Sit 'n Go Strategy study group -- Part I: Low Blind Play

[Slim Pickens]

What you've done looks pretty good so far. You must have filled in some other stacks to do the equity calculations, which is exactly what you have to do. The context is pretty clear that the other stacks should be close to t2000 and mostly even, with t18,000 total on the table. Using the convention in the book (?) the small blind has already been pulled out of your stack, so your actual stack is t1970 before posting. You always have to add the blinds back in, but not the antes. Good thing I'm a huge nit. The SB thing and maybe filling in the other stacks slightly differently accounts for the tiny difference between your numbers and mine.

(The ICM macro seems to be accurate to a fixed number of decimal places, rather than a certain fraction of the prize pool. I used $50/$30/$20 as my payouts instead of 0.5/0.3/0.2 to get around this.)



Let's start by looking at the exact scenario presented in the book. Your choice is between pushing and getting called by 66 or folding. For the option of folding, I like your assumption that MP1 bets the flop and everyone folds. It's not perfect, but it makes the solution much simpler. Also, it happens to give a nice lower bound for your prize pool equity, since in a qualitative sense large disparities in stack size improve the prize pool equities of those in the middle relative to more even stacks. The effect wouldn't be that big anyway, so I feel fine ignoring it and taking a probable lower bound. My number is $EV_fold=$10.83.

If you push and he calls 100% with 66, he is a 54.6/45.4 favorite. This gives your prize pool equity if you push as:

$EV_push = 0.546*(0) + 0.454*(21.82) = $9.91
assuming he always has 66 and he always calls with it

This, as you also showed, is a demonstration that under those exact conditions, folding is better than pushing. That doesn't really fit with our "poker instinct," nor Collin's conclusion on the hand, nor would any decent poker player ever recommend folding there. The reason is sometimes he has a different hand, and sometimes he folds to your push. So how to account for this? We need some hand ranges. Here are the next steps.

<ul type="square">[*] For simplicity, assume every other player other than MP1 always folds.[*] Decide on an open-raising range for MP1.[*] Decide on a push-calling range for MP1.[*] Use an ICM calculator to determine your prize pool equity if MP1 folds.[*] From those two ranges and the basic probabilities of being dealt certain hands, figure out how often he calls your all-in raise and how often you win the pot uncontested. Hint: SNGPT can shortcut this step for you, although it can't do the actual calculation without some twisting.[*] Using a tool like PokerStove or the ProPokerTools Simulator, determine how often you win with AKo against his push-calling hand range.[/list]

[mcpst17]

Pre -Hand
UTG 2000 11.12 Fold
UTG+1 2000 11.12 Fold
MP1 2200 12.10 raise t200
MP2 2000 11.12 Fold
MP3 1970 10.97 Fold
CO 2100 11.61 Fold
Button 1760 9.900 Fold
Hero 1970 10.97 Push
BB 2000 11.12 Fold
Total 18000 100.00


MP1 Folds to Hero Push
utg 2000 11.12
UTG+1 2000 11.12
MP1 2000 11.12
MP2 2000 11.12
MP3 1970 10.97
CO 2100 11.61
Button 1760 9.90
Hero 2230 12.25
BB 1940 10.81
Total 18000 100.00

MP1 Call Hero Push
utg 2000 11.36
UTG+1 2000 11.36
MP1 230 1.42
MP2 2000 11.36
MP3 1970 11.21
CO 2100 11.87
Button 1760 10.12
Hero 4000 20.24
BB 1940 11.06
Total 18000 100.00


Percentage of hands MP1 Range
0.107 Raise Pre 22+,ATs+,KTs+,QTs+,JTs,AQo+
0.083 Call Push 22+,AQs+,AQo+
0.024 Fold to Push


Ok so it appears MP1 will fold to the hero’s push .224 (.024/.107) and call the push .776 (.083/.107) of the time based on the ranges I chose. I ran the ranges though poker stove and used the equity calcs of win = .47338 and lose .52662 (Hero’s AKo vs MP1 call push ranges)

Fold = .224 (12.25) = $2.75
Call Win = .776 (.47338) (20.27) = $7.43
Call Lose = .776 (.52662) (0) = $0.00
Total = $2.75+$7.43+$0 = $10.18

So this seems to be a bit closer to the $10.80 if the Hero Folds to MP1 raise, but I still do not see a clear push in this example so I reran the numbers adding in the two calls from the CO and button which added t400 to the pot. I assumed that they would both fold to the Hero’s push and used the same hand ranges in the example above.

Fold = .224 (14.16) = $3.18
Call Win = .776 (.47338) ( 21.82) = $8.01
Call Lose = .776 (.52662) (0) = $0.00
Total = $3.18+$8.01+$0 = $11.19

This appears to give a better answer. It appears that without the dead money, assuming the hand ranges I picked, folding looks like the better play. But again I may be too tight in the hand ranges I picked or I just messed up the calcs. Thanks again Slim for going through these examples with me. I think once I have this down I will be able to work though most other ICM calcs.

I am sorry for the formatting but I could not paste excel or take a screen shot and paste it into the post.

[Slim Pickens]

[ QUOTE ]
Percentage of hands MP1 Range
0.107 Raise Pre 22+,ATs+,KTs+,QTs+,JTs,AQo+
0.083 Call Push 22+,AQs+,AQo+
0.024 Fold to Push

[/ QUOTE ]

You seem to have the procedure down, so now we can get to the real heart of this problem, which is the hand ranges. Pretty much all of the discussions on this board are really about hand ranges whether people know it or not.

I thing the ranges are more like this:

Initial raise: 22+,A9s+,KJs+,QJs,ATo+,KJo+ (12.1%)
Call a push: 66+,AJs+,AQo+,KQs,KJo (6.86%)

As a note, the idea of people having "absolute" ranges like that isn't as rigid as it might look. I'm having him raise with all pocket pairs, but fold 22-55. That doesn't mean he always has to do exactly that. Let's say he always calls with TT+, but folds 22-99 (taken as a whole) half the time. That's saying maybe he always folds exactly 22-55 and calls 100% with exactly 66-99. It could also be saying that he calls with 22-99 50% of the time, depending on wind direction at the time of his raise. Since all of those hands have about the same pot equity against AKo, it doesn't change the calculation much to use ranges like that to factor in "he folds a mid/low pocket pair about half the time" without having to know exactly what fraction of the time he calls with each hand. You'll never have that strong a read on a player anyway.

I've done the same sort of thing by throwing "KJo" into his calling range. That means I think he's calling with dominated unpaired hands at a frequency something like the fraction of dominated unpaired big-card hands from his raising range that are in his calling range.

[mcpst17]

Good points for me to consider in my next calcs. In doing these calculations I can see why the heart of the most problems are the hand ranges. Thx, looking forward to part II.

[mcpst17]

When does discussion on part II start?

[xPeru]

First time I've ever done this ... bump!

Nice work Slim.

[Slim Pickens]

[ QUOTE ]
First time I've ever done this ... bump!

Nice work Slim.

[/ QUOTE ]

Can you (or anyone) post a start-to-finish summary of their work on Hand 1-4? Part II should start Sept 1 or so.

[Slim Pickens]

As a general comment, the next two parts of the book are more of this analysis, so make sure these calculations make some sense. Part 2 is usually a lot more complicated. Part 3 will be much simpler.

[tangerine]

I have not buy the book yet, but trying to work out example 1-4 using details provided by Slim.

blinds 30/60
Case 1 (Hero folds)
MP1 raise t200, Hero folds, Co and Button call
(*Using Slim's assumption, MP1 bet flop all folds)
Hero $equity 10.8%

Case 2 (Hero pushes and everyone fold)
Hero $equity 14.2%

Case 3 (Hero pushes, MP1 call but CO and button fold, and WIN)
(Assume CO and Button will never overcall, or they will call if MP1 fold)
Hero $equity 21.8%

Case 4 (Hero pushes, get called, and lose)
Hero $equity 0%

Using Slim's range
Initial raise: 22+,A9s+,KJs+,QJs,ATo+,KJo+ (12.1%)
Call a push: 66+,AJs+,AQo+,KQs,KJo (6.86%)

So MP1 will call (6.86/12.1*100) 56.7% of the time and fold 43.4 of the time.

PokerStove
equity

49.482% { AKo }

50.518% { 66+, AJs+, KQs, AQo+ }

$Equity when Hero pushes
(0.434*0.142)+(0.567*0.4948*0.218)+0=12%

Since Hero $equity when he/she pushes is higher than when he/she fold
so Push is a better option?

Slim, may I know where could I find the spreadsheet with ICM functions that you mentioned in this post earlier?

*Could you send to me as well?

Thanks

[Slim Pickens]

tangerine,

[img]/images/graemlins/smile.gif[/img]

Slim

PS: Anyone wanting the Excel file with the ICM macro in it PM me an email address.