I have TT, you have AA. I have a set, how often will I lose?

This screen from PokerStove tells me I'm going to lose 18.508% of the time.

Everyone else I've discussed this with on 2+2 thinks I'm wrong because it only considers the case when the first card gives me a set, rather than any flop card.



To me whether a ten comes as the first card on the flop, any card on the flop, the turn, or river I'm losing 18.508% of the time.

Could someone explain in very simple terms the other point-of-view?

If I am understanding your point, I think you are correct. I think you are saying that TT vs AA (all-in and called) loses 18.508% of the cases when all you are told is that a third ten comes somewhere on the board (you are told absolutely nothing about the other four board cards).

Real-life poker players are used to seeing three cards come on the flop, obviously, then a turn card, and then a river card. So it may be hard for them to understand the "conditional probability" argument you are making.

We had a similar thread on a related point relatively recently regarding equity calculations.

The flop has three cards, not one.

Do you mean you are dealt TT, I am dealt AA, and there is a ten but no ace on the flop? If so, we need to know the other two cards on the flop. (Because AA has a better chance if the three flop cards are TJQ or if the three flop cards are all the same suit as one of the aces than if the three flop cards are TJ2 or not all of the same suit).

I imagine that is correct if you know one card on the flop but nothing else. But that never is the case.

That makes no sense to me.

That sounds correct to me.

I cannot explain a point of view that makes no sense to me.

According to the simulation (which I'll assume to be correct) if you're dealt TT, your opponent is dealt AA, when there's a ten on the board, you'll only lose 18.508% of the time. When you lose it will be to trip aces, a straight, a flush, a full house, quad aces, or a royal flush. Without knowing the other flop cards we cannot know if a straight, flush, or royal flush is possible for your opponent with AA.

Buzz

I'd say you're right, *except* that by specifying it this way, you're actually making it possible for one of the other flop cards to be an A. So the way you have it laid out is kinda like the dealer dealt out the flop, turned over one card, which was a T. You could now say, without seeing the other cards, that your chance of winning is 18.5%

But if he turns over the other 2, and neither is an A, then your chance is higher.

I don't know of a good way to describe this situation to pokerstove or other poker calculating tools. But for example look at a flop like T28 - now you're at like 89% to win.

So really it's a just a question of what do you know? If you only know 1 card on the flop, then sure, you're right. If you see 2 other cards, and they're not aces, you're wrong.

Here's the thread where this discussion initiated.

http://forumserver.twoplustwo.com/17...stion-1553139/

The major failure of understanding is: It only matters what is the chance of winning, or EV if you like, at decision points.

As Rusty points out, there isn't a decision point midway through the flop.

So figuring out what your EV is when there are still 4 cards yet to be revealed is nonsense.

In the referenced thread there was quite a discussion on when you hit the set. Some claimed OP’s approach only showed the first flop card which OP disputes. Anyway the question was when will your set of tens be outset given villain has AA.

The Poker Stove entry is labeled Board so it is not limited to only flops. There is a difference between “flopping” a set and “boarding” a set. If you flop a set you can still get quads whereby the chances of quads is much reduced if you set on the turn and zero for the river. Since the same obviously holds for the AA. I think OP’s interpretation is correct- "when" doesn't matter for the question asked. Rusty’s approach is a nice one except all five board cards should be involved.

Also, Poker Stove is not displaying EV results, a term that some posters use. It only gives equities, which are an input to EVs

Equity is calculated by calculating win and ties on the river. If you specify 0, 1, 2, 3, 4, or 5 cards, then any other cards yet to be revealed are assumed to be random. That's how equity calculators work.

Random cards can NEVER change your average equity.

I referred to it as winning and losing in the OP. Equity is the correct description. Thanks!

I'm hoping to find an equity we can use in an EV calculation. This is the first step. Is .815 a number we can correctly use?

If we bet 100 dollars every time we hit a set, are we on average making 63 dollars from post-flop betting?

Rusty, I really appreciate you responding. I hope you'll elaborate on your response, to clear things up for one of us.

We're trying to calculate our average equity, across all possible runouts when we have a set against an overpair.

I'm not sure what you're saying here. PokerStove is telling me that when one of the board cards is a ten, that is when I have a set somewhere in the hand, I have 81.5 equity. We can assume the ten is any particular card, first, second, third, fourth, or fifth without changing our equity; without changing how often our tens will win. If we assume it's the fifth card, another ten could've come on the first card. There's no loss in generality by specifying some particular card is a ten.

I think PokerStove is evaluating the scenario of: One of 5 cards is a ten. Other four cards could be anything.

I can say the 4th card is a ten and I get the same equity:

http://propokertools.com/simulations...2=AA&s=generic

Knowing we have TT against an ace, and knowing that we're going to have a set, our average equity is the same after each card is dealt.

It's exactly the same as the TT against AA case where we don't know if we're going to flop a set. Our average equity is the same after 0, 1, 2, 3, 4, or 5 cards are dealt; it's 19.25%. If average equity varied card-by-card where would the equity go?

Rusty isn't disputing what you're saying.

Fyp.

The reason it's 81.5 (and not higher) is because you haven't yet seen any other non-aces on the board (ie, villain still has 4 chances to hit an ace). If you were to then see 2 other non-aces (ie if you flop a set and villain doesn't), your equity obviously improves. Like, if you see the window card and it's a ten, at the moment your equity is 81.5. But then once the rest of the flop is spread and you see there is/isn't an Ace, your equity changes. (You're right that the average change is 0, as discussed in this recent thread.)

That's the point Lapidator was making. IRL you either know 0, 3, 4, or 5 board cards, so the 81.5% equity never factors into a poker decision (however, I wouldn't go as far as Lapidator to say it's nonsense, I'd just say it's a non-useful but somewhat fun fact).

And now ask yourselves for fun if there is any flop that gives you set and no set/quads for the AA but you actually have less than even 57% to win it rather than the 81.5% with only the T known.

Imagine TcTd vs AsAh and flop comes TsJsQs. The AsAh now has a miraculous 43.03% already.

No. In case it isn't already clear to you from other answers, the other 4 cards are specifically random, i.e. they must be unknown. That is the only scenario where you have the equity indicated. If you know the value of any of the other 4 cards, that changes the equity. And the way poker is played, you ALWAYS know the value of at least 3 cards on the board. Never just one.

Put another way, the figure you have shown could be seen as the average equity among all possible equities that you could have, but it is not the specific equity you actually have in any scenario.

I think that's what he meant by "could be anything".

Ofc if all 4 of the other cards were known, hero's equity would either be 100%, 0% or 50%.

why would you calculate how often AA will win after u hit set TT? are u going to fold every time u don't hit set of T? and as you are non-allin on the flop, the other guy still has a range of cards not AA only.

There exist such things called thought experiments that are not going to necessarily be directly related to how a hand could or should be played.

So 18% for AA to win against TT on T-x-x-x-x board.

In order for it to win it needs to hit:
Higher Set
Straights
Flushes

Board runs out chop (EV: x% * 1/2 pot)


There are 22,100 distinct flops. And if he has A A , there are X combos of: T combinations, same for 's. Which AxAy on Txxx has 34% equity against and has yet to flop a set but is still doing fairly well against.

yep. its the average equity among all possible flop combinations given one T and 2 unknown flop cards + turn + river.

In terms of flops, T-A-A being the worst where you have 0% equity. And T-T-x being the best where you have 99.9% equity. And everything in between. + turn + river runouts.

Don't forget that AA has the best kicker. It can win even if it doesn't hit a set, flush or straight. AA wins on a TJJJJ board.

IRL, on average, knowing the other cards doesn't provide much information.

The equity of 22 against 33+ on a 2xx flop is almost exactly the same no matter what xx are unless the flop is monotone or contains multiple twos. In general the equity is very close to 81% on the huge majority of flops.

Knowing the average equity is part of an EV calculation. Once you know the average you can adjust it for special cases. What do we gain by saying that the average is nonsense?

If you know the average equity is 40%, 80%, or 100% that changes how you should play pocket pairs.

indeed, . Also, any JJJ/QQQ/KKK runouts that do not include a T (for last card).

11 quadrun outs
2222
3333
4444
5555
6666
7777
8888
9999
JJJJ
QQQQ
KKKK

and
Higher fh runouts

xKKK
KxKK
KKxK
KKKx

(+JJ/QQ where x != 10)

----

Kind of interesting to approach it from just 1 card shown on the flop as OP did. How do we calculate amount of total runout combinations given only 1 known board card?

We know 5 cards (assuming villain AA and a T on the board), and so the total board combinations is C(47,4) = 178365

Which EV calculation?

How you should play them when? Preflop? Sure, if you're psychic and already know you're going to flop a set, you should get it all-in with your 22 against his AA.

People who aren't psychic use the preflop equity, which is also the average flop equity (when you don't yet know any of the board cards).

If there were a round of betting after seeing the window card, then your stat would be useful for non-psychics.

Rounds of betting are totally irrelevant when calculating equity. When have you ever seen an equity calculator ask you about what bets you're planning on making?

Equity is always calculated by how often you win/tie/lose assuming a random run-out of cards and everyone checks.

Nobody, I hope, evaluates whether to set-mine by pre-flop equity.

Exactly. PokerStove generates how often you win out of 178,365 times:

178,365 games 0.016 secs 11,147,812 games/sec

Board: Td
Dead:

equity win tie pots won pots tied
Hand 0: 19.469% 19.23% 00.24% 34303 423.50 { AcAd }
Hand 1: 80.531% 80.29% 00.24% 143215 423.50 { ThTs }

You didn't mention setmining until now, and I admit I hadn't thought of that possible motive for this stat. Yes, I agree this stat can be relevant for whether/not to setmine.

Right, but they're relevant to EV and therefore to which equities are useful. E.g. if there were no postflop rounds of betting, then setmining stats would be useless and only preflop equity would matter.