Foxwoods, 1/2

EP Villain: Mid 40's women sitting on about $180. Not clueless but a pretty passive player. I have seen her lead a few times but never raise in the past 2.5 hrs.

LP Villain:About $200, new to the table. No real reads. Probably in his 30s, black male. Have seen him c-bet and take a couple pots and have seen him fold to a few flop bets.

Hero on the Button: Covers, gets dealt QQ

EP villain opens for $10, LP Villain calls. Hero makes it $45 to go, both call.

FLOP:KQ10 (pot: $135)

EP Villain donks $50, LP villain raises all in for about $155 total.

Hero does not know what to do and tanks for a bit. I feel pretty confident that one of my villains has flopped the nuts on this board based on the action. I am also confident that EP player is committed to this pot and thus will call the all in bet.

So I realized I am really lacking when it comes to my poker math as I have no idea how to figure out if the decision I made was the right one. Assuming I am correct in my assumptions (need the board to pair to win, have to call $155 to win a pot that will end up being aprox $580) is this a call or a fold?

Hoping someone can talk me though this one so that in the future I can do this kind of analysis away from the table on my own. Also interested how I might do this math against a range of hands for the villains.

Thanks

Pot is $135 to start with 155 left. You can never fold a hand this strong with such a low SPR. V could make this play with AK, KQ, TT.

propokertools.com simulations are a great way to check out your equity against different ranges. I put EP Villain on AA,KK,AK and LP Villain on AJ,TT,AK,KQ. Against those ranges you're a favorite:

ProPokerTools Hold'em Simulation

600,000 trials (Randomized)

board: KQT

Hand	Pot equity	Wins	Ties
QQ	47.64%	283,833	6,087
AJ,TT,AK,KQ	35.75%	190,885	49,289
AA,AK,KK	16.60%	75,993	49,289

Definitely open up the simulator and play with ranges to see how you're doing, it helps you get a feel for the math in these spots (you can click the title and "Edit Simulation" to play with the one above).

PF: Fine.

F (138): SPR is ~1. I'd call it off. LP V could easily have TT or AJ here. You don't give suits fo the cards, so maybe he has a flush draw or a flush and straight draw. Our SPR is 1, we have a set; I'm not folding.

As far as the math. You've got 7 outs right now: (3) Kings, (3) Tens, and (1) Queen. Of course this assumes that one of the Villains doesn't have a set of Tens. So you've got a 28% (2.6:1) chance to hit by the river. Plus the turn card will give you an additional 3 outs. You have to call $155 to win ($138+$50+$155) or $343:$155 or 2.2:1. Now, if you think that EP V will call, your odds go up to ($138+$50+$155+$85):$155 or $428:$155 or 2.8:1.

So assuming the EP V will call, you are getting 2.8:1 (26%). Since your pot odds are larger that your winning odds, then calling is fine. Or another way to say it is, you winning odds percentage (28%) is higher that your pot odds percentage (26%), so you should call.

I'm not sure how you are getting $580.

Snap call and it's not even close.

A handy rule of thumb (that doesn't really apply here, but is still useful):

If you have N outs, with one card to come you have about 2% * N chance of making the hand. With two cards to come, it's about 4% * N.

You should memorize some common situations.


For a flush or straight draw, you're about 4.2:1 with one card, about 2:1 with two cards

For a set, you are about 2:1 against boating or quadding by the river.

A gutshot is about 11:1 against on the next card.




The actual method of calculating is.

On the flop, there are 47 unseen cards (52 - 3 on the board - 2 in your hand = 47).

Your odds of NOT hitting the hand on the next card are therefore (47 - N outs) / 47.

If you don't hit your hand, there will be 46 unseen cards (since one more card will have been seen on the turn).

Your odds of NOT hitting your hand on the river are therefore (46 - N outs) / 46.

The odds of NOT hitting your hand on either the turn or the river are the product of these two probabilities:

[(47 - N) / 47] * [(46 - N)] / 46.

The probabibility of hitting your hand is 1 - the probability of NOT hitting it.



Plugging in numbers for the set...

(47 - 7) / 47 = 0.85
(46 - 10) / 46 = 0.78 (if the board didn't pair, you pick up three more outs to pair the turn card)
0.85 * 0.78 = 0.67

The chance of making your boat is 1 - 0.67 = 0.33 = 2:1 against.


In this case, pot starts at 135. EP V donks 50 (185 total), LP V raises 155 (340 total). You have to call 155 to win 340 if EP V folds or to win ~445 if EP V calls). Pot odds (at least 2.2:1) are greater than your odds to make (2:1 against) so you should call. If EP V calls, this gets even better (since your boat will very likely beat both of them if it comes).

Rabbit,

Before anyone can give you the steps for the math, you need to provide us with hand ranges for your villains.

Math not needed here tho

You and I know this is true for the given example.

However, OP asked for a lesson.

You and I could team up on this one...

I assume it's rainbow, but that probably doesn't matter much against these players. I call because they could have two pair or AK and we have a few outs if they have the nuts. If one of them has KK, good game -- just spike your Q.

this, wtf

EDIT

I see you are asking about the maths, that's fair. For $155 to get $580 you need 26%. Use an equity calculator (I like Equilab) to plug in your cards, the flop and what you perceive to be their range. You can see that you're going to have that much equity or more in all but the bleakest scenarios. vs. some plausible ranges you are ahead.

LP called $10, then called $45. He doesn't have KK. But could have TT (6 combos), AJ (shouldn't be calling $45 OOP, but might have. 4 combos of AJs, 12 combos of AJo and perhaps we should discount those). Maybe going crazy with KJ (should be folding pre... potentially 12 more combos). Is he bad enough to call the pre-flop action with J9s? If so, add 4 more combos. Would he call twice with AK? If so, 12 more combos. Some lower limit players won't 3! with AK but will call 3! and 4! all day.

EP more likely than LP to have AK in her range (12 combos). Would she flat $45 OOP with KK? I wouldn't. But possible (3 combos). Also consider AJ, TT. The real question is what does she donk here with? Does she lead out with AJ? Set of KKK? Both are good hands for trapping against hero's 3! range (99+, AQ+).

Is this a rainbow flop? If so, LP wouldn't shove with the nuts, would he? Why not flat $50 and see if Hero wants to come along for the ride.

Calling all-in here is clearly correct from a math standpoint, even if We caught a peek at either V's cards and saw AJ there. In the long run, the math is close enough (I.e., if hero is behind here) that there isn't a huge difference between calling and folding. With the possibility that hero is ahead of AK/TT/KQ it would s a definite call.

Agree with this, but I think you have to take AJ out of EP's range, since there is no way she is opening PF oop w/AJ even if suited. Also, depending on Hero's image and activity at the table, there is good chance you have to add KQs/KJs/KTs/QJs/JTs..etc to LP range. His shove is actually a good play for Hero since it makes it a bit less likely he has AJ, would be more likely to min raise or peel one if he felt he has nuts, less likely he wants either hand to fold on flop. Look for LP to have any J in his hand and quite possibly a re draw to flush. Definitely call.

For LP, hero has "no real reads." So we have to treat him as an ordinary, routine player. Not terrible, not an expert. This may be incorrect, but until we gain some reads we should assume he plays like the average player.

I don't see the average $1/2 player with a stack of $200 calling $45 pre with all of KQs/KJs/KTs/QJs/JTs.

A mistake we often make is constructing a range for the post flop action that ignores V's pre flop play. For an average player, most (perhaps all) of these hands are eliminated after he calls $45 pre. How many average players call $10 from EP with KTs, then $35 more from BTN? When we make this mistake, we call too much because we have widened V's range to include more hands that we beat, but really are not in his range.

I see players do it more often than you'd believe. Seriously. To the average player, any two face cards or a face card with an A is a great hand and they aren't folding once they put $10 in. They don't know "stack size," etc. Also, I've seen many players raise from UTG w/ AJ -- even AT or basically any A. It definitely happens and those cards cannot be discounted.