Low buy-in folding equity

[AJay]

[ QUOTE ]
Meh...this seems pretty random.

All this probabilities your are assigning, where are they coming from? This is where you need to discuss hand ranges.

Also, your assumption that when you limp it folds around the BB is terrible. Once you limp, it makes it much more likely that more will limp and the sb will complete.

These calculations are tough to discect and comment on because there is no explaining for all your probabilities.

I just don't see how you can do these calculations without putting people on hand ranges, figuring out the odds of them hitting a flop, odds of you hitting the flop, odds that you have them beat when you both hit the flop, etc...

[/ QUOTE ]

My apologies. Somewhere above I thought I had discussed hand ranges, but regardless, I should have spelled it out.

At a low buy in, people will call pushes with a lot. That's the point of my original post. For this example, I was assuming that someone would call with Ax, any pair, and any two face cards.

I just realized, however, that I forgot to confirm that those hands would show up 1/3rd of the time. According to Poker Stove, the chances of someone getting that card range is 27.6%. At a table with 3 other people, the chances of someone NOT getting one of those hands is close to 1 in 3, so I think that part of the numbers is still valid.

I had then put AK vs the above hand range into Poker Stove. Pre-flop, I'm a 3:2 favorite. Post flop, if an A or K falls, I'm a 3:1 favorite. And A or K will hit the flop 1 out of 3 times. That's the support for most of those numbers.

Then it's just a matter of a) pointing out something I missed and/or b) debating the likelihood of someone folding/calling/raising.

[AliasMrJones]

You're going to have to spell out what all those fractions are supposed to represent. So - put the calling ranges for villain(s) on there. And, yes you need to assume that SB is going to complete a lot of the time. Label what the heck all those fractions are supposed to be, put it all together and then let's talk.

[AJay]

Thanks for the feedback everyone. Sorry for the confusions / lack of clarity on my part.

As for the fractions, I tried to put them in the exact same order as the descriptions on the left, so on the line where I have:

Limp/No Re-raise/Hit/Push/He Folds

I have:

(2/3) x (1/3) x (2/3) x 150

Since my limping / pushing is my choice and not a probability, those values are always 100%. So the probabilities right above would apply as follows:

2/3rds of the time, no re-raise when I limp in
1/3 of the time I hit the flop
2/3rds of the time, my opponent folds when I push on the flop

And of course, the 150 is the SB+BB.

I realize the SB will complete often, but I was trying to make the math simple. It's not intuitively clear to me how that will affect the results (though I would tend to think it would "de-value" limping admittedly...and I know I could do the math, but then, it seems, there's just too many assumptions.)

As for the villian calling ranges, do I need to add anything other than that I think my opponents at these low levels would call a push with Ax, any pair, any broadway?

[DevinLake]

Ok, I'm starting to get the little spreadsheet a little better. However, without putting it all together there seems to be some very fundamental errors.

Lets use the scenario where you Limp/Get re-raises/push/ :

What I'm taking from this spreadsheet and your last post is that he's re-raising you with 33% of hands, hence 1/3.

Of the 1/3 he re-raises you, you push 1/2 the time.

Three things can happen when you push.
1) He fold
2) He calls and you win
3) He calls and you lose.

Therefore, when we talk about the 1/3 re-raise - 1/2 re-push scenario, the probilities of 1,2 and 3 must be equal to 1.

However, you your spreadsheet you have:
1) 1
2)3/4
3)1/4

This equals 2. So, I'll make the assumption if you made this error here, you did with all other scenarios.

[AJay]

[ QUOTE ]
Ok, I'm starting to get the little spreadsheet a little better. However, without putting it all together there seems to be some very fundamental errors.

Lets use the scenario where you Limp/Get re-raises/push/ :

What I'm taking from this spreadsheet and your last post is that he's re-raising you with 33% of hands, hence 1/3.

Of the 1/3 he re-raises you, you push 1/2 the time.

Three things can happen when you push.
1) He fold
2) He calls and you win
3) He calls and you lose.

Therefore, when we talk about the 1/3 re-raise - 1/2 re-push scenario, the probilities of 1,2 and 3 must be equal to 1.

However, you your spreadsheet you have:
1) 1
2)3/4
3)1/4

This equals 2. So, I'll make the assumption if you made this error here, you did with all other scenarios.

[/ QUOTE ]

No, for that line I'm saying I'll get re-raised 1/3rd of the time. When I push, he will call 1/2 of the time (I bumped up the calling range since he had re-raised pre-flop). The other half he won't. 1/2 + 1/2 = 1.

The 3/4 and 1/4 is for GIVEN that I have been called, I win or lose. 3/4 + 1/4 = 1.

To use your listing:
1) 1/2 = he folds
2) 1/2 * 3/4 = he calls, I win
3) 1/2 * 1/4 = he calls, I lose

That adds up to 1.

[AJay]

...furthermore, I would argue that one of the key components of the above calculations is putting the likelihood of being called pre-flop vs. post-flop at close to equal.

If I tweak the other numbers in the calculations (the ones that are flexible, i.e., changing the likelihood of being called when I bet on the flop after missing and being checked to), I would be surprised to see large swings in the values. I'm pretty sure I could come up with some assumptions that swung things in favor of pushing, but I think it would take some drastic changes in most of the assumptions to generate a large lead for pushing.

Of course, I understand that cEV isn't the same as $EV. As for how that affects this argument...well, I don't understand THAT well.

[DevinLake]

[ QUOTE ]
No, for that line I'm saying I'll get re-raised 1/3rd of the time. When I push, he will call 1/2 of the time (I bumped up the calling range since he had re-raised pre-flop). The other half he won't. 1/2 + 1/2 = 1.

The 3/4 and 1/4 is for GIVEN that I have been called, I win or lose. 3/4 + 1/4 = 1.

To use your listing:
1) 1/2 = he folds
2) 1/2 * 3/4 = he calls, I win
3) 1/2 * 1/4 = he calls, I lose

That adds up to 1.

[/ QUOTE ]

Ok, that makes sense then. However, if he's re-raising you with 33% and calling your push 1/2 the time, that means he is calling with 16.5% of hands. You are not 75% (3/4) to win against that range.

According to poker stove:

equity (%) win (%) tie (%)
Hand 1: 61.3780 % 58.05% 03.32% { AKs, AKo }
Hand 2: 38.6220 % 35.30% 03.32% { 66+, A7s+, A5s, K9s+, Q9s+, JTs, ATo+, KTo+, QJo }

[AJay]

[ QUOTE ]
Ok, that makes sense then. However, if he's re-raising you with 33% and calling your push 1/2 the time, that means he is calling with 16.5% of hands. You are not 75% (3/4) to win against that range.

According to poker stove:

equity (%) win (%) tie (%)
Hand 1: 61.3780 % 58.05% 03.32% { AKs, AKo }
Hand 2: 38.6220 % 35.30% 03.32% { 66+, A7s+, A5s, K9s+, Q9s+, JTs, ATo+, KTo+, QJo }

[/ QUOTE ]

I'm planning on trying to tweak the spreadsheet some and see how sensitive it is to changes in assumptions....and I'll try to factor winning %s in too. It will take a little time, however...not to mention the supper / putting kids to bed / SNG to be done between now and then :-)

Meanwhile, thanks for the replies all.

[DevinLake]

Now, another question I have for you is related your your no re-raise/hit/push scenarios.

I would really like to see how you arrived at those numbers. I understand you are saying that you are hitting the flop 1/3 of the time and hence, BB is as well.

You're also making the assumption that he's calling every time he hits the flop, is this reasonable? Also, when he does call your a 75% favourite? Seems high to me.

[AliasMrJones]

The other thing to tweak is stack sizes and blinds. Most people go push fold at about 10xBB. The calucations are very sensitive to benefit/risk. The blinds are the benefit and going broke when you lost is the risk. The higher the blinds, the higher the benefit/risk ratio and hence the better the argument for pushing vs. limping.