Dumb Noob Question (Trips in the Hole)

[bbartlog]

Please explain to me how AA39o is a better hand than AAA3o

AA39 = twice as likely to make set/FH, twice as likely to draw out to trips like 333/999. Maybe most important, AA39 can make two pair, while AAA3 can't. Anyway Split Suit already showed you the percentages.

[Phil153]

The percentages have to be wrong. There is no way AAA3 can be a dog to a random hand. In fact the numbers should be barely different to AA39o

[ QUOTE ]
AA39 = twice as likely to make set/FH

[/ QUOTE ]
yes, but that's a 20% chance (for trips) and only matters when someone makes two pair or better. So this is worth maybe ~5% extra.

[ QUOTE ]
twice as likely to draw out to trips like 333/999

[/ QUOTE ]
Only 999, which is exceedingly rare.

Both of the things should be offset by the lowered chance of someone having A2/A3 or running into another AA.

[SplawnDarts]

I think the numbers are irrelevant here anyways. AAAX, especially AAA2 or AAAA, is a "snowing" hand analogous to 2222X in KCL but a hair more common. It has limited value on it's own, but it pretty much ensures no one else has an opener they can like.

Against tight opponents, it can be bluffed. Some versions, where X makes a low, even have ways to win on both sides and aren't hopeless if you get called. If you raise up AAAA, and get called, no one can possible have a nut low (draw) and that gives you a huge edge against thinking players who won't play for half the pot.

Trips not involving AAA (other than possibly A222) are pretty worthless.

[bbartlog]

Chance of 3 nines on the board is small, but chance of two nines is somewhere between 4-5% (assuming we see all five cards). The chance for two pair is higher, maybe 6-7% vs 0 for the AAAx hand. Then there's the 20% vs 10% chance of making your AAA set.
These aren't huge percentages, but look how small the advantage you get from holding one more ace in your hand is:
With AA3x, odds of a random hand against you having a better low (A2) are less than 4%. This gives them a 40% chance of getting 50% of the pot; so a random hand has less than 1% of its equity against you from its chance of besting you for low. Cutting that equity in half by holding one of the remaining aces in your hand doesn't help that much.
But it may be that the analysis changes if you start to think about a FR situation rather than random hand matchups.

[Phil153]

Look, I'm right, and you're wrong. Your analysis is flawed, because these situations only matter when the board is not paired and our opponent doesn't have 2 pair.

Compare AA39o and AAA3o in twodimes vs any hand you care to choose. You will see the numbers differ by a few percent. That's all. Split Suit's numbers are wrong - in fact the most basic intuition should tell you that AAA3 is a decent favorite over any random hand. It should also tell you that it's barely different to AA39.

Unfortunately propokertools isn't working so I can't give you the official results.

[bbartlog]

You're right that the increased chance of making (insert random high) only matters some of the time. But, for example, your opponent's chance of holding two pair for high is about 30%; high equity accounts for what, 70-80% of all equity? So the 15% greater chance of making trips/set is going to give you a 3% equity edge vs a random hand (against the less than 1% equity edge that opponent's reduced low chances gives you).
Agree that the 65% vs 47% spread looks bogus though.

[Phil153]

You low calc failed to take into account

- fewer aces = fewer counterfeited lows
- A3 which splits for low
- A4 type hand on 4 or 5 low board where the 3 is counterfeit.

If you compare EVs against various hands, it looks like much of the value of AA93 vs AAA3 comes not from two pair or trips but rather from

- Ax hands we strongly dominate (there are fewer when we have AAA)
- 9 card acting a blocker for two pair and middle straights

These add up to about a 3% differential overall as best I can tell.

BTW, your trips calculation (5%) has to be off. By your numbers, any four card, no paired hand would make trips by the river 20% of the time.

[ QUOTE ]
So the 15% greater chance of making trips/set

[/ QUOTE ]
This number is incorrect. It's 12% for AA and we lose a little over half of that dropping an A. And 9 trips is closer to 2.5% I think. So you're looking at around 9% greater chance * the 20% mentioned earlier = <2% difference.

[I dunno]

I love AAAW hands in PL. You can steal a lot preflop and on the flop, you can push in preflop and never be (as far as I know) less than 50-50, and maybe you'll put somebody on tilt when you scoop.

As far as the debate over whether AA39 or AAA3 is better, IMO it's irrelevant because unless you get it in preflop, it really just comes down to situational post flop play.

Correction: AAA4r is 51-49 dog to a hand like A23Kds. Whatever.

[Phil153]

I dunno - I agree.

But people in this thread advocate folding AAA3r preflop, while suggesting that AA39r has some magical properties that makes it a good hand.

[bbartlog]

- fewer aces = fewer counterfeited lows
- A3 which splits for low
- A4 type hand on 4 or 5 low board where the 3 is counterfeit.

Yes, because these are also very small edges. OK, by having another ace in your hand you've reduced the number of counterfeit cards from 5 (for AA3x) to 4 (AAA3). Now your chance of getting counterfeited is 5% lower, which matters only if you've made a low (~40%), and then for half the pot. So maybe this is worth another 1%. The reduced chance of opponent having A3 starts from a lower base than A2 (because you already have one of the 3s) and matters half as much, since you're talking about a split low, so somewhere less than 0.5% equity bonus vs a random hand. I'm not sure what you're saying about an A4 hand... your odds of facing one and then getting counterfeited are less? This is a tiny edge given that (versus a random hand) you're talking about a 5% chance of A4, 40% chance of low, ~5% difference in the chance of getting counterfeited. I expect that if you add all of these edges you get from changes to your opponent's hand probabilities and your own counterfeit chances together you'll be lucky to break 2% equity.

BTW, your trips calculation (5%) has to be off.

I don't believe so. Odds of a particular unpaired card in your hand getting matched = (1 - ((45/48)*(44/47)*(43/46)*(42/45)*(41/44))) = 28.7%. Odds of one of the four remaining cards on the board being one of the remaining two cards of that rank = (1 - ((45/47)*(44/46)*(43/45)*(42/44))) = 16.5%.
28.7% * 16.5% = 4.7%. You can't just use (4.7% * 4) as your chance of getting trips with an unpaired hand by the river, though.

It's 12% for AA and we lose a little over half of that dropping an A.

Chance of hitting set on the flop is about 12%. Significantly higher by the river.

For what it's worth, I wouldn't fold AAA3r preflop either and think it's a fine hand with a lot of advantages as regards bettability. But on the specific question of whether I'd rather go all-in against a random hand with AAA3 or AA39 I have to go with the AA39.