# Poker Math Question

Red Chipper Posts: 669 ✭✭✭
edited October 2015
My poker math is lacking and the following hand came up that had me wishing I was studying that aspect more. My opponent had bet enough to put me all in on the turn. So this, mostly just comes down to math.

Brief description of action at 1/2:

Hero: \$275
Villain covers

2 players limp/call my \$15 raise (round) to \$50

Villain check calls \$35 rounded pot \$120

Villain: Check/Shoves
Hero: \$75/Calls

Technically I could be drawing dead, but that's too slim. Also, I didn't believe Villain had a flush based on previous play.

When it's to me to call there's: \$50 + \$70 + \$75 + \$225 = \$420. I have \$150 remaining.

Is it \$150 to win \$420? Or do I include the \$150 so it's \$150 to win \$570? I believe that any :K? , or :8? wins the pot for me. Though, to be honest (and embarrassed), I didn't realize the :8? was an out until I reviewed the hand later.

## Comments

• Red Chipper Posts: 4,376 ✭✭✭✭✭
420
• Red Chipper Posts: 5,007 ✭✭✭✭✭
If you get down to counting outs to compare to pot odds, what I'd do here is say your opponent has a flush sometimes, has a flush draw sometimes, and has no spade sometimes. I'd average that out to 1 fewer spades left in the deck, so I'd count 8 outs for the flush instead of 9, so 14 outs total if your read is correct. I would discount that as well though, because your opponent could already have a straight (1 fewer K or 8 left in the deck, only a chopped pot if you hit), or a set or 2 pair (in which case is not an out for you.) Discounting outs is kind of an art form, but let's just say you have 12 outs total. With 12 outs you need 3:1, and you're not quite getting that. If you count your outs the way you were probably doing it, you'd be at 15, which is 2:1, and an easy call. So it's enough to change a call to a fold, IMO.
• Red Chipper Posts: 124 ✭✭
jeffnc wrote:
With 12 outs you need 3:1, and you're not quite getting that. If you count your outs the way you were probably doing it, you'd be at 15, which is 2:1, and an easy call. So it's enough to change a call to a fold, IMO.

So basically just bet \$10 more on the turn, and you have an easy call off 8-)

No but seriously, I think Jeff's analysis is pretty on point. Based on the action, I would actually give some weight to the flush and maybe even subtract another out or two; but since you have a read that a flush is unlikely, you may be able to add an out. It's worth noting that if he has exactly :J? or :K? :Q? (with one of them being a ), he could potentially take this line, which means your ace is good a non-zero percent of the time too.
• Red Chipper Posts: 5,007 ✭✭✭✭✭
ivandurst wrote:
which means your ace is good a non-zero percent of the time too.

Also true.
• RCP Coach Posts: 1,876 -
Skors3 wrote:

When it's to me to call there's: \$50 + \$70 + \$75 + \$225 = \$420. I have \$150 remaining.

Is it \$150 to win \$420? Or do I include the \$150 so it's \$150 to win \$570? I believe that any :K? , or :8? wins the pot for me. Though, to be honest (and embarrassed), I didn't realize the :8? was an out until I reviewed the hand later.

The gorilla math I do at the tables (This is rough and tumble estimations, but it can be done at the tables):

How many "\$150's" do I stand to win? Two of them is \$300, There is \$70 left after that so I stand to win 2.5 times my call.

Let's bracket this between easy numbers:
If I was winning two times my call, I would need 33% equity to break even.
If I was winning three times my call, I would need 25% equity to break even.

Lets just say I need 30% equity to break even.

If I need 30% equity, the rule of two says I need 15 outs if I am behind to break even.

We have 9 clean flush outs (ignoring unicorn straight flushes and straight flush draws)
We have 6 mostly clean straight outs (he might have a straight beat already)
We might have 3 Ace outs
We might be ahead with Ace High

We have some uncertainty here as to which cards are outs. At (non-unicorn) worst, we have about 20% of the final pot locked up just with the nut flush draw.

The final pot will be \$720, we are entitled to about 20% of it: \$140 we are putting in \$150 and there are lots of other good things in our favor that might put this even further in our favor.

Call
Co-founder Red Chip Poker,
Author Poker Plays You Can Use
Author Poker Workbook for Math Geeks
• Red Chipper Posts: 262 ✭✭
Seems like the Q helped him: Q8, Q9, QT, QJ, JT, J9... 12 to 13 discounted outs seems reasonable and getting nearly 3:1 pot odds justifies a call.

I'm interested in how hero could have avoided this close decision. I'm pretty sure the double barrel is correct but if you're hero how do you size your bets on flop and turn?

Say you do bet 35 on the flop and not 25 or 30, on the turn would you commit and bet slightly larger (this would also increase fold equity)?
• Red Chipper Posts: 4,376 ✭✭✭✭✭
ivandurst wrote:
jeffnc wrote:
With 12 outs you need 3:1, and you're not quite getting that. If you count your outs the way you were probably doing it, you'd be at 15, which is 2:1, and an easy call. So it's enough to change a call to a fold, IMO.

So basically just bet \$10 more on the turn, and you have an easy call off 8-)

No but seriously

It's not really a joke. Skors bet a strong 70% of the pot on the flop then eased up on the turn. Not only should he keep the pressure on if that is his line with a turn bet of 90+, if he bets an amount that maximizes his f/e while pricing himself into his draw it's never really a confusing spot, say 135 to win 435 as a pretty clear call given description.
• Red Chipper Posts: 5,007 ✭✭✭✭✭
Yes bet a little more if it's the right thing to do for other reasons, but I understand the joke. It's a mistake I see players make sometimes, which is what I call subsidizing their own pot odds.

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