Equity quiz.

You have AA vs average player. Flop is 9d 8c 4c.

A) what is a typical range that villain will check/call a bet with ?
B) what is your equity against that range? (No pokerstove!)
C) Now you have A9 on the same flop. What is your equity ?
D) Since we couldn't use pokerstove for this quiz, list at least 2 factors that you used to conclude on an equity number.

edit: Ranges for A) are not the most important part of this quiz. Assume if you want that you opened in 2nd position and he called in the BB

A) I don't get by calling range? What will Villain call a bet with? (I'd get it against any hand).
B)If Villain pushes? probably around 62% Do we have the club?
C)It's probably lower because he can play it the same way with TJ.
D) A few factors I used. Draw heavy board. Whether we have the Club to the nut flush. The possibility that Villain has overs in the A9 hand.

A few clarifying questions:
Which ace do i have?
A)What do you mean by typical calling range? What a typical player calls with? And what is a typical player?
Assuming 100bb stacks? Preflop action?

Edited for clarity. I meant what range check/calls the flop on that board assuming a normal (weakish passive) SSNL player.

Doesn't matter for the question. Estimating the equity of all AA combos is not much harder than for a single AA combo

More info? Stacks? Bets preflop? Villain tight or loose?

At the end of the day, you compare likely hands vs what beats you vs what you beat.

If you end up with lots of hands you beat that match, you have high equity, if you match lots of hands you loose to you have low equity. About the only way to do it on the table.

Not enough information to give a fair range of 'likely' hands to go through that process though.

eh...how did we get to the flop again?

A) Depends on stacks to pot ratio, and previous action but say

99,88,44
TJc, 67c,56c,AKc,
89s
QQ+

Does that work ? Now let me think about the next questions.

Yeah, that's a good start. BTW, the range you chose is a bit too tight for an unknown IMO.

yes, its way too tight and our equity is great since any better hands raise that flop, same goes with a9 except for the times when he plays TT passively pre-flop and post-flop.

he's calling with mid-high flush draws, some mid pairs, a few straight draws maybe a top pair here or there and even an overpair once or twice. our equity has to be about 75% cause a good chunk of his range is drawing to 2 or fewer outs.

With A9 I guess we're closer to flipping cause lots of the flush draws and half of the straight draws also have two overs.

A) J9o, T9o, T8o, 87o, 77, 66, 55, 33, 22, Axcc, KTcc+, QTcc+, SC clubs, JTo, 76o, A9o.

Plus all the monsters, TT+, sets and 2prs. But, I'd discount them some because he'll re-raise TT+ quite a bit pre and will raise the flop with monster a lot of the time as well.

Because of this, I'd think A9 would have similar equity.

Also, because I feel people peel so light on these type boards, I double barrel them a lot with or without a made hand.

A) A9, A8, 9T, TJ, TT, JJ, 44, 88, 99, many Ax and connecting club possibilities. I think with QQ, KK or the other AA the typical player will typically have reraised preflop or led out or check-raised on flop with 2 clubs on board. With 89 I'd also usually expect either a bet or check-raise on flop. Sets are probably strong enough for a simple check-call even with 2 clubs on board.

B) Against entire range I'm probably 60% favorite. This is a calculation I would never normally make because I'm getting to see the turn card which will obviously alter the figure.

C) With A9, I'm probably about 50/50.

D) With AA, I am ahead of almost everything in my range except a set. I am 90% against TT, JJ, A9 or A8. I'm 80% against 9T and 75% against TJ(not clubs). I'm 65% against flush draws with no pairs or straight draws. Flush draws with other possibilities(pair or straight draw) seem like the most likely holding since there are so many variations possible. A few of these would be favored against me and the rest I'd be only a very slight favorite against. I'd say 50% of the hands I'm against are these, so 50/50 there. I'd say another 45% are the hands I mentioned above where on average, I'm about 75/25. The other 5% of the time I'm up against a set and am a 9-1 dog. 0.5(0.5)+0.45(0.75)+0.05(0.1) = 0.25+0.3375+0.005 = 59%. I did use a calculator for this, but my initial impulse was 60%. I'm not going to break it down for A9 but I'm now also a dog against TT and JJ, I'm even money with A9 and not as big a favorite against any flush draw with overcards to the 9 or to TJ. I'm also now drawing almost dead to a set but this doesn't factor in much since I was drawing slim anyway. I'd estimate my total chances of winning with A9 around 50%.

Sorry for hijack, whats the deal with all these "LP" avatars?

QJ, JT, J9, T9, T8, 98, 87, 76, 99-44, A9, A8, Axcc, KQcc, QTcc, KJcc, KTcc, 56cc, Kxcc (obviously, some of these are raising some % of the time)

Id guess around 73% when he just calls

hmmm, hes less likely to have a 9x hand now, and now many of his unpaired draw hands have an overcard or 2, I also have less equity against the hands he has that are beating me. Id say it prolly drops to like 65%, but it also means I wont get as much value on the turn since im more likely to play pot control on lots of cards.

estimation of the most likely hands he has via estimating hand combos, and the outs those hands have vs me, and multiplied by 4 for his approximate equity, then just took the complement. Adjusted up or down slightly based on how I thought he would play the hands that beat me, or the hands that had more outs than what the mean hands had.

edit: I just stoved it, I pretty much nailed it with AA for my estimation (got 71%) , but the A9o plummeted my equity much more than I thought it would, it fell to 58% .

ok let me add a few more hands then

A)
99,88,44,89s : 12 hands- 10% equity
56c,AKc,QJc,TJc,67c : 5 hands- 50%
TJs, 67s (suit<>club): 6 hands - 65%
JJ+, A9s: 21 hands (ignoring AA) - 90%

B) total equity:
My answer: 60% equity, see below for "details"

I think this is equivalent to

29 hands with 50% equity, 6 hands with 65, 9 hands with 90%

or

29 hands with 50%, 15 hands with 80% (should be 30-15 if we add the other AA)

or

2 hands 50%, 1 hand 80%

My final answer: 60% equity


C) With A9, you have 18 more hands in the 10% group. I think the final answer would be around 35%, but I'm doing this quickly (I'd say 2/3 of hands we have globally a 50% equity, 1/3 about 10%)

D) number of hands in a given group of hands, equity against that group



Now let's see if my answers are ridiculous. BTW it took me a while to compute this, I wouldn't do that at the table.

Edit: results in white vs a
JJ+,99-88,44,AcKc,A9s,QcJc,JTs,98s,76s,6c5c range

AA: 61%, A9: 28% (A9s=34%, A9o=26%)
not too bad I guess

A)
TJs, 67s,
56cc, AXcc, QJcc, KJcc, KQcc, KTcc, QTcc
TT, 9Xs, A8s, 77, 66, 55,

B) umm rough estimate? i suck at this... maybe ~67% vs the range i gave? im obv expcting the avg player to raise sets and 2 pair on flop









edit - this was like a 90sec post so my range could be off... and obv my equity estimate could be way off

ok I just realized the question was check-call, when I thought it was "go all in with" (i.e. if we bet/3bet etc). So my range sucks a bit.

im assuming ave tag

77-55,T9s,98s,87s
80%
80%

60 and 68

Any pair, any piece.
PPs: 22/33/55-77/
Sooted: AcXc (assuming we don't have Ac)KcXc
Connectors: QJ/QT/JT/J9/T9/T8/97/87/86
Other: AK obviously lol.

Hmm. Against that whole range? I'd guess 62-ish.

Interesting. We have the best hand against the whole range I put up there, hmm.. maybe 56?

We obviously haven't got lots of outs with AA, we can counterfeit turned 2 pair hands which we can't with A9. With A9 any turncard connected to the flop will probably alter our equity pretty much.

This was fun, I should practice this a lot more (I may be way off). Gonna go stoving now.

Wow I'm surprised about the results. I was about right about the relative strength between AA and A9 but the equity was a bit off.

The question of a typical player's range does depend on the game: whether it is online/live, what casino/site, what time of day, previous action at table, etc.

I guess my range was a bit more narrow than DevinLake's. Part A is fairly subjective depending on what typical is. With the range he gave, I would guess AA is about 70% and A9 about 65%. He's right: there are more hands that A9 is dominating and so the equities in the two hands would be closer than they were in my range.

Just to note, I excluded all 2 pair hands and sets assuming he'd donk or checkraise them.

A.) Mid pairs, occasional straight draw etc.
B. 70%ish
c. 60%ish
d. intuition based on previous uses of poker stove. also, there are three levels; the hands in his range that you crush, the hands in his range that crush you, and the hands that you are flipping with. estimate how many are in each, act accordingly.