Chart - EV of Calling on the River... (is folding as bad as we think?)

[Surfbullet]

Great reply cartman.

One of the important things to notice here is that "big pot" is 20+ BB. That's HUGE. A 9 BB pot on the river leaves us with 10% needed to break-even, and we should certainly be able to estimate within 10%, correctly.

I think this chart really makes manifest how critical it is to make correct rivir decisions, because they can be so costly. I think i'm gonna 2table for a bit and really go crazy over hand-reading. [img]/images/graemlins/smile.gif[/img]

Surf

[Danenania]

Wow, excellent post. Good things to think about.

In my conversation with Victor, I ignorantly overlooked the fact that the river bet ($20) does not represent 100% on the river, but only 10% (the amount needed to break even). Therefore, being good only 6% of the 10% is a 40% mistake, not 4%. That's $8 instead of 80 cents! HUGE difference.

Mark, you did an excellent job in helping us realize what mistakes can be made and how they can cost us.

However, as Imitation and Cartman (among others) pointed out, we will often have a tough time quantifying "significant" mistakes. I don't think there's a person here that can tell the difference between being good 7% of the time and being good 9% of the time. Obviously, our judgment, experience and player reads will be the most help in close river decisions.

Also, keep in mind that in many drawless HU pots, we will often decide whether or not to call down on the turn, not the river. If a river blank falls, we're calling the river after calling the turn a good portion of the time in those situations. It looks like you know your math a lot better than I do. Do you know how calldowns decided on the turn should be calculated and how the margin of error affects us from there?

[ QUOTE ]

<font class="small">Code:</font><hr /><pre> Pot Size
Win % 9 10 11 12 13 14 15 16 17 18 19 20
1/1 100.0% 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00
1/2 50.0% 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50
1/3 33.3% 2.33 2.67 3.00 3.33 3.67 4.00 4.33 4.67 5.00 5.33 5.67 6.00
1/4 25.0% 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25
1/5 20.0% 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20
1/6 16.7% 0.67 0.83 1.00 1.17 1.33 1.50 1.67 1.83 2.00 2.17 2.33 2.50
1/7 14.3% 0.43 0.57 0.71 0.86 1.00 1.14 1.29 1.43 1.57 1.71 1.86 2.00
1/8 12.5% 0.25 0.38 0.50 0.63 0.75 0.88 1.00 1.13 1.25 1.38 1.50 1.63
1/9 11.1% 0.11 0.22 0.33 0.44 0.56 0.67 0.78 0.89 1.00 1.11 1.22 1.33
1/10 10.0% 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10
1/11 9.1% -0.09 0.00 0.09 0.18 0.27 0.36 0.45 0.55 0.64 0.73 0.82 0.91
1/12 8.3% -0.17 -0.08 0.00 0.08 0.17 0.25 0.33 0.42 0.50 0.58 0.67 0.75
1/13 7.7% -0.23 -0.15 -0.08 0.00 0.08 0.15 0.23 0.31 0.38 0.46 0.54 0.62
1/14 7.1% -0.29 -0.21 -0.14 -0.07 0.00 0.07 0.14 0.21 0.29 0.36 0.43 0.50
1/15 6.7% -0.33 -0.27 -0.20 -0.13 -0.07 0.00 0.07 0.13 0.20 0.27 0.33 0.40
1/16 6.3% -0.38 -0.31 -0.25 -0.19 -0.13 -0.06 0.00 0.06 0.13 0.19 0.25 0.31
1/17 5.9% -0.41 -0.35 -0.29 -0.24 -0.18 -0.12 -0.06 0.00 0.06 0.12 0.18 0.24
1/18 5.6% -0.44 -0.39 -0.33 -0.28 -0.22 -0.17 -0.11 -0.06 0.00 0.06 0.11 0.17
1/19 5.3% -0.47 -0.42 -0.37 -0.32 -0.26 -0.21 -0.16 -0.11 -0.05 0.00 0.05 0.11
1/20 5.0% -0.50 -0.45 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05
1/21 4.8% -0.52 -0.48 -0.43 -0.38 -0.33 -0.29 -0.24 -0.19 -0.14 -0.10 -0.05 0.00
1/22 4.5% -0.55 -0.50 -0.45 -0.41 -0.36 -0.32 -0.27 -0.23 -0.18 -0.14 -0.09 -0.05
1/23 4.3% -0.57 -0.52 -0.48 -0.43 -0.39 -0.35 -0.30 -0.26 -0.22 -0.17 -0.13 -0.09
1/24 4.2% -0.58 -0.54 -0.50 -0.46 -0.42 -0.38 -0.33 -0.29 -0.25 -0.21 -0.17 -0.13
1/25 4.0% -0.60 -0.56 -0.52 -0.48 -0.44 -0.40 -0.36 -0.32 -0.28 -0.24 -0.20 -0.16
1/26 3.8% -0.62 -0.58 -0.54 -0.50 -0.46 -0.42 -0.38 -0.35 -0.31 -0.27 -0.23 -0.19
1/27 3.7% -0.63 -0.59 -0.56 -0.52 -0.48 -0.44 -0.41 -0.37 -0.33 -0.30 -0.26 -0.22
1/28 3.6% -0.64 -0.61 -0.57 -0.54 -0.50 -0.46 -0.43 -0.39 -0.36 -0.32 -0.29 -0.25
1/29 3.4% -0.66 -0.62 -0.59 -0.55 -0.52 -0.48 -0.45 -0.41 -0.38 -0.34 -0.31 -0.28
1/30 3.3% -0.67 -0.63 -0.60 -0.57 -0.53 -0.50 -0.47 -0.43 -0.40 -0.37 -0.33 -0.30
</pre><hr />

Conclusion:
It sure looks like folding on the river in a big pot isn't nearly as bad as we make it out to be. Was Ed Miller wrong?

Example from chart:
Pot is 20BB and our opponent bets into us. We need to be good 5% of the time for the call to be correct. This is obvious.

Now if our winning chances are actually 6.7% (1/15) then we net a profit of 0.25BB's. But if our winning chances are only 3.3% (1/30) then we lose 0.33 BB's on the hand. Both of these scenarios represent a 1.7% change from our break even point. But, we can also look at the case where we are 1/25 (4%), which would be the a change of 5 hands in the denominator (6.7% is 1/15 and 4% is 1/25 and the breakeven point is 1/20...) and find that we lose 0.2 BB's per hand which is a similar amount to what we win when we look at it in the opposite direction.

Help me understand the results of this table which is basically looking at our EV of calling 1 big bet on the river in a pot of various size vs. our chance of winning that pot. It appears that incorrectly calling for one bet on the river is worth almost the same as incorrectly folding. (If calling is worth +0.25 then folding is -0.25.)

ps. To simplify the results it apears to me that folding the river incorrectly is not nearly as bad as we think it is. If we incorrectly call just as often as we incorrectly fold the EV of both of these plays are very very similar, and this is not what we have been told. And not what I have believed for a long long time.

pps. In fact, it appears that calling on the river incorrectly is AT LEAST as big of mistake as folding the river incorrectly.

[/ QUOTE ]


I need to eliminate some confusion. There are several mistakes in the example you provided.
First off, you are using the column for a 19BB pot, not 20BB.
Secondly, if our winning chances are 6.7% (1/15), then we net a profit of 0.33BB's, not 0.25BB's (you accidentally read from the 1/16 row), which is exactly equal in magnitude to what we lose if our winning chances were only 3.3% (1/30). Your EV is symmetric around 5% with respect to the offset in your judgement.

Next, the case of 1/25 (4%) is not a change of "5 hands in the denominator." The denominator does not represent the 'number of hands,' it is just the denominator of a fraction expressing how often you think you're good - it has no physical representation.

So what does all this tell us?
It tells us that if we judge that we have a 5% of being good in a 19 BB pot, and our judgement is 100% accurate, then we neither gain nor lose by calling or folding. If our judgement is too optimistic by x% then we lose the same amount on a call that we would gain if our judgement was pessimistic by x%.

But do judgements really work that way? Is it just as likely that your guess of being good 5% of the time is really 7% as it is 3%? I don't think so. Think of it this way. Let's say you judge your chances of being good at 5%. If you were WAY OFF being optimistic, the biggest you could be off is by 5%! That would put you at a 0% chance of being good. If you were way off being pessimistic, your real chances of being good could be as high as 100%. There is much more room on the positive side when you're a big underdog than the negative side.

I don't want to take away from this post. I think the chart is very nice. But don't read it for more than it is: it tells you the EV cost or gain for calling on the river as a function of pot size and your chances of being good. It gives you an idea of how big various mistakes can be. But I don't think you can draw any conclusions whatsoever about whether or not calling down in marginal situations is right.

[Ed Miller]

[ QUOTE ]
Some people don't understand this. Most good players do. Folding the river for 1 bet is not a big mistake because it costs you the pot. Ed Miller, I believe, was simplifying a rule for the unwashed masses. Those of us that aspire to greater heights have to leave behind the comfortable (but -EV) river calls.

Krishan

[/ QUOTE ]

I have to say that it sometimes amazes me how much "pokerthink" has changed since I started writing SSH two years ago. Ideas that seem like dogma now were fighting the uphill battle just two years ago.

Calling on the river with marginal hands was one of those ideas. Two years ago, the Small Stakes Forum (there was no Microlimit or MHSH or SSSH or whatever) was full of people who thought the key to winning limit hold 'em was finding the right spot to lay down top pair. And for them, the right spot was basically any time they got raised.

I'm really not kidding. Often they didn't even have to get raised to fold. If the flop got bet and called, their A7 on an A94 board was going straight in the mucker even if they had the button, even if the pot had ten bets in it, and even if the bettor was kinda crazy. Get raised on the turn? Top pair is auto-mucked. Flush comes on the river and a new person bets? Auto-muck.

In large part, some of my writings in SSH were designed specifically to counteract those ideas. I was writing to people who were folding way way too much.

Well, now "pokerthink" has swung the other way it seems. I think people on this forum generally play a whole lot better than they did two years ago, but I would be remiss if I claimed that no SSH-induced leaks existed.

Yes, learning to fold correctly on the river is an important skill. If you call routinely with hopeless hands, you have a big problem.

I'll give a quick river tip that will hopefully help some people. Bets mean something, but raises mean a whole lot more. They mean more still if you've called in between. For instance, just last night I folded K [img]/images/graemlins/diamond.gif[/img]J [img]/images/graemlins/diamond.gif[/img] on a 9 [img]/images/graemlins/diamond.gif[/img]5 [img]/images/graemlins/heart.gif[/img]4 [img]/images/graemlins/heart.gif[/img]4 [img]/images/graemlins/diamond.gif[/img]T [img]/images/graemlins/diamond.gif[/img] board for a single bet, closing the action in a 23BB pot. Why?

Because the action on the river went bet, I called, and then someone behind me raised. Given the player, the previous action in the hand (they went nuts on the turn, and I got carried along for the ride... calling the last bet knowing full well there was a fair chance I was drawing dead), and the river raise after a bet and a call, this was 100% a full house. While the strong turn action could have been A4, this player absolutely does not raise after the flush card comes and there's a bet and a call without a boat. So I folded. He had 55.

This is an extreme example, but one that shows quite clearly that there is an exception to every rule. On the river you need to use your judgement. If you are 2% to win, and you are getting only 12-to-1, you have an easy fold. But don't start folding top pair again just because someone else breathes on you. [img]/images/graemlins/smile.gif[/img]

[baronzeus]

[ QUOTE ]
On the river you need to use your judgement.

[/ QUOTE ]

The best part of the post by far.

[krishanleong]

[ QUOTE ]

Calling on the river with marginal hands was one of those ideas. Two years ago, the Small Stakes Forum (there was no Microlimit or MHSH or SSSH or whatever) was full of people who thought the key to winning limit hold 'em was finding the right spot to lay down top pair. And for them, the right spot was basically any time they got raised.

I'm really not kidding. Often they didn't even have to get raised to fold. If the flop got bet and called, their A7 on an A94 board was going straight in the mucker even if they had the button, even if the pot had ten bets in it, and even if the bettor was kinda crazy. Get raised on the turn? Top pair is auto-mucked. Flush comes on the river and a new person bets? Auto-muck.

In large part, some of my writings in SSH were designed specifically to counteract those ideas. I was writing to people who were folding way way too much.

[/ QUOTE ]

I totally agree. I also think you did a brilliant job swinging the pendulum. And I also think great players understand what you meant by "folding the river for 1 more bet" given the metagame context the book was written in.

Krishan

[MarkD]

I see now that I made some mathematical mistakes in my first post. I apologize for that (I understand what I did wrong). When I finished the chart and first looked at it it was an eye opener to me. I posted without really checking my math at all because I was kind of excited by what I saw.

Prior to doing this chart I understood that folding the river wasn't as bad as it was made out to be - that much was always obvious to me, but I did not know that mistakes in both directions were equal in expectation until I saw this chart. I also did not realize how big of a magnitude these mistakes are.

This chart, and this thread, has prompted me to really focus on making good river decisions (bet, call, raise, fold). I think I became complacent over the past year because of all of the dogmatic rhetoric on these boards. That is my fault though.

I have a lot of areas of my game where I can improve (last night I played horrible) and river decisions is definitely one of those areas. I wish I was better able to focus on these areas and make more improvements in my game rather than passively coasting along at a pathetic winrate.

Lots of good discussion generated in this thread though, so I'm glad I posted it.

BTW, I folded two big pots last night that I would have won and think both of my decisions were "good", until about 10 minutes later when my opponents were no longer unknown and were both horrible donks. We always remember those big pots... maybe I'll start calling more. [img]/images/graemlins/wink.gif[/img]

[ QUOTE ]
BTW, I folded two big pots last night that I would have won and think both of my decisions were "good", until about 10 minutes later when my opponents were no longer unknown and were both horrible donks. We always remember those big pots... maybe I'll start calling more.

[/ QUOTE ]
The margin of error against unknowns is a lot greater than the chart allows for.

Hi all very thought provoking thread, thanks to the OP even if some early calcs were off. I have a question, given how big of a mistake it can be to consistently misjudge river calls/bets, and the assertion by some in this thread that a +-/5-10% estimate is attainable, I have to ask, how are you guys arriving at that certainty?

Are you consistently plugging in the range of hands considering the betting action/player into some formula? Poker stove? Once you have those results, how do you factor in the chance that someone is just bluffing? Do you increase your %equity after using the previous estimates? Does it not come into consideration?

I find it hard to believe that via only your hand and online reads you can guestimate within +/- 5% by only eyeballing the given situation (at least not right away). I'm asking for is what systematic approach you all use in determining your % chance good on the river for one bet.

Obviously the opponents' betting patterns, aggressiveness, trickiness, pre-flop tendencies (what did they start with), position, and the board/cards themselves have impact in deriving your actual %chances for calling on the river. But how much do you weigh each factor in coming up with that +/-5%?

I'm asking because up until now I've been using a heuristic approach that considers the above factors, but is not really precise. Now that I see how many decent size mistakes we can make here (and I probably do), I'm wondering if I'm considering all the factors correctly.

Thanks and regards!