The old coin-flip debate

[Jsb]

in your calculations you came out with that Hero had a 55% chance of getting first, a 22.5% chance of second, and a 22.5% chance of third. i think Phil was talking about those percentages in particular. i don't know how to do most of this statistics stuff yet, but it seems against my intuition for hero to have an equal chance of catching second and third. In this case that one of the lesser players gets first, you say that Hero has an equal chance of getting either second or third, but my instinct is that he has a greater chance of getting second than third. my instinct could very well be wrong, it just strikes me as kind of odd. and i think that was what phil was saying as well.

[Phil Van Sexton]

We have already calculated that 50% of the time, one of the shortstacks will win.

In this case, you will be playing against the other shortstack for 2nd. Think of this as a 2 player tournament where the winner gets $30 and the loser gets $20. We know that your chance of winning a tournament is equal to your chip count, so the calculation is simple....4000/6000=66.67%.

Since we are only talking about the 50% of the time that you don't get first, you're chance of getting 2nd is 66.67% * 50% = 33.33%

The calculation is easy because the shortstacks both have the same amount. If they didn't, you'd have to do this calculation for each player and do a weighted average. This will get much messier for more than 3 players, but likely doable with a computer.

[PrayingMantis]

I completely understand the model AM has used in his calculation, and I'm familiar with Sklansky's statements in TPFAP. However, as other posters have stated here, and combined with other reasons, it seems to me as it's lacking in some respects. I don't have a better model (I know Bozeman has worked on simulating similar problems), and AM also admitted that his calculation is not perfect, but I can suggest a few different variables that can be added here:

1. (as was already said), It doesn't look reasonable that big-stack has the same probability for finishing 2nd as 3rd (with stacks at 2x,x,x). This has to do with the $EV of getting into the money as the big-stack.

2. In the title here I wrote "coin-flip", but I'm actually more interested in situation where hero is, say, 2:1, against someone who pushes against him (this has implications for coin-flips too, of course). According to the original model here, calling is only marginally +$EV. However, it seems that if hero is consistently avoiding 2:1 confrontations (over whatever long-run), he's consistently making -CEV moves. This is clear, especially if the blinds are significanly high, which means he's getting great pot-odds. By doing so (folding), he is *by definition*, increasing his opponent (aggressor) $EV, and by that reducing his own. Another point (that really complicates it, IMO), is that we can no longer assume all players have equal ability, if Hero is making a consistent CEV mistake against his opponents.

3. That leads to another, similar, complication (or a "paradox"): if all opponenets are equally skilled, Hero should take ANY +CEV opportunity he has, since he hasn't got any skill advantage. Not taking even the slightest +CEV opportunity is, according to our "equally skilled" assumption, a mistake. Therefore - our Hero should call all-in even if he's less than a coin-flip, if the pot-odds justify it. With high blinds, these spots are very common.

There are some other points to consider. For instance: how high and what is your position in relation to the blinds, when is the next level coming, etc.

Anyway, the main question remains: what are the criteria for judging whether a certain all-in call (equal stacks, on the bubble), is +$EV.

[fnurt]

What you didn't mention is that when two players go all-in, everyone who is not in the hand gains EV, because someone is going to get busted out.

So when you fold in a favorable situation, your opponent gains EV, but you don't take the corresponding negative EV hit all by yourself. The other players also lose significant EV that they would have realized if you had called.

So you lose EV by making these repeated decisions, but everyone else is in the same boat; either they lose the same EV when they're on the hot seat, in which case you're back to even, or they call and someone gets eliminated. You rate to gain EV when you force someone other than yourself to make the decision.

[PrayingMantis]

What you're saying is correct, but in a way it is (or should be) embodied in Hero's $EV (or rather: the $EV of calling / folding). Because the "general" $EV the whole field (all 4 players) gains by a specific move done by any player, is always 0. Therefore, if you're making a -$EV, the rest of the field (i.e, all others, as a "collective"), has gained, since it's by definition +$EV for them (however, it's possible, of course, that it's +$EV for some of them, but -$EV for others).

An implication from your point, goes something like this:

When you're making a -EV move at a certain point (by folding, in the cases we're taking about), you are making it based on the assumption that some other player will "soon enough" make a bigger -EV mistake, or you, for that matter, will get an opportunity to make a higher EV move (by applying aggression, for instance). But how much can you wait? How many negative EV decisions can you make against these equally skilled, equally stacked, players, during the bubble time? (also notice, that if the stacks were equal at the begining of the hand, and if everyone included you folded to the aggressor, at the end of the hand he has the chip lead. If you were on the BB, for instance, you're now 4th stack.)

[AleoMagus]

[ QUOTE ]

...he's consistently making -CEV moves... By doing so (folding), he is *by definition*, increasing his opponent (aggressor) $EV, and by that reducing his own. Another point (that really complicates it, IMO), is that we can no longer assume all players have equal ability, if Hero is making a consistent CEV mistake against his opponents.

if all opponenets are equally skilled, Hero should take ANY +CEV opportunity he has, since he hasn't got any skill advantage. Not taking even the slightest +CEV opportunity is, according to our "equally skilled" assumption, a mistake. Therefore - our Hero should call all-in even if he's less than a coin-flip, if the pot-odds justify it.

[/ QUOTE ]

From what I can tell, these and a few other points seem to confuse two issues that are not directly related.

Chip EV (CEV) and Dollar EV ($EV)

Making consistent -CEV plays in a tournament does not 'by definition' imply an increase in opponent $EV and does not imply an decrease in one's own $EV. Extending this, I think it is safe to say that even though equally skilled, we should not be inclined to take ANY +CEV edge we can get if $EV is what we are really concerned about.

$EV is a kind of a strange thing to even talk about in the context of a single play though I and others attempt to do it all the time. It would seem though (strange as it is) that -CEV plays can be +$EV in the context of tournament play.

Imagine for example a four handed situation like this

You (BB) have t3600
SB has t3600
Button has t400
UTG has t400

Blinds are 200/400 and antes are 50. After UTG and button pass, SB pushes all-in. You hold TT. SB is not a wild player, but is certainly capable of a push in this situation with less than premium hands. In fact, lets just assume you know his hand is JQo.

This is clearly a +CEV call, and may even be a +CEV situation for both you AND the SB even after you have called.

Strangely though, the two small stacks experience a major boost in $EV if the two of you collide and one of you is eliminated here. What this does imply is that despite your +CEV situation, both you and the SB have just lost $EV by getting into this big confrontation.

This actually brings me to an interesting thought. On any all-in steal on the bubble, the move itself does not seem to have a $EV independent of your opponent's reaction. If, for example, you are stealing with A7s and your opponent calls with KJo, it may be +CEV for both the steal and the call, and may even in some sense be +$EV for the steal and a fold, but if your opponent decides to call anyways (playing according to CEV concerns), he effectively lowers BOTH of your actual $EV in the tournament and increases the $EV of the small stacks.

Well, this may be unclear (or simply flawed) so before I ramble anymore, I'll see how this goes over first.

Regards
Brad S

-edit. In rereading this and the previous posts, I think I have noticed something that may be more accurate in describing what I mean. Making -CEV plays may actually increase your opponents $EV, but less than if you called. More importantly, avoiding slight +CEV situations on the bubble when facing elimination, though it will almost certainly lessen your $EV may still be better than making the +CEV play which will lower your $EV by even more.

[Tharpab]

Lets consider the example:

1st - $50
2nd - $30
3rd - $20
Total Prize $80

Total chips 2000
Other guy 500 25%
Other guy 500 25%

Villain 500 chips 25%
You 500 chips
You 'own' 25% of the chips and therefore $20(of the total prize) After coin Flip $40/2(half of the time you lose) = You will 'own' $20 of the total prize

So in this case we have an $EV+-(Actually its + since the blinds will hurt an low stacked and therefore hurt the chances of winning than a bigger stacked) call, but it also must be took in account the skill of the players in their equity(like in a scale from 0 to 10 how much is likely they to win) as a way to creating their equities. Looks good on paper, but some math genius could comment this

[fnurt]

One thing that's missing here is the impact of the blinds. If you're somehow on the bubble with the blinds at 10/20 maybe it doesn't matter. But in the real world, the blinds are much higher, and you're either in the BB with money already in the pot, or in another position where the blinds provide you with an overlay. A model that basically assumes the blinds are 0/0 and you can keep this up forever doesn't reflect reality.

[donkeyradish]

I'm on the avoid confrontation side of the fence, ever since a couple of weeks ago I improved from 10th to 4th in a 300-player tournament by simply folding every hand!

At the final table I had the smallest number of chips I could have without dropping out a round. I fully expected to be 10th, but it seemed like everyone else wanted to win at all costs and the chips were flying around the place as everyone put themselves all-in.