Did I just stumble onto something important?

[cartman]

<font color="blue">If we value bet the river optimally, shouldn't our "WSD% when we Bet/Raised/Check-Raised the River" multiplied by our "W$SD% when we Bet/Raised/Check-Raised the River" = 50%?</font>

Is this a statistical way to tell whether we are value betting enough on the river?

My river aggression has always been extremely low (&lt;1.5). I have been trying to figure out where I need to bet more, raise more, or fold more.

When you click the "more detail" button on the main PokerTracker page and get all of your stats, the section right after the Agression Factors and right before the "Folded to River Bet" gives our results (Ww/oSD%, Fold%, WSD%, W$SD%) for when we Bet/Raised/Check-raised each street and for when we Just Called.

When I looked at my River section, I found that when I Bet/Raised/Check-raised, my WSD%(went to showdown%) was 72.29 and my W$SD%(won $ at showdown) was 79.88. Multiplying these together I get 57.75%. Doesn't this mean that, of the times I bet the river and got called, I won 57.75%? That would mean that I am playing way too conservatively on the river, right? After all, assuming we are heads up, shouldn't we bet the river whenever we think that we will win the pot at least 50% of the times that we get called?

This of course neglects bluffing and inducing bluffs, and I don't know how they factor in. But it seems to me that if the product of these two numbers is more than 50%, then a player isn't value betting enough. If the product is lower than 50%, then he is value betting too much.

What do you guys think?


Cartman

[Cerril]

Well the first part is sample size. In order to get any meaningful numbers you're probably looking at several tens of thousands of hands.

Additionally, WSD and W$SD are notoriously difficult to analyze. Running good, bluffs, ultra passive and ultra aggressive opponents make massive changes to these numbers over the course of time.

That said, I'm fairly sure there are some optimal numbers given other stats, but I couldn't tell you what they are. W$SD and agg on river are composite numbers, made up of bluffs, value bets, bluff catching, too passive opponents, and so on... Style is also hugely important. A more LAGgish winning player and a much tighter winning player will probably look pretty different here.

However, with a low AF, a high W$SD, a low river agg, and a high sample size, you can probably see a need to show a little more aggression on the river. Whether that means you're giving up too many turns, or too many rivers, or just checking behind too much is sort of up to an analysis of what you've found yourself doing a lot of.

edit: One goal may not be to equal 50% any more than your goal for W$SD is 50%. I've got a 51.5% W$SD and a 55% product of the two terms you discussed. I'm thinking there'd be a problem with a large disparity there, but if they're fairly close together it isn't an obvious problem.

[exist]

i think i remember reading in TOP that to compensate for needing to call a raise on the river, you should think you are ahead at least ~55% of the time when you value bet. in this light, your stats are fine.

[marand]

[ QUOTE ]
<font color="blue">If we value bet the river optimally, shouldn't our "WSD% when we Bet/Raised/Check-Raised the River" multiplied by our "W$SD% when we Bet/Raised/Check-Raised the River" = 50%?</font>

Is this a statistical way to tell whether we are value betting enough on the river?

My river aggression has always been extremely low (&lt;1.5). I have been trying to figure out where I need to bet more, raise more, or fold more.

When you click the "more detail" button on the main PokerTracker page and get all of your stats, the section right after the Agression Factors and right before the "Folded to River Bet" gives our results (Ww/oSD%, Fold%, WSD%, W$SD%) for when we Bet/Raised/Check-raised each street and for when we Just Called.

When I looked at my River section, I found that when I Bet/Raised/Check-raised, my WSD%(went to showdown%) was 72.29 and my W$SD%(won $ at showdown) was 79.88. Multiplying these together I get 57.75%. Doesn't this mean that, of the times I bet the river and got called, I won 57.75%? That would mean that I am playing way too conservatively on the river, right? After all, assuming we are heads up, shouldn't we bet the river whenever we think that we will win the pot at least 50% of the times that we get called?

This of course neglects bluffing and inducing bluffs, and I don't know how they factor in. But it seems to me that if the product of these two numbers is more than 50%, then a player isn't value betting enough. If the product is lower than 50%, then he is value betting too much.

What do you guys think?


Cartman

[/ QUOTE ]

An interesting post and if you are correct I am not even close to value betting enough (which I have been thinking about also!!). My W$SD% is 86.68 and WSD% is 75.15 after my first 21k hands at 10/20 so your product gives me 65%!

However I think there might be some more things to consider.

If you bet the river and get raised and then you call. Will that hand be calculated into "Bet/Raised/Check-Raised" or "Just Called"?
If that hand is put into "Just Called" since you just called the last bet then there is a problem with your reasoning.

Before you valuebet you don't know if you will get raised or not. The hands in "Bet/Raised/Check-Raised" where the opponent only calls obviously means that he doesn't have a great hand, but you dont' have that information for the current hand when you decide to value bet. You need to win more than 50% because of the extra cost when you get raised.

Another problem is when you are first to act. If you value bet against a loose player who also is very aggressive. Lets say the following as an example: If you bet he will call with 75% of his hands and you will win 60% of the time when he calls so a bet for value is clearly +EV and you might think that you are not betting enough in this situation. But, if you would check your hand against this opponent he might bet all his hands, either for value with his good or mediocre hands or as a bluff with his poor and terrible hands. Then you would gain a bet from all his weaker hands and not just his weak hands that he would call a bet with. So even though you win more than 50% when you get called check/calling would be more profitable. (But check/raising your better hands would be best of course.)

So in short there are two problems:
1) You need to win more than 50% to make up for raises you have to pay off.
2) When you are out of position inducing a bluff is sometimes more profitable.

[cartman]

[ QUOTE ]

If you bet the river and get raised and then you call. Will that hand be calculated into "Bet/Raised/Check-Raised" or "Just Called"?

[/ QUOTE ]

Your points are excellent as are those in the other responses. Inducing a bluff is tough to quantify and it is something that I do quite a bit of, even indirectly. An example is with a less than stellar holding that I definitely want to show down against a habitual turn raiser who will almost automatically bet when checked to when I am out of position. Against a player like this I will often check and call the turn and the river instead of just betting on the turn and being forced into a decision in which I may be forced to fold the best hand. With a stronger hand I bet and welcome the raise. With weaker hands I bet and fold to the raise.

Does anyone know the answer to the question quoted above?

Cartman

[DMBFan23]

what about the times we value bet and our opponent folds?

[stevepa]

If your Won Money at Showdown when you Bet/raise is 80%, that means that when you get called, you win 80% of the time...There's no showdown if they don't call. The Went to Showdown tells you how often you're called (or fold after betting).

Regardless, shouldn't you win at showdown substantially more than 50% of the time you're called? In general, the WORST hands you bet on the river should win 50% of the time they're called. There's also all the times you bet/raise the nuts or another strong hand on the river. (This obviously neglects bluffs and some exceptions when you're out of position but I would still expect the optimal W$SD when you bet/raise to be &gt;50% when called)

[cartman]

[ QUOTE ]
Regardless, shouldn't you win at showdown substantially more than 50% of the time you're called? In general, the WORST hands you bet on the river should win 50% of the time they're called.

[/ QUOTE ]

You are exactly right. I went braindead.

Thanks,
Cartman

[Jeff W]

[ QUOTE ]
<font color="blue">If we value bet the river optimally, shouldn't our "WSD% when we Bet/Raised/Check-Raised the River" multiplied by our "W$SD% when we Bet/Raised/Check-Raised the River" = 50%?</font>

[/ QUOTE ]

I believe there are two errors in your logic.


[/ QUOTE ]
1. You assume that our hands will be better than our opponents when called exactly 50% of the time. Actually, the minimum advantage we need to value bet(in position) is 50%(when called), so our W$SD should be an aggregate of all of our hands from 50% W$SD hands(when called) up to the nuts.

I think you get my basic idea. There are two complications.

A: Bluffing.

B: Situations where it is correct value bet with a hand that wins less than 50% of the time when called. Let me construct such a situation:

Heads up on the river.

Pot is 10 BB.

Your hand wins 1/5 times when called.
Your hand wins 1/11 times when you check and call your opponent's bet.
Opponent will never bluff raise.

I had a hard time with the math for this. To come up with a more useful model, I'd have to spend more time.


[/ QUOTE ]
2. Sometimes your value bet will be raised or reraised. This means that you have to value bet more conservatively because sometimes you will be bluff-checkraised off the better hand and sometimes you will be raised by a better hand and pay off.

Example:

6 BB pot HU on river

Your hand is best 50% of the time when called and your opponent calls your river bet 50% of the time. 40% of the time your opponent will fold the worst hand.

Your opponent will check-raise 1/10 times and this check-raise will be 10/11 value and 1/11 bluff.

Thus, your expectation for a 50% value bet if you fold to the C/R is:

.1*-1=-.1 BB

If you call, it is

.1*-2*.91+.1*9*.09

-.182+.081=-.101 BB


[/ QUOTE ]

I think there is one more error in your logic, but I'll have to think about it some more. Anyway, very interesting post--it inspired me to do some thinking about river play and revealed that I still have a lot to think about.

Anyone who finds an inaccuracy in my post, please inform me.

Thank you.