33 vs AQs: multiway and HU

darthdimsky

darthdimsky

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33 vs AQ in a 3 way is an underdog (against unknown 3rd party hole cards) as opposed to being 51% ahead when HU. Anyone know the reason or the math behind this? Screenshots below.
 

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karl coakley

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Pretty much a small pair vs 2 larger cards you are close to a coin flip. You added another hand and all of a sudden instead of 6 outs (AAA,QQQ) you added 6 more outs in theory. There are a lot more cards and combinations that beat 33. This is not where you want to be, needing to hit a 3 to hopefully take the pot.

Pull up a holdem calculator and play around with it some. Pretty much, you NEVER want to be in a multi-way pot. Even AA doesn't play well 3 ways.
 
darthdimsky

darthdimsky

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True. Plus there's also the board pairing twice, counterfeiting your bottom pair.

But what I'm really interested in is understanding why 33 in this case is a heavy underdog vs AQ in a 3-way (33% vs 42%) but is a slight favourite HU (51% vs 49%). This is basically determining the relationship b/w 33 and AQ relative to a HU or a 3-way.

Correct me if I'm wrong but usually it's a more linear relationship, meaning if any 2 cards are ahead of another while HU they tend to be somewhat still ahead (against the same 2 cards) even if more people are involved. In this case the relationship b/w EV inverts, which is why I'm finding it fascinating.
 
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ccres

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Correct me if I'm wrong but usually it's a more linear relationship, meaning if any 2 cards are ahead of another while HU they tend to be somewhat still ahead (against the same 2 cards) even if more people are involved. In this case the relationship b/w EV inverts, which is why I'm finding it fascinating.


Hi. This is an interesting one to think about. The linear relationship you mentioned I don't think works out when the hands derive their strength from different sources. One of the ways to consider the difference the unknown third hand makes is to look at how the strength of the two hands are impacted, that's how it kind of makes sense to me.

At the risk of stating the obvious:

The main strength of the AQs hand is mostly making top pair if an Ace or Queen hit, with a lesser contribution from hitting the nut flush or hitting the nut straight. Those strengths hold up very well with the addition of an unknown third hand.

The main strength of the 33 hand is holding on to beat any unpaired hand. That strength is weakened considerably with the addition of another two random cards that the run out can hit.

From that perspective I think it makes sense that the value of the small pair drops off considerable more then the value of the AQs.
 
proud2Bwhack

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The odds that the unknown cards are higher than a 3 is very high which means there are more outs against you. If anyone hits a card higher than a three you switch to big underdog with just 2 outs (the remaining 3's).
 
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