The old coin-flip debate

[PrayingMantis]

I reread recenly this interesting thread by Aleo ( A bad way to play on the bubble ), and had some new thoughts.

I want to specifically adress this paragraph (and calculation):

[ QUOTE ]
If I take a coinflip, I have a 50% chance of busting and a 50% chance of being the big stack with three left.

So I have 50% chance of $0
and a 50% chance getting into the final 3 with about 4000 to 2000 to 2000

this should mean 1st 50% of the time I survive- $25 equity (10+1)
2nd 25% of the time - $7.5 equity (10+1)
3rd 25% of the time - $5 equity (10+1)

so all together this means .5(0)+.25(50)+.125(30)+.125(20)
or, $18.75 equity

BUT...

if I avoid confrontation when I know it's gonna mean a showdown I have the same equity (slightly less if I'm in the blind) as before. This is

1st 25% of the time - $12.5 equity
2nd 25% of the time - $7.5 equity
3rd 25% of the time - $5 equity
4th 25% of the time - $0

so all together this means .25(0)+.25(50)+.25(30)+.25(20)
or, $25 equity


[/ QUOTE ]

The point of Aleo here is, that getting into coin-flip situations on the bubble, with equal stacks and equal ability, is -$EV, since by folding you remain in a +$25 EV position, and taking the coin-flip reduces your EV to +$18.75.

However, according to this reasoning and evaluation, taking a 7:3 showdown, is only marginally +$EV:

Taking it:

0.7*37.5 (your overall portion of the prize pool, according to the same calculation, when stacks are 2x,x,x) = $26.25

Avoiding it: $25.

And of course, any situation where it's 66:33, is neutral in terms of $EV (about 0 $EV), for instance: AQ vs. KJ.

I believe that part of the problem is in the assumption of having "only" $37.5 EV, once in the money, with stacks at 2x,x,x.

I would suggest it's in the vicinity of $40, for a strong player (I'd hope someone who's very familiar with these calculations, like Bozeman, will help here), and on the other hand - a player that is constantly avoinding confrontation once it's 4 handed with equal stacks (I assume pretty massive blinds, of course), as suggested in the original post, has probably less than 25% of the prize pool as an approximate EV, especially if he's dealing with loose-aggressive players.

Any thoughts?

Edit: all the $EV numbers are calculated for a $10 SNG, but that's only for the sake of convinience, of course.

[stupidsucker]

These equations baffel me a little, but I understand them enough to get the jist of what you are saying. Forgive me for asking a stupid question, but how do you know its a "coinflip" without seeing the cards.

My calling hands are of a higher standard then my pushing cards. If I push I dont know if I am getting called. If I call then I know its going to be a race, but I have no idea what the % chance is. I may be on either side of a domination.

Please understand that I am not trying to belittle the thread. I really want to understand what you mean.

[PrayingMantis]

You can never *know* of course, if it's a coin-flip, until you see the other-opponent's cards (whether you called, or he called your push). But against most opponents, you might have a strong enough "feel" of their pushing (raising) and calling standards, and have a pretty good guess of where you would "normally" stand.

Aleo is saying, for instance (he would say it better than me, and I hope he'll reply in this thread), that calling all-in on the bubble, with equal stacks, when you hold 99, is a wrong move, because most of the time you'll be in a coin flip situation (i.e, against over-cards), or worse: bigger pair (However, since it's short handed, and high blinds, you can not put your opponents on big pair every time they push, and it's much more probable they are on over-cards. Hence, coin-flip). Calling with 99, according to some assumptions, is -$EV. You're losing money, despite the fact you're probably getting the right, if not good, pot-odds.

Now comes the more subtle point of what is your read on the raiser "looseness". With what Ax will he push? Will he push with any A? any pair? etc. If he will, many times you'll be in a far better than coin flip - 7:3 or much better. Does it worth the call? Do you still consider it as a coin-flip in normal circumstances? is it +$EV? Marginally +$EV? Auto-call? That was the point of my post (or some of it). I hope this is more clear.

[AleoMagus]

Hi PM

For anyone who hasn't seen that thread, it is here

I was toying with those ideas when I first posted this and I think it is important to read Phil Van Sexton's criticism, which I think is valid.

Still, The idea of calling equal stack ALL-IN raises on the bubble with equal stacks still seems like a horrible move to me. As I said in that original post, I wouldn't even do it if I knew myself to be slightly ahead.

What troubles me about the reasoning though is the thought that in some way, we hurt our chances of making the money when we start to play too timidly and it is hard to know where to draw the line between what hurts us most, especially on an agressive bubble where your blinds are constantly being challenged.

The implications of my original argument, if correct, run both ways after all. We should be raising a lot on the bubble, and maybe even all-in against good players, because there is very little they can actually call with that makes the move correct for them, even if they are ahead. In a really strong game this might mean players going all-in almost any chance they can be the first in the pot until one player finally gets a big pair and can call down the raiser.

In that original thread I never did get any responses from math types about my reasoning and I too, would love to see some.

I'm gonna write more about this, I promise

Regards
Brad S

edit - In re-reading your post, I think you may be touching on at least Part of where this reasoning might be flawed. Having 2x,x,x stacks may give you greater $EV than my assumption, but I am also not an expert on those approximations. That combined with the potential -$EV implications of playing too timidly on the bubble almost certainly lessens my original argument. To what degree remains to be seen.

[PrayingMantis]

[ QUOTE ]
Still, The idea of calling equal stack ALL-IN raises on the bubble with equal stacks still seems like a horrible move to me. As I said in that original post, I wouldn't even do it if I knew myself to be slightly ahead.

[/ QUOTE ]

How much is "slightly ahead"? That is the main problem here. I think that in this forum there is a big tendency to see everything in terms of aggression and folding equity (I do it many times myself). However, It seems that by not calling (all-ins, that is), consistently, when there's a good possibility you're around, say, 2:1 favorite, is giving the aggressor in that spot a very big advantage (I'm talking high blinds of course), and in these last stages of a tourney, that can be significantly -$EV for you.

Of course the gap still applies: you can raise with a much wider range of hands, but against certain strong opponents, especially in the higher buy-ins, big calls are a dangarous weapon too. The higher the blinds, the narrower the gap. Part of what you achieve (if you manage to survive) is tightening your opponents, which is also +$EV for you. I know many in this forum won't accept it, but your opponents might actually *fear* your calls.

[AleoMagus]

For me, slighltly ahead usually means small to medium pocket pairs. These hands will really only be behind against a bigger pair and as you have stated, you can't always be scared of that.

I have softened somewhat on hands like TT and JJ because that I think so many opponents will push with Ax on the button or even K7+. The possible addition of a small card makes hands like TT (and maybe even 99) better than perhaps I have first suggested.

88 or smaller pairs are trouble though and I think still are better folded in the situations we are discussing. I'm actually still folding 99-TT to big raises on the bubble and I like my bubble stats of late. I'm sure this is relative to opposition and may be different at higher or lower limits. I am playing mostly Party 30+3 these days with a few 50+5 thrown in to the mix. If I think a player begins repeatedly going after my blinds, I will lessen these requirements. If he lets me keep my blind a lot of the time, I'll be happy to give him the occasional one even if I do have 99.

Slightly ahead may also mean hands like AT or smaller aces if you think an opponent will push with any two cards over 9 or even with Kx. I'd never call an all in raise from a big (equal) stack with even AJ in these situations unless I knew a player was continuously gunning for my blinds and I needed to make a stand. Most times, if I can leave myself with 3-4 BB after a loss, I will call with more. Another problem with medium aces is that so often you will be dominated if you guess wrong.

As for opponents fearing calls, the problem is that if you survive, that opponent is eliminated or crippled and his fear is no longer very important. I just don't give credit to players for actually paying attention to what happens to other people. I definitely think players pay attention when they are in a hand, but not much otherwise. If I want fear or need to slow a guy down, I think re-raises all-in are still ideal. That's pretty obvious I guess.

Regards
Brad S

[stupidsucker]

Ok so correct me if I am wrong..

This pretains to calling only.

With hands like medium pairs where you are probably a coinflip with overcards. Or other situations where its probably a flip, like K9s or JQ.

I guess I agree for the most part, and the most important factor to me is stack size.(You did mention it was equal stacks) I would have a hard time laying down 99 when pushed against from the button or SB.(If I am BB) I already Have BB invested, and I know I personaly will push with a lot of hands on the bubble into an equal stack. Perhaps my standards for pushing are way to low. I guess if I feel I am up against a moron or a good player I have to call with 99. Because in either case they could have almost anything and I feel I am ahead enough to warrent the call. If the pusher seems passive and tight then I am more inclined to lay it down, but probably still wont.

I am curious what is the proper move, and thanks for the good post.

[Pitcher]

Hi Brad,

[ QUOTE ]
I have softened somewhat on hands like TT and JJ because that I think so many opponents will push with Ax on the button or even K7+. The possible addition of a small card makes hands like TT (and maybe even 99) better than perhaps I have first suggested.

[/ QUOTE ]

Bingo Brad,

At the higher buyins (200's) this is a borderline auto-call in some games because many very good players will push with Ax or K-7-8. You just can't give hands like 99-TT up in these situations, especially when the blinds are large. Plus, players pickup on the fact that you won't defend immediately and challenge you even more. I also almost always call with AJ (amazing how often this is dominant) and AQ-AK are near autocalls. Of course, some of this is read dependent (I know of one player who will only push with PP's 88 or above or AK, AQ. Of course, I won't call this player with overs in that situation. I would like to be on the "good side" of the flip...the guy with the 11-9 edge), but these are pretty standard for me at these levels. I like my bubble results but want just a few more 1sts [img]/images/graemlins/smile.gif[/img]

Pitcher

[BradleyT]

I never fold 99-TT on the bubble when they come up.

You don't get push hands often enough on the bubble to wait for a stronger hand than 99 or TT. And the fact that you're only behind 4-5 hands (higher pairs) makes it even more reason to push with these hands.

[AleoMagus]

Yeah, we are talking about calling here only. 99 or TT is definitely a raise and probably a push if the blinds are big enough. these hands are often even re-raise pushes if you think an opponent might still be re-stolen from.

It is the fact that you are guaranteed a showdown that makes a all-in call so undesirable, even if you think you might be ahead.

As stated by many, folding 99-TT to all pushes might be too timid a play. There are times for calling, and many will always call (successful players).

Just one example I can think of where I think it is bad might be:

4-handed with all stacks at ~2000.
blinds are still only 100/200

you are in the BB and the SB (who has slightly more) pushes against you.

For me, I definitley fold 88 or smaller and unless it is a weak raiser who I know has been gunning for my blinds, I probably fold even 99 and TT.

basically what it comes down to is the thought that I am about 75% (more actually) to make the money when I find myself equal stacked in the final 4. If I suspect I will be facing two overcards, why would I want to take 50% odds on my survival here.

Yes, doubling up here increases the chance of a win, but that is what the calculation PM is speaking of addresses. I attempt to show that the $EV of folding is still greater than calling. As yet, no math gurus have commented (that I know of).

Regards
Brad S