Mathematical Hand Analysis (the EV of pushing 99 from MP)

[A_PLUS]

Ok, I posted earlier about doing a more complete mathematical analysis of a questionable play. I did a quick and dirty version of the analysis. First, I ignored the fact that there would be more than one caller. This will lead to an inflated EV number in my analysis (although not to dramatic, b/c the addition of another hand, even if it is AA-KK, does not eliminate the equity of 99, instead almost halfing the EV of a showdown). Also, I ignored other options (opportunity cost, sorry I'm an Econ grad student).

ANALYSIS

Situation: 110 players remain, 40 places pay. I have 3200 TCs, average is 4400. Blinds 100/200. I am sitting in MP with 5 players yet to act behind me (including the blinds).
Everyone is comfortably stacked, ranging from 2600-5500. Play has been fairly tight, but not overly so.

Calculations
Two possible outcomes, I get called, or I win the blinds
I give my opponents the calling range of AA-77, AK-AJ


% of time called =
Total number of hand combinations remaining after removing 99 = c(50,2)=1225

The number of hand combinations that my opponents will call with = (7*6)[PP other than 99] + (16*3)[AK-AJ] + 1[99] = 91

This next part is not exact, and may very well be dead wrong

1225 total hand possibilities, 5 random hands = c(1225,5)=
22 trillion and change

1134 total hand possibilities that will not call (1225-91), 5 random hands = c(1134,5) = 15 trillion and change

So c(1134,5) / c(1225,5) = .6794

67.94% chance of stealing the blinds

So....

Steal the Blinds 300
% of time 0.679359427
subtotal 203.8078281

Showdown pot 6550
equity vs range 0.463
EV of showdown -167.35
% of time 0.320640573
subtotal -53.65919987

TOTAL EV 150.1486283

Now assuming that CEV = $EV, does anyone see a problem with my calculations? I am a little worried about how I handled the % of times that I will steal the blinds. For instance, someone will fold A7, but that will affect the number of Aces available for hands like AK that will call.

[A_PLUS]

shameless bump

[durron597]

[ QUOTE ]
For instance, someone will fold A7, but that will affect the number of Aces available for hands like AK that will call.

[/ QUOTE ]

No it doesn't. Other players folded hands are treated as if they were part of the original card pool. If they weren't, poker math would get ridiculously complex very quickly. And since doing it that way is really not far off, don't worry about it.

[Luke]

I actually created a spreadsheet that I use to run analysis like this. I plugged in your numbers and got a slightly EV: +$167.

One difference is how I calculate the chances of winning the blinds. I look at each individual player's chances of picking up a calling hand (evaluate hand combos) and take into account the number of players there are: ((1-7.92%)^5) = 66.2%)

I think your method might inflate this number slightly because it doesn't isolate each opponent's chances of calling. But even still, you number is higher here which should increase your EV, yet my EV for you is still greater.

The other input that might be different is the value we are getting from PokerStove. I'm getting a winning % for 99 of 46.35%. If this number were slightly changed, your EV could move quite a bit (around 46%, the effect is roughly $22 of EV for every 1% change in winning %).

Once last thing I noticed is that your pot size is 6,550. How did you get that number? Your chips are 3,200 and the blinds are 300 so (3,200 + 3,200 + 300 = 6,700).

Did you take an average of the 5 stacks (with larger ones only counting as 3,200) and add that number to 3,200 and 300? I think this is actually a good idea but I didn't have that info so I just plugged in 3,200.

Luke

[A_PLUS]

[ QUOTE ]
I actually created a spreadsheet

[/ QUOTE ]
Same here, PM me and I'll email you mine.

[ QUOTE ]
((1-7.92%)^5) = 66.2%)

[/ QUOTE ]
I think my method may be slightly more accurate here, but Im not sure. Mine represents al possible 2 hand combos dealt to five players, and shows the % of these 5 player sets that do not contain a hand in the calling range.



[ QUOTE ]
I'm getting a winning % for 99 of 46.35%

[/ QUOTE ]
I used 46.3%

[ QUOTE ]
your pot size is 6,550. How did you get that number?

[/ QUOTE ]

I just doubled my stack, and took 1/2 of the blinds. I did this to approximate the change in pot size if the caller was one of the blinds, vs the button, etc. There are much more exact ways to do it, probably pretty easy too, I will add that in my next run.

As for the changing pot size for smaller stacks calling, I dont think it is really necesary. If the goal of this analysis is to decide wether to push, EV will always be higher if you are only going to be called by a small stack.

The % of times stealing blinds shouldnt change, but the negative showdown equity will be less. This obviously wont matter when you are a favorite, b/c you want as much money in as possible.

[AlwaysWrong]

I think your call range is too large. AA-TT, AK, AQ seems more reasonable. You're pushing more than 10x the BB.. getting called by 77 seems a little far-fetched.

You're also at a spot in the tournament where $EV starts to deviate significantly from chip EV, so that assumption seems poor. I'd reccomend just using the ICM (independant chip model) here.

BTW, I don't think this is a questionable play, I think it is a bad play. Even if it turns out to be slightly +EV it is a bad play, as other plays will be more +EV.

[A_PLUS]

[ QUOTE ]
I think your call range is too large. AA-TT, AK, AQ seems more reasonable.

[/ QUOTE ]

Very possible. This was based on my table image. I had been working my way back from a short stack for a few orbits and had open pushed a few times.

[ QUOTE ]
You're also at a spot in the tournament where $EV starts to deviate significantly from chip EV, so that assumption seems poor. I'd reccomend just using the ICM (independant chip model) here.

[/ QUOTE ]

Can you explain why you think CEV and $EV deviate so much here? Also, there is a ICM for 110 players? I was under the impression this was a final table tool.

[ QUOTE ]
Even if it turns out to be slightly +EV it is a bad play, as other plays will be more +EV.

[/ QUOTE ]

I addressed that in my post. I was ignoring other possibilities and seeing if this play was + or - EV.
Also, Im not sure I am crazy about making a standard raise and playing 99 out of position either.

I appreciate criticismm, so please expand on your points so I can understand your point of view.

[AlwaysWrong]

ICM is used mostly for SNGs / final tables. But there's no fundamental reason for this. There isn't a tool that I know of that lets you input arbitrary numbers of people and arbitrary prize structures, so I guess if you actually want to use ICM you'd have to write it.

When you're very far from the money chip EV is close to $EV. At the beginning of a tournament 10% of the people will get paid, and most of that goes to the top 5 spots. If you're in a tournament that only pays one spot, chip EV always = $EV. Very far from the money it's fairly obvious that the assumption that the two are equal is a good one. Conversely, this assumption breaks down the most late in the tournament when you're close to the money (on the bubble eg) or close to a pay jump.

Your tournament is like a tournament that pays 36% of the seats. This is more than gets paid in a SNG. If you want to just get a really rough idea, doubling up on the first hand of a SNG only gets you to 1.84x your original $EV. If you assumed you were getting to 2x you'd be making a significant error - one big enough that you wouldn't want to trust your results it was at all close.

This is super-rough, as it doesn't take into account people "starting" the tournament with different stack sizes or prize structure, or anything, but it's an illustration of how far wrong the CEV=$EV assumption could be.

As to table image, I think good players tend to overestimate their opponents' adjustments. Unless you've been pushing A TON so that it's completely obvious that you're often pushing on trash, people will be overly cautious in dealing with you. Since your stack is pretty decent now, someone with 77 just can't be too excited about gambling. Even if you're raising light they're probably not that much of a favorite.


If you make a standard raise here, most of the time you'll also steal the blinds, and most of the time you fail you'll be heads-up with the big blind. Playing out of position shouldn't be too big of a concern, imo.

[sdplayerb]

it is positive EV.
but that doesn't mean it is the best course of action.
I would much prefer doing a standard raise here.

[A_PLUS]

I know what the ICm is, and the logic behind it. I think the leap you made is probably wrong, or at least needs to be explained.

You can not treat a MTT with 110 people left 40 paying the same as an with 11 people and 4 paying.
Firstly, b/c the '4 places' pay at least 14 different payouts in a MTT. Also b/c if it works for 110 people, where do you draw the line and why?

This is not a bubble situation. Please explain why you think CEV varies from $EV here. I can not say it doesnt, but I am leaning that way until someone can explain why it doesnt.


Again, very possible that I overestimated range, I agree.

Question for you:

If I will 'most likely' be called by the big blind with a standard raise, creating a 6.5xBB pot. 50% of my stack, and I am giving him 3 cards to beat my hand. Deeper, this is how I play it, I just dont know if I love it with these stacks