90.0%</TD><TD>0.1592</TD><TD>0.1564</TD><TD>-0.00278</TD></TR><TR><TD>BB</TD><TD>6750.0</TD><TD><TD>0.1183</TD><TD>0.1061</TD><TD>-0.01218</TD></TR></TBODY></TABLE>
Explanation:- <LI>Stack: Players stack before posting blinds.</LI> <LI>Push%: Percentage of hands a player open-pushes.</LI> <LI>EQPre: ICM equity before blinds.</LI> <LI>EQPost: ICM equity after hand.</LI> <LI>EQDiff: ICM equity change during hand.</LI>
<TABLE class=simple border=1 cellSpacing=2 cellPadding=3><TBODY><TR><TH width=40>PU</TH><TH width=40>CA</TH><TH width=40>OC</TH><TH>Range</TH></TR><TR><TD>UTG</TD><TD><TD><TD>24.9%, 44+ A2s+ A9o+ A5o-A4o K4s+ KTo+ Q9s+ QTo+ J9s+ JTo T9s </TD></TR><TR><TD><TD>UTG+1</TD><TD><TD>4.2%, 99+ AQs+ AKo </TD></TR><TR><TD><TD><TD>CO</TD><TD>0.5%, AA </TD></TR><TR><TD><TD><TD>BU</TD><TD>0.9%, KK+ </TD></TR><TR><TD><TD><TD>SB</TD><TD>0.5%, AA </TD></TR><TR><TD><TD><TD>BB</TD><TD>0.9%, KK+ </TD></TR><TR><TD><TD>CO</TD><TD><TD>2.6%, TT+ AKs </TD></TR><TR><TD><TD><TD>BU</TD><TD>0.9%, KK+ </TD></TR><TR><TD><TD><TD>SB</TD><TD>0.5%, AA </TD></TR><TR><TD><TD><TD>BB</TD><TD>0.9%, KK+ </TD></TR><TR><TD><TD>BU</TD><TD><TD>7.1%, 88+ ATs+ AJo+ </TD></TR><TR><TD><TD><TD>SB</TD><TD>2.6%, TT+ AKs </TD></TR><TR><TD><TD><TD>BB</TD><TD>4.2%, 99+ AQs+ AKo </TD></TR><TR><TD><TD>SB</TD><TD><TD>5.4%, 99+ AJs+ AQo+ </TD></TR><TR><TD><TD><TD>BB</TD><TD>1.4%, QQ+ </TD></TR><TR><TD><TD>BB</TD><TD><TD>9.7%, 55+ A9s+ ATo+ </TD></TR><TR><TD>UTG+1</TD><TD><TD><TD>43.3%, 22+ Ax+ K2s+ K7o+ Q2s+ Q9o+ J4s+ J9o+ T6s+ T9o 96s+ 86s+ 76s 65s 54s </TD></TR><TR><TD><TD>CO</TD><TD><TD>3.8%, TT+ AQs+ AKo </TD></TR><TR><TD><TD><TD>BU</TD><TD>0.9%, KK+ </TD></TR><TR><TD><TD><TD>SB</TD><TD>0.9%, KK+ </TD></TR><TR><TD><TD><TD>BB</TD><TD>0.9%, KK+ </TD></TR><TR><TD><TD>BU</TD><TD><TD>8.7%, 77+ A9s+ ATo+ </TD></TR><TR><TD><TD><TD>SB</TD><TD>4.2%, 99+ AQs+ AKo </TD></TR><TR><TD><TD><TD>BB</TD><TD>5.6%, 88+ AQs+ AQo+ </TD></TR><TR><TD><TD>SB</TD><TD><TD>7.1%, 88+ ATs+ AJo+ </TD></TR><TR><TD><TD><TD>BB</TD><TD>1.4%, QQ+ </TD></TR><TR><TD><TD>BB</TD><TD><TD>16.9%, 55+ A3s+ A7o+ KTs+ KJo+ </TD></TR><TR><TD>CO</TD><TD><TD><TD>43.9%, 22+ Ax+ K2s+ K8o+ Q3s+ Q9o+ J5s+ J9o+ T6s+ T8o+ 96s+ 98o 86s+ 75s+ 65s 54s </TD></TR><TR><TD><TD>BU</TD><TD><TD>8.7%, 77+ A9s+ ATo+ </TD></TR><TR><TD><TD><TD>SB</TD><TD>4.2%, 99+ AQs+ AKo </TD></TR><TR><TD><TD><TD>BB</TD><TD>5.9%, 88+ AJs+ AQo+ </TD></TR><TR><TD><TD>SB</TD><TD><TD>7.1%, 88+ ATs+ AJo+ </TD></TR><TR><TD><TD><TD>BB</TD><TD>1.4%, QQ+ </TD></TR><TR><TD><TD>BB</TD><TD><TD>21.3%, 44+ A2s+ A5o+ K9s+ KTo+ QTs+ </TD></TR><TR><TD>BU</TD><TD><TD><TD>34.2%, 22+ Ax+ K3s+ K9o+ Q8s+ QTo+ J8s+ JTo T7s+ 97s+ 86s+ 76s </TD></TR><TR><TD><TD>SB</TD><TD><TD>17.8%, 33+ A3s+ A7o+ KTs+ KJo+ </TD></TR><TR><TD><TD><TD>BB</TD><TD>7.1%, 88+ ATs+ AJo+ </TD></TR><TR><TD><TD>BB</TD><TD><TD>29.1%, 22+ Ax+ K6s+ K9o+ Q9s+ QTo+ JTs </TD></TR><TR><TD>SB</TD><TD><TD><TD>90.0%, 22+ Jx+ T2s+ T3o+ 92s+ 94o+ 82s+ 84o+ 72s+ 74o+ 62s+ 63o+ 52s+ 53o+ 42s+ 43o 32s </TD></TR><TR><TD><TD>BB</TD><TD><TD>42.8%, 33+ Ax+ K2s+ K3o+ Q4s+ Q7o+ J7s+ J9o+ T8s+ </TD></TR></TBODY></TABLE>
Explanation:- <LI>PU: Pushing Player. Applies when no other player entered the pot yet.</LI> <LI>CA: Calling Player. Player pushes after another player (PU) is already in the pot.</LI> <LI>OC: OverCalling Player. Player pushes after two other players (PU, CA) are already in the pot.</LI>
-
So I tried to start with simple stuff that everyone could agree on. I am going to get a little more controversial as we go along.
You notice we have not talked about hands, cards, blinds position, or anything like that.
ICM doesn't care.
A good way to explain how ICM works, is anytime you ask ICM anything is stops the tournament, and conducts its lottery drawing. -
OK Saukendar. I am not quite ready to be shot at yet.
Since you seems to be here to help, could you please try again with the Nash calculator. You have inadvertently added another stack to make it 7 handed, and botched the prizepool a little.
Also just so we are all on the same page, we are going to be 600/1200/75
Anyways we are going to be considering our decision vs SBs ATC push. -
Fixed - Just tossed it out for show - SnGWiz & other tools use this under the hood to generate critiques.....
Originally Posted by Cashweekly
OK Saukendar. I am not quite ready to be shot at yet.
Since you seems to be here to help, could you please try again with the Nash calculator. You have inadvertently added another stack to make it 7 handed, and botched the prizepool a little.
Anyways we are going to be considering our decision vs SBs ATC push.
I've never found the pool equity aspects to be of much use except in chop negotiations myself.....
The hand ranges & seeing who is and isn't following them when hands get shown down are mondo useful........ -
So it folds to the SB.
He shoves, and we have to decide if we should call off all of our chips.
You can imput the numbers into an ICM calculator and get the following.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=511><TBODY><TR><TD height=0 vAlign=bottom width="14%"></TD><TD height=0 vAlign=bottom width="14%">1st
</TD><TD height=0 vAlign=bottom width="14%">2nd
</TD><TD height=0 vAlign=bottom width="14%">3rd
</TD><TD height=0 vAlign=bottom width="14%">4th
</TD><TD height=0 vAlign=bottom width="14%">5th
</TD><TD height=0 vAlign=bottom width="14%">total
</TD></TR><TR><TD height=0 vAlign=bottom width="14%">fold
</TD><TD height=0 vAlign=bottom width="14%">$9.81
</TD><TD height=0 vAlign=bottom width="14%">$7.24
</TD><TD height=0 vAlign=bottom width="14%">$4.98
</TD><TD height=0 vAlign=bottom width="14%">$3.21
</TD><TD height=0 vAlign=bottom width="14%">$2.38
</TD><TD height=0 vAlign=bottom width="14%">$27.62
</TD></TR><TR><TD height=0 vAlign=bottom width="14%">call/win
</TD><TD height=0 vAlign=bottom width="14%">$24.74
</TD><TD height=0 vAlign=bottom width="14%">$15.78
</TD><TD height=0 vAlign=bottom width="14%">$8.90
</TD><TD height=0 vAlign=bottom width="14%">$4.18
</TD><TD height=0 vAlign=bottom width="14%">$1.55
</TD><TD height=0 vAlign=bottom width="14%">$55.15
</TD></TR></TBODY></TABLE>
you can divide in the totals column and see that ICM tell us to call with any hand that has greater than 50% equity, vs his ATC shove. -
After the parameter changes the new values are:
Originally Posted by Cashweekly
So it folds to the SB.
He shoves, and we have to decide if we should call off all of our chips.
SB open range - 90.0%, 22+ Jx+ T2s+ T3o+ 92s+ 94o+ 82s+ 84o+ 72s+ 74o+ 62s+ 63o+ 52s+ 53o+ 42s+ 43o 32s
BB call range - 42.8%, 33+ Ax+ K2s+ K3o+ Q4s+ Q7o+ J7s+ J9o+ T8s+ -
Well that is fine, but let's say this is live, and you know he did not look at his cards.
Originally Posted by saukendar
After the parameter changes the new values are:
SB open range - 90.0%, 22+ Jx+ T2s+ T3o+ 92s+ 94o+ 82s+ 84o+ 72s+ 74o+ 62s+ 63o+ 52s+ 53o+ 42s+ 43o 32s
BB call range - 42.8%, 33+ Ax+ K2s+ K3o+ Q4s+ Q7o+ J7s+ J9o+ T8s+
He is on ATC. I am trying to get to something here. I actually at first thought it would convince alot of people of some things, but realize now it won't.
Still someone may be interested, so onward I go.
I am talking about something that is perfectly clear to me.
That is the fact that you will not achieve the equity that ICM promises you at various points, by following the reccomendations of ICM.
IN other words by folloowing ICM you are making suboptimal Chip EV decisions based on math that (sort of) assumes you are not doing so. -
That fact that the pool equity is a snapshot at a given point in time based on EV assuming a large (statiscicly valid) number of trials is why I don't find it useful - except in chop negotiations.
Originally Posted by Cashweekly
Well that is fine, but let's say this is live, and you know he did not look at his cards.
He is on ATC. I am trying to get to something here. I actually at first thought it would convince alot of people of some things, but realize now it won't.
Still someone may be interested, so onward I go.
I am talking about something that is perfectly clear to me.
That is the fact that you will not achieve the equity that ICM promises you at various points, by following the reccomendations of ICM.
IN other words by folloowing ICM you are making suboptimal Chip EV decisions based on math that (sort of) assumes you are not doing so.
The variance on any given trial is exceptionly high. We all know getting in as a 4:1 favorite 5 times will more than likely get you busted - it's just poker.
It's also true that proper ICM play assumes your villian is playing proper ICM - not always the case by any means. Thats why knowing who is and isn't following ICM is important - good reads always are, especialy in live play....
[edit]
In your example if ICM gives 90% or ATC as the SB open but in pratice he's open folding 2 of 3 orbits you can be certian that playing back at him with any top 50% hand is a mistake even if thats the ICM range. -
So we call with 49.32% of hands, and win 58.13% of the time.
Originally Posted by Cashweekly
So it folds to the SB.
He shoves, and we have to decide if we should call off all of our chips.
You can imput the numbers into an ICM calculator and get the following.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=511><TBODY><TR><TD height=0 vAlign=bottom width="14%"></TD><TD height=0 vAlign=bottom width="14%">1st
</TD><TD height=0 vAlign=bottom width="14%">2nd
</TD><TD height=0 vAlign=bottom width="14%">3rd
</TD><TD height=0 vAlign=bottom width="14%">4th
</TD><TD height=0 vAlign=bottom width="14%">5th
</TD><TD height=0 vAlign=bottom width="14%">total
</TD></TR><TR><TD height=0 vAlign=bottom width="14%">fold
</TD><TD height=0 vAlign=bottom width="14%">$9.81
</TD><TD height=0 vAlign=bottom width="14%">$7.24
</TD><TD height=0 vAlign=bottom width="14%">$4.98
</TD><TD height=0 vAlign=bottom width="14%">$3.21
</TD><TD height=0 vAlign=bottom width="14%">$2.38
</TD><TD height=0 vAlign=bottom width="14%">$27.62
</TD></TR><TR><TD height=0 vAlign=bottom width="14%">call/win
</TD><TD height=0 vAlign=bottom width="14%">$24.74
</TD><TD height=0 vAlign=bottom width="14%">$15.78
</TD><TD height=0 vAlign=bottom width="14%">$8.90
</TD><TD height=0 vAlign=bottom width="14%">$4.18
</TD><TD height=0 vAlign=bottom width="14%">$1.55
</TD><TD height=0 vAlign=bottom width="14%">$55.15
</TD></TR></TBODY></TABLE>
you can divide in the totals column and see that ICM tell us to call with any hand that has greater than 50% equity, vs his ATC shove.
so do the math on the above chart. We get.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=511><TBODY><TR><TD height=0 vAlign=bottom width="14%">fold
</TD><TD height=0 vAlign=bottom width="14%">$4.97
</TD><TD height=0 vAlign=bottom width="14%">$3.67
</TD><TD height=0 vAlign=bottom width="14%">$2.52
</TD><TD height=0 vAlign=bottom width="14%">$1.62
</TD><TD height=0 vAlign=bottom width="14%">$1.21
</TD><TD height=0 vAlign=bottom width="14%"></TD></TR><TR><TD height=0 vAlign=bottom width="14%">call win
</TD><TD height=0 vAlign=bottom width="14%">$7.09
</TD><TD height=0 vAlign=bottom width="14%">$4.52
</TD><TD height=0 vAlign=bottom width="14%">$2.55
</TD><TD height=0 vAlign=bottom width="14%">$1.20
</TD><TD height=0 vAlign=bottom width="14%">$0.45
</TD><TD height=0 vAlign=bottom width="14%"></TD></TR><TR><TD height=0 vAlign=bottom width="14%">total
</TD><TD height=0 vAlign=bottom width="14%">$12.07
</TD><TD height=0 vAlign=bottom width="14%">$8.19
</TD><TD height=0 vAlign=bottom width="14%">$5.08
</TD><TD height=0 vAlign=bottom width="14%">$2.82
</TD><TD height=0 vAlign=bottom width="14%">$1.65
</TD><TD height=0 vAlign=bottom width="14%">$29.81
</TD></TR></TBODY></TABLE>
We can do $12.07/$121, and see ICM now thinks we will win this 9.98% of the time. We can also see that the $12.07 is a large part of our total equity. (the single largest component) We know from above that ICM thinks this because it stops the tourney and draws for prizes.
If you think about how to equate this to a poker tourney, you might surmise it thinks we have just as good a chance of making chips as anyone else. I am certainly welcome to entertain other theories why this may be so. -
Anyways. Let us go back to our winner take all tournament. First is still $121, but there are no other prizes.
We can now call for potodds. I doubt we can fold any +chipev hand with so few chips relative to the blinds. In any case that (calling when we have potodds) is what ICM tells us to do.
We then call with any hand that is better than 39.67%.
You should understand why in the following chart this (39.67%) is row1/row2 in the 1st column.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=511><TBODY><TR><TD height=0 vAlign=bottom width="14%"></TD><TD height=0 vAlign=bottom width="14%">1st
</TD><TD height=0 vAlign=bottom width="14%">2nd
</TD><TD height=0 vAlign=bottom width="14%">3rd
</TD><TD height=0 vAlign=bottom width="14%">4th
</TD><TD height=0 vAlign=bottom width="14%">5th
</TD><TD height=0 vAlign=bottom width="14%">total
</TD></TR><TR><TD height=0 vAlign=bottom width="14%">fold
</TD><TD height=0 vAlign=bottom width="14%">$9.81
</TD><TD height=0 vAlign=bottom width="14%">$7.24
</TD><TD height=0 vAlign=bottom width="14%">$4.98
</TD><TD height=0 vAlign=bottom width="14%">$3.21
</TD><TD height=0 vAlign=bottom width="14%">$2.38
</TD><TD height=0 vAlign=bottom width="14%">$27.62
</TD></TR><TR><TD height=0 vAlign=bottom width="14%">call/win
</TD><TD height=0 vAlign=bottom width="14%">$24.74
</TD><TD height=0 vAlign=bottom width="14%">$15.78
</TD><TD height=0 vAlign=bottom width="14%">$8.90
</TD><TD height=0 vAlign=bottom width="14%">$4.18
</TD><TD height=0 vAlign=bottom width="14%">$1.55
</TD><TD height=0 vAlign=bottom width="14%">$55.15
</TD></TR></TBODY></TABLE>
anyways we call 83.41% and win 52.69% and get the following.
<TABLE dir=ltr border=1 cellSpacing=0 cellPadding=12 width=511><TBODY><TR><TD height=0 vAlign=bottom width="14%">fold
</TD><TD height=0 vAlign=bottom width="14%">$1.63
</TD><TD height=0 vAlign=bottom width="14%">$1.20
</TD><TD height=0 vAlign=bottom width="14%">$0.83
</TD><TD height=0 vAlign=bottom width="14%">$0.53
</TD><TD height=0 vAlign=bottom width="14%">$0.40
</TD><TD height=0 vAlign=bottom width="14%"></TD></TR><TR><TD height=0 vAlign=bottom width="14%">call win
</TD><TD height=0 vAlign=bottom width="14%">$10.87
</TD><TD height=0 vAlign=bottom width="14%">$6.94
</TD><TD height=0 vAlign=bottom width="14%">$3.91
</TD><TD height=0 vAlign=bottom width="14%">$1.84
</TD><TD height=0 vAlign=bottom width="14%">$0.68
</TD><TD height=0 vAlign=bottom width="14%"></TD></TR><TR><TD height=0 vAlign=bottom width="14%">total
</TD><TD height=0 vAlign=bottom width="14%">$12.50
</TD><TD height=0 vAlign=bottom width="14%">$8.14
</TD><TD height=0 vAlign=bottom width="14%">$4.74
</TD><TD height=0 vAlign=bottom width="14%">$2.37
</TD><TD height=0 vAlign=bottom width="14%">$1.08
</TD><TD height=0 vAlign=bottom width="14%">$28.82
</TD></TR></TBODY></TABLE>
You can do $12.50/$121 and see we now win 10.33% of the time. (but lose ICMs in the other prizepool) Compare with above 9.98% by following ICM.
As you follow ICM in all your past present and future decisions in a poker tourney you will not achieve the ICM promised at various points, because you will not be winning often enough.
Like I said, for some reason I thought this would be clear to some people, but I kinda doubt it. Anyway I am not good at explaining things. -
<TABLE class=simple border=1 cellSpacing=2 cellPadding=3><TBODY><TR><TH>Player</TH><TH>Stack</TH><TH>Push%</TH><TH>EQPre</TH><TH>EQPost</TH><TH>EQDiff</TH></TR><TR><TD>UTG</TD><TD>15000.0</TD><TD>24.9%</TD><TD>0.2077</TD><TD>0.2108</TD><TD>0.00313</TD></TR><TR><TD>UTG+1</TD><TD>18000.0</TD><TD>43.3%</TD><TD>0.231</TD><TD>0.2342</TD><TD>0.00322</TD></TR><TR><TD>CO</TD><TD>12000.0</TD><TD>43.9%</TD><TD>0.1803</TD><TD>0.184</TD><TD>0.00378</TD></TR><TR><TD>BU</TD><TD>5750.0</TD><TD>34.2%</TD><TD>0.1036</TD><TD>0.1084</TD><TD>0.00483</TD></TR><TR><TD>SB</TD><TD>10000.0</TD><TD>90.0%</TD><TD>0.1592</TD><TD>0.1564</TD><TD>-0.00278</TD></TR><TR><TD>BB</TD><TD>6750.0</TD><TD><TD>0.1183</TD><TD>0.1061</TD><TD>-0.01218</TD></TR></TBODY></TABLE>
Originally Posted by Cashweekly
f you think about how to equate this to a poker tourney, you might surmise it thinks we have just as good a chance of making chips as anyone else. I am certainly welcome to entertain other theories why this may be so.
Your confusion is in how the EV calculation works and when the pool equity values are real and projected.
Your pool equity is real before the deal on any hand (The EQPre). All the probabilities for possible matchups are summed and the new pool equity (EQPost) and the change (EQDiff) are listed. In pratice it is distributing the blinds and antes into all the hands at a rate dependant on position and stack size.
If you compute a spicific matchup (ie. SB vs. BB) that is a different question and has a different answer.
The formula to compute your EV for a given heads up situation is widely available. Run it to get your EV for the play. Add the EV to your stack pre, subtract it from the villians and recompute your pool equity. As always that will never be the answer you get in pratice, just the long run EV.
Also many times plays can be EV+ for both players so who's side you calculate it for will change the answer you get. -
Your assertion that I am confused about something, confuses me.
Originally Posted by saukendar
<TABLE class=simple border=1 cellSpacing=2 cellPadding=3><TBODY><TR><TH>Player</TH><TH>Stack</TH><TH>Push%</TH><TH>EQPre</TH><TH>EQPost</TH><TH>EQDiff</TH></TR><TR><TD>UTG</TD><TD>15000.0</TD><TD>24.9%</TD><TD>0.2077</TD><TD>0.2108</TD><TD>0.00313</TD></TR><TR><TD>UTG+1</TD><TD>18000.0</TD><TD>43.3%</TD><TD>0.231</TD><TD>0.2342</TD><TD>0.00322</TD></TR><TR><TD>CO</TD><TD>12000.0</TD><TD>43.9%</TD><TD>0.1803</TD><TD>0.184</TD><TD>0.00378</TD></TR><TR><TD>BU</TD><TD>5750.0</TD><TD>34.2%</TD><TD>0.1036</TD><TD>0.1084</TD><TD>0.00483</TD></TR><TR><TD>SB</TD><TD>10000.0</TD><TD>90.0%</TD><TD>0.1592</TD><TD>0.1564</TD><TD>-0.00278</TD></TR><TR><TD>BB</TD><TD>6750.0</TD><TD><TD>0.1183</TD><TD>0.1061</TD><TD>-0.01218</TD></TR></TBODY></TABLE>
Your confusion is in how the EV calculation works and when the pool equity values are real and projected.
Your pool equity is real before the deal on any hand (The EQPre). All the probabilities for possible matchups are summed and the new pool equity (EQPost) and the change (EQDiff) are listed. In pratice it is distributing the blinds and antes into all the hands at a rate dependant on position and stack size.
If you compute a spicific matchup (ie. SB vs. BB) that is a different question and has a different answer.
The formula to compute your EV for a given heads up situation is widely available. Run it to get your EV for the play. Add the EV to your stack pre, subtract it from the villians and recompute your pool equity. As always that will never be the answer you get in pratice, just the long run EV.
Also many times plays can be EV+ for both players so who's side you calculate it for will change the answer you get.
On your charts you missed a row, you need fold, call/win, call/lose with the expected rate for each or you are missing a big part of the picture.
Nowhere am I talking about pre and post equities, as it relates to nash. (don't get me started, you should really think a little more about the things you wrote concerning them)
I am just using the ATC SBpush to illustrate a point. I know it is only a slice of the actual hand.
As far as missing a row, obviously it is all zeros. I suppose it would be easier to follow, but I had mostly given up on this anyways. I doubt I will ever explain things well.
Cheers tho... -
OK too late.
Originally Posted by Cashweekly
Nowhere am I talking about pre and post equities, as it relates to nash. (don't get me started.......
I assume from what you wrote, you realize that a model that could correctly model a poker tournament until its conslusion, would have an equilbrium that was consistant from hand to hand. -
I assume its confusion when you say: "As you follow ICM in all your past present and future decisions in a poker tourney you will not achieve the ICM promised at various points, because you will not be winning often enough."
Thats not what ICM does for you, it never "promises" anything. In general ICM gives you the equity of each player in the total remaining prize pool at the start of a given hand, it also gives opti/max hand ranges for each action for position/stack given blinds, antes and % breakout of the remaining prize pool.
One spicific issue in your charts is you didn't account for all the folds you make when the pot is opened and called before action even gets to the SB. In any case, computing the expectaion for any one matchup to the exclution of all others is a different question and has a differnt answer.
As I said in my original posts "I've never found the pool equity aspects to be of much use except in chop negotiations myself...." -
Ummmmmm....... now you are really confused..... "an equilbrium that was consistant from hand to hand." would require all chance be removed from the game. All probability would be gone and the game would be known from beginning to end.
Originally Posted by Cashweekly
OK too late.
I assume from what you wrote, you realize that a model that could correctly model a poker tournament until its conslusion, would have an equilbrium that was consistant from hand to hand.
The equilbrium is known before the deal on each hand. Then the hand is played and a new equilbrium is established based on the random distribution of cards and the choices made be players.
Shaking you - WAKE UP!!!
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