SG suggested I might learn some math to figure out if I should bet (or not) some rivers. Ah, he's such a kidder! (but correct, I am sure)

But, for those who can learn math, I have this hand, I made a choice about the river based on my own praxian logic that is, as we all know, entirely mathless.... but I'd like to know, from the good Doctor - or y'all - what math applies here and what action math dictates? I promise to read, and really try and follow, the discussion.

no, seriously....

Razz ($1/$2), Ante $0.10, Bring-In $0.50 (converter)

3rd Street - (0.70 SB)

Seat 1: xx xx A___calls___calls
Seat 2: xx xx K___brings-in___folds
Seat 3: xx xx 5___raises___raises___calls
Seat 4: xx xx Q___folds
Seat 6: xx xx 3___folds
Hero: 5 6 3___raises___raises
Seat 8: xx xx 7___folds

4th Street - (13.20 SB)

Seat 1: xx xx A 3___checks___calls
Seat 3: xx xx 5 2___bets
Hero: 5 6 3 5___calls

5th Street - (8.10 BB)

Seat 1: xx xx A 3 T___calls___folds
Seat 3: xx xx 5 2 Q___raises___calls
Hero: 5 6 3 5 A___bets___raises

6th Street - (15.10 BB)

Seat 3: xx xx 5 2 Q J___calls
Hero: 5 6 3 5 A 7___bets

River - (17.10 BB)

Seat 3: xx xx 5 2 Q J xx__
Hero: 5 6 3 5 A 7 K___?

Total pot: (17.10 BB)



(show your work - or at least explain it a bit, tnx)

I'm feeling a little lazy but here's where you start. You need to lay out all the potential outcomes, and how much you gain or lose in each one, depending if you do or do not have the best hand. So the "first level" are the easy ones.

1. you bet / he calls : you win or lose 1 bb depending on who wins/loses
2. you bet / he folds : you win 0
3. you check / he bets / you call : same win/loss as #0
4. you check / he bets / you fold : if you have best hand, you lose pot, otherwise, you lose 0
5. you check / he checks : you win 0
(when I say you win 0, I mean you win 0 compared to if there was no action made at all on the river, you win or lose no EXTRA than you already have)

So you can see this gets crazy even on the first level. Then there's check-raising, bet/3betting, bet/folding, etc.

Out of position like here I usually start with the simplest model. I divide his range into 3 parts:
A) the range he will call and lose with
B) the range he will call and win with
C) the range he will raise and lose with
D) the range he will raise and win with
if the player is capable of bluffing, I add in the percentage of the time he will raise as a bluff. In a case like this I assume that I will never fold to the raise.

So you have these outcomes:
A : you win 1bb
B : you lose 1bb
C : you win 2bb
D : you lose 2bb
So for example I might decide he would raise any 75 or better, call with any 8, and fold anything else (this is just an example - actual ranges would be based on your judgement). Then I'd count each potential river hand, figure out which "bucket" it goes into, add up the results, and divide by the total number of outcomes.

You may decide that some of the "buckets" above don't apply, like perhaps you might decide he'd never raise a hand and lose, so C doesn't apply.

Because I'm lazy I'll give the simplest example. Say he's VERY conservative and will never raise, but will call you with any 8 low. You beat everything better than 7653A and lose to everything worse.

Also because I'm lazy I won't count them exactly but say he'd with if he rivered any 4, 6 or 7 and lose with an 8. There's one 6 and one 7 dead by my glace so there's 10 cards he could have to win and 4 to lose.
So 10 times you lose $1 by betting and 4 times you gain 1
EV(bet) = (-10*1 + 4*1)/14 = (-10+4)/14 = -6/14 for a net loss.

But that just tells you how much you lose by betting. The question is, is it BETTER to bet or check? So you'd have to do the same math for checking. If he would bet any hand you beat, and check any hand that beats you, then your EV would be
(-1*10 + 4*0) / 14 = -10/14 - so that's worse!

Of course, in this ficticious case the best play is to check-fold.


So anyway this is really just the surface. When I analyze hands I sometimes end up with spreadsheets full of this crap. At the table this usually ends up boiling down to experience, reads, etc, that hopefully have been honed by doing this kind of analysis AWAY from the table.

However - you do get to the point where you notice certain situations where betting is nearly always correct without having to do the numbers. These are not situations like the above - usually it's when your opponent will *nearly always call* no matter what, *rarely raise*, and you know that there are more rivers for him where you win, than where you lose. Change the Q to an 8 and this is a much easier problem to deal with.

uh-huh

Heh, ok. Well you can really boil it down a lot of the time. If you're first to act, and you're considering betting, he's either going to call/raise/fold or call/fold

If he'll call or fold, then you just need to win more than 50%
If he'll call sometimes and raise sometimes, then you need to win more than 50% - the exact percent depends on what range he'll raise.

If your opponent is drawing to beat you, then the more he'll fold the *worse* off you are because all that matters is the ratio between hands where he calls and loses vs hands he calls and wins. If he folds a lot of the worst part of his range then those are hands he can't call and lose with.

This is why you can value bet more liberally when it looks like your opponent has an 8 and you have a 7 - even though he's drawing to beat you, he will call almost all the time with an 8

OK, this is good. 50% even I understand. Most of the time, what I, and I guess most of us, face is having the best hand on 6th - but a vulnerable hand. This issue if you have him locked is a whole other deal.

How to balance the check/call which: saves me a bet when he hits big, catches a bluff which makes me a bet, I think the save/lose evens out when the hands are very close, like we both have good 7s and lose or win with the bottom card - with the

Bet/call: (because I never never bet/fold if I bet because they actually do SIWAS you) which loses a bet when he folds something marginal and then I don't get to see his hand, gains me a bet when he calls down lite, loses a bet when he hits and raises and I call, gains me a bet when he SIWASes.

If you take that hand I posted, what would you do? I didn't have any reads on this guy he was new to me. I don't see how math helps me decide what to do. SG seemed to think it could.

But whether I need to win 50% or more or a lot more or less - what does that actually mean when I play?

If it's about what he is likely or not likely to do, that's instinct and I don't need math for that. If there is something about the cards, about the actual hand that enters into it, then maybe math is useful in some way to me.

I guess what I'm saying is that all this esoteric stuff sounds like it must be really important, I just don't see it's practical in-the-moment application.

The deal is, if you know what he would do with each given hand that he has, then basic counting/math tells you exactly how much money you can make from him with each potential line (checking or betting oop for example) on average.

I avoided giving a (math based) opinion on the specific hand so far because when I originally replied I was tired and didn't want to think/count/add, maybe I'll look at it a bit later. I do think the math is most immediately applicable when either:

* you'd like to value bet, and your opponent is showing a board that indicates he will usually call no matter what
* you'd like to bluff, and your opponent is showing a board where he will usually fold (if he missed)

Good analysis overall, but this numbers are not true. The pot isn't zero, so we have to consider an alternative to betting to convert our pot equity on the river. If our assumptions are those that check/calling or check/folding are both worse than betting, a bet that has an inherent expectation of maybe -0.2 might still be correct. This is known as a "crying valuebet" or more technically, evading a negative freeroll (villain calls with a lot, but bets only what beats us). I don't know enough about razz to evaluate if that applies here. Our board looks damn strong, had we only 3 open babies i guess we would get paid by worse than an 8 here considering potsize and it might be a case where this thinking could apply if we had say a smooth 9.

edit: Just saw you covered most of that in your first post, so take it as a further explanation and not a disagreement.

Right in the short version I'm just giving the criteria for the bet to have an automatic positive expectation. It's possible for betting to be -EV and STILL be the best choice, if checking is more -EV. It's not always possible to have a positive expectation line.

Imagining the look on your face when reading Rusty's first response itt was the biggest LOL I've had since August.
The math has to work along with your reads. But don't sell yourself short about reading this villain even if he is new to you. What would a random Stars 1/2 villain do with different hands in this spot if you bet or if you check? I think it's fair to say your WO was probably drawing to a wheel (or at worst a 6 low) so what do you expect him to do with a 6 low/wheel? a 7-low? an 8 low? worse?

There you are! Hey, nice nice run in the WCOOP - it was so exciting. Hope we see it again with commentary. ANYWAY...

I never sell myself short about reading, that's where twenty-nine gabillion hands of microRazz really pays off. Here's how I did what I did:


3rd Street - (0.70 SB)

Seat 1: xx xx A___calls___calls
Seat 2: xx xx K___brings-in___folds
Seat 3: xx xx 5___raises___raises___calls
Seat 4: xx xx Q___folds
Seat 6: xx xx 3___folds
Hero: 5 6 3___raises___raises
Seat 8: xx xx 7___folds

4th Street - (13.20 SB)

Seat 1: xx xx A 3___checks___calls
Seat 3: xx xx 5 2___bets
Hero: 5 6 3 5___calls

3rd street action led me to thinking he paired that 2. I would have raised him HU but multiway, even with check-boy (who might have an 8 back) I call because I might actually have to fold 5th.

5th Street - (8.10 BB)

Seat 1: xx xx A 3 T___calls___folds
Seat 3: xx xx 5 2 Q___raises___calls
Hero: 5 6 3 5 A___bets___raises

This would change my mind at higher stakes but doesn't here. I think he thinks I paired the 5, or I'd have raised 4th to get check-boy out. This is the new thing at micro Stars - raising when you could have a wheel draw on 5th. Doesn't matter what he has, anyway, I want to make sure the T leaves, so I play the same regardless.

6th Street - (15.10 BB)

Seat 3: xx xx 5 2 Q J___calls
Hero: 5 6 3 5 A 7___bets

Uh-oh. The pot's big and he is hoping I paired twice? I misread and he has the wheel draw?

River - (17.10 BB)

Seat 3: xx xx 5 2 Q J xx__
Hero: 5 6 3 5 A 7 K___?


I think he'll call me with a Jhi if he's calling 6th. I think screw it if he had the draw and made it I still don't believe him and I bet. He tanked and called with (A2)52QJ6.

So that was my "read" such as it was.

Rusty's answer, as complex as it looks, really seems to me to just be quantifying common sense. But when you say there is something to apply then I have to believe you have a specific in mind that would be of real use to me.

If so, my notebook is out and pencil sharpened.....

If indeed that was your read as you played the hand and not just after seeing the results (as I'm sure most readers are figuring), then it was a hell of a read. I really can't imagine anyone calling with (A2)52QJ vs. a board of (xx)35A7, even in a huge pot. Then again, I don't play stars 1/2. I have to think that if he's calling if he hits his J low, he's calling UI as well since there's basically no difference (but then again, I don't play Stars 1/2). So if he did have the wheel draw, are we to assume he also calls UI with a J low?

How strong would he have to be to raise if you bet out? My guess would be a 7-low, but I don't play Stars 1/2. If there's a 50% chance he didn't pair the 2 (say with A4 ith) then he has 6 outs to make a better hand. With 32 cards unaccounted for, that means villain will call and lose about 90% of the time, but raise the other 10%. Now if you check, then what hands would he bet with? Certainly made 7's, and say he'd bet made 8's and an occasional bluff (seems ridiculous, but then I don't play Stars 1/2). With the made 8's and bluffs, it doesn't matter if you bet out because you figure he'd call you with them anyway so you'll each put in 1 BB either way. With the made 7's, it only costs you 1 BB extra to lead out since he'd bet them if you check.

So to sum up, in your example, at Stars 1/2, you win 1 extra BB ~70% of the time (since it's a wash if he'd bluff you or has a made 8) and lose 1 extra BB ~10% of the time. Does this seem like a +EV spot to bet then? The answer is, it's a lot like quantifying common sense.

Really? No, I think this is just normal, they almost never raise 3rd without three prime wheels. There were two threes and an A out so - I just always thought he'd paired - maybe it was a timing tell? I dunno. Half the time I get these things exactly right, call them down with my made rough hand and they suck out anyway. But at least I knew what they had!

Of course you can't. Who would? They also check/raise the river with made JTs. I loathe playing at this level, but what can you do? And - what's worse is how often they take the pot.

I should post some of these. I mean, when was the last time you jammed 4th with 5899 against xx34 and xxA7 both raising? Or saw anyone do it? Or raised into two completers with xxA and xx4 with your (Q4)3?

They just think everyone plays like they do, I guess. Then there are the other ones who never put any money in and won't call a completion, but every one of them will limp in behind with their junk. And, of course, I do sometimes play one real bad brick hand when I sit down so they'll play with me, might have had an effect here.

However bad they are, they are fairly transparent when jamming 3rd and I think I'm going to resent the hell out of anyone thinking I just... hey - I have enough **** to write without Razz fantasies. I'm lousy at a lot of poker stuff but I'm very good at this one thing.

I wrote a Razz article for 2p2 about a 10/20 hand and I called your hole cards either exactly or almost. I think they were exact. You know why I could do that? Did do it? Because you make Razz videos and give your game away. How hard can it be to play with someone a few times and not be able to do this? Jeez, why should only NLHE guys on TV be able to put people on hands? If y'all would learn to do it instead of playing "ranges" maybe it would be a helpful thing.

AND aren't you the one who wrote a whole complex deal I can't understand about when it was likely someone paired? Why can't I do at the table what you did with math? I don't do math, I do people.

I just posted a whole deal about being broke, it's not like I have some fabulous image to uphold here.

Prax<---keeps forgetting there are no actual friends in poker

Actually, it can be quite hard. It's hard for you to understand that because you're an excellent hand reader imo. Just like it's hard for me to understand how some people can't do math, cuz it comes natural like to me. And I believe you had this guy pegged in this hand, but I was sure there would be plenty of doubters. So if your read is right, or even right half the time as I used for my calculations, betting the river is totally standard and checking is horrible (only outpaced by folding). That's what the math tells you once you've made your reads.