EV of pushing every hand

[Michael Davis]

Anybody have a guess as to the EV of moving all-in every hand in a one table SNG on Party?

How much of my investment am I losing?

-Michael

[Pitr]

I can't really think of a good reason for want to know this. It's way negative. Probably something like 99.99% against good players who'll wait for hands to punish you with.

Against pp people on, say, an average 5-1 or 10-1? Probably 95%, but it's just a gut instinct from guessing at the chances of you winning the coin toss of having a better hand enough to not bust. I'd say on an average 10-1 table, you've got better than a 50% chance of busting on the first hand, and probably another 20% chance of just stealing that mighty 25 chips.

[Michael Davis]

I am having an argument with a friend about this. I think 95% loss is way too heavy a penalty. Even if you assume I'm a 4-1 underdog every time all the chips go in the middle, which is definitely not going to be the case, I'm still going to triple up one in nine times. (Obviously this is oversimplified, depends on stack counts, etc., but the point still holds.)

-Michael

[AleoMagus]

Yeah, there's no way you'd be -95%. I'd guess more like -50%, but that's a pure guess. I wouldn't be surpised if it was an even better ROI yet, like -30%.

It should be easy to calculate this in an oversimplified way. Something like just assuming that you get called everytime by one player and have a 35% chance of winning each push.

Regards
Brad S

[rachelwxm]

[ QUOTE ]
Yeah, there's no way you'd be -95%. I'd guess more like -50%, but that's a pure guess. I wouldn't be surpised if it was an even better ROI yet, like -30%.

It should be easy to calculate this in an oversimplified way. Something like just assuming that you get called everytime by one player and have a 35% chance of winning each push.

Regards
Brad S

[/ QUOTE ]

My guess is this is pretty bad. Here is my analysis:
you assume you are 35% against calling hands, any two vs. AA is 14%, I estimate if table is tight, it was close to 20%, but we look at your numbers too.

So we assume that we double up x% of time everyhand, neglect blinds since you are not expected to last until level4+, for simplification assume winner takes all, then your winning odds is x^(log(10,2))=x%^3.3.

Plug numbers
x=35% equity 3% ROI -97%
x=20% equity 1% ROI -99%

Just my guess. /images/graemlins/cool.gif

[Delphin]

[ QUOTE ]
Anybody have a guess as to the EV of moving all-in every hand in a one table SNG on Party?

How much of my investment am I losing?

[/ QUOTE ]

Obviously, the answer depends entire on what strategy the table adopts for calling you. Let's assume that no one will call-all in unless they have a top 10% heads up hand (AA, KK, QQ, JJ, TT, 99, Aks, 88, AQs, AJs, AKo, KQs, ATs, AQo, 77, KJs, AJo, KTs, A9s, KQo, ATo).

38.7% of the time you will win the blinds
38.7% of the time you will have exactly one caller
17.2% of the time you will have exactly two callers
04.5% of the time you will have exactly three callers
00.7% of the time you will have exactly four callers
we'll ignore the .2% of the time you have more than that

Your chip EV for every hand is then:

1.5*BB*.387 + (1.5*BB+SS)*A*.387 + (1.5*BB+2*SS)*B*.172 + (1.5*BB+3*ss)*C*.045 + (1.5BB+4SS)*D*.007 - SS*((1-A)*.387+(1-B)*.387+(1-C)*.172+(1-D)*.045)

Where A is the chance your random hand wins against one top 10% hand, B is the chance your random hand wins against two top 10% hands, C win against three top 10% hands, D win against four hands, BB is the big blind (assume small blind is 1/2 and no all-in players are in the blind this hand), and SS is your stack size (assume the other player(s) has you covered stackwise)

Someone with poker stove post estimates of A,B,C,D and I can update this calculation.

Lacking those I'll assume A=33% B=16% C=8% D=4%.
I'll also assume that your stack size is about 50xBB, which is true for Party $5+1 through $30+3.

EV per hand is then around -T400 which means you won't last long. On average you should expect to lose half your stack per hand.

Another way to look at it, is to forget blinds and stack sizes and just calculate your loss probability for an average hand. Using the assumptions above, it is 78.194%. So you will lose 78% of the time you get called given the above assumptions. The good news is that if you win the first one, you can lose the second one and still have your starting stack. The second push is also easier to win because the probabilities of an opponent (or two or more) having a top 10% hand goes down with less players).

Okay so party players in the low buy-ins may call with more than the top 10% hands, especially once they figure out you are going to continue pushing every hand. The result is only going to be slightly affected by that though. The result will be affected to a much greater extent by the number of players and the blind sizes. When I'm at home with access to poker stove, I'll post the EV for short handed high blind situations with real numbers and we can see how good a strategy pushing every hand is in that situation.

I'm curious what the answer to the original question is, but without doing a monte carlo simulation I don't think there is a very easy way to answer it.

I think the answer is somewhere between -99% and -99.9999% ROI for a typical SNG. At most you'll finish ITM about 1:50 times, at worst it's more like 1:10000 times. It depends a lot on how much effect your stack size has since you will double everytime someone calls and you win.

Stay tuned.

[Pokerscott]

[ QUOTE ]
I'm curious what the answer to the original question is, but without doing a monte carlo simulation I don't think there is a very easy way to answer it.



[/ QUOTE ]


The good news is I have a Monte Carlo simulator that can (sort of) answer this question /images/graemlins/smile.gif

Here is the setup:

-10 player SnG
-1 unit buy in with 5/3/2 payout for 1st/2nd/3rd
-Blinds are zero (blinds are a parameter in the simulator, but it is a pain and you get most of the answer assuming they are small relative to the aggressive players stack)
-Aggressive player bets all in
-Only action at table involves the aggressive player (other players are not knocking themselves out, etc)

Key parameter: probability aggressive player wins all in
Key output: Expected payout for every $1 invested given this aggressive strategy

Results:

50% win probability ==> $0.55 for every $1 invested
45% win probability ==> $0.31 for every $1 invested
40% win probability ==> $0.17 for every $1 invested
35% win probability ==> $0.08 for every $1 invested
30% win probability ==> $0.02 for every $1 invested
25% win probability ==> $0.006 for every $1 invested

Pokerscott

[Delphin]

I did a monte carlo simulation assuming the "hero" goes all in every hand and neglecting any blind stealing. The other players only call if their hand is in the top X% of hands. I varied X from 10% (ATo or better) to 100% (call with any 2).

Results:

X ITM%
100% 10%
90% 9.9%
80% 9.4%
70% 8.6%
60% 7.1%
50% 5.1%
40% 2.9%
30% 1.1%
20% 0.2%
10% 0.005%

ITM% is how often you finish in the top 3. The reason it is 10% instead of 30% for the case where everyone always calls is that I didn't account for cases where everyone goes out on the same hand with the same starting # of chips. Who gets 2nd and 3rd in that case (UTG and UTG+1)?

So given a tight table, playing only the top 10% of hands, going all in every hand will only get you to the money 1 in 20000 SNGs. I ran monte carlo simulations for 2.5M SNGs for each of the above examples.

[Pokerscott]

[ QUOTE ]
I did a monte carlo simulation assuming the "hero" goes all in every hand and neglecting any blind stealing. The other players only call if their hand is in the top X% of hands. I varied X from 10% (ATo or better) to 100% (call with any 2).

Results:

X ITM%
100% 10%
90% 9.9%
80% 9.4%
70% 8.6%
60% 7.1%
50% 5.1%
40% 2.9%
30% 1.1%
20% 0.2%
10% 0.005%

ITM% is how often you finish in the top 3. The reason it is 10% instead of 30% for the case where everyone always calls is that I didn't account for cases where everyone goes out on the same hand with the same starting # of chips. Who gets 2nd and 3rd in that case (UTG and UTG+1)?

So given a tight table, playing only the top 10% of hands, going all in every hand will only get you to the money 1 in 20000 SNGs. I ran monte carlo simulations for 2.5M SNGs for each of the above examples.

[/ QUOTE ]


Nifty.

I would redo the simulation assuming something like the best hand calls or the first hand in the top X% called. That way you can reduce it down to head-to-head (much more realistic anyway) and can avoid all the ties.

Pokerscott

[Delphin]

[ QUOTE ]

I would redo the simulation assuming something like the best hand calls or the first hand in the top X% called. That way you can reduce it down to head-to-head (much more realistic anyway) and can avoid all the ties.


[/ QUOTE ]

The ties are insignificant once you get down to calling 50% or below, which are the only interesting situations anyway. I could have modified the hands that the second or later callers would call with, but it's easier to just assume they have the same standards as the first caller.

[AleoMagus]

What can I say... This surprises me.

I think that neglecting blind stealing is lowering the EV significantly, but probably not enough to make my -50% estimate close.

Regards
Brad S