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

I posted this at the end of Victor's "stupid 1010 hand" thread, but I'm so thoroughly confused by the resulting chart that I think it deserves it's own thread so I'm reposting. Mods can delete if they think this thread is worthless on it's own

The quoted post was made by Guy McSucker and he was quoting a portion of a post made by Victor in the aforementioned thread.

This post inspired the chart I present. The left two columns represent our winning chances expressed as a fraction and as a percentage. The next few columns are pots of various size (from 9BB's to 20BB's) and our hero's EV for each pot size.

[ QUOTE ]
[ QUOTE ]

Our House: let's say you needed him to lose 10% that hand
Our House: and it's really 6%
Our House: you're a 4% dog on one bet
Our House: you're losing 4% of $20
Our House: 80 cents bro
Our House: not $20
Victor: makes sense


[/ QUOTE ]

Math weenie jumps in to say: this is wrong.

If you're getting 9-1 (so you need to win 10%) and will actually win 6% (which I am going to approximate as one time in 16), it stacks up like this:

15 times in 16 you lose $20: -$300
One time you win $180: +$180

for a net loss of $120 over 16 trials, i.e. $7.50 a hand.

This is a pretty significant mistake.

Guy.

[/ QUOTE ]

Based on this I whipped up a real quick spreadsheet and found the results to be quite interesting so I thought I would share them.
<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.

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

I like this post. I am often calling on the river solely based on the big pot theory, and having a good hand. But, if I were to do any significant hand reading, I would see that my chances of being good are not at the required level.

Somehow I still manage to have my FRB at a rather high 46%, but I am guessing this stems from other problems. I am always feeling like I am making hopeless calls on the river that I need to stop. Doing this, while lowering my FRB will be hard, but I feel I can do it somehow! [img]/images/graemlins/confused.gif[/img]

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

I'm with you here (although I don't know my FRB percentage right now), but I do call often "because the pot is big". It appears that these mistakes are just as wrong as folding too often, unless I am interpretting the chart incorrectly.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

river decisions that seem close never matter much in terms of $ won or lost on that particular hand, but if you start making a lot of these decisions incorrectly your bb/hr will significantly decrease.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

[ QUOTE ]
river decisions that seem close never matter much in terms of $ won or lost on that particular hand, but if you start making a lot of these decisions incorrectly your bb/hr will significantly decrease.

[/ QUOTE ]

Umm... I think that what you say is obvious to everyone in this forum. It also has nothing to do with the chart in my original post.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

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

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

Almost any reasonable poker decision is quite "small". A decision worth 0.25BB is actually quite a healthy size.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

[ 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 agree with this.

Surf

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

[ 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 always knew that what Ed said was an over simplification and understood that folding wasn't as big of a mistake as it was made out to be but until I saw this chart I didn't realize how close the mistakes of folding and calling really are. I didn't know they were of bsimilar magnitude. I was under the impression that folding was much less of a mistake than calling if you were off by the same percentage in either direction around the break even point. I had never done the calculation (I am not sure why - I guess I just blindly believed Sklansky and Miller on this and never explored it myself).

That's why this chart was such an eye opener for me.

Now I wonder why we still always talk about how we should call "because the pot is big" in this forum. I see it all the time, and I often say to myself "ayup, that's good reasoning".

I expect my fold river % to go up in future sessions. I also expect my EV to go up as a result since I will be listening to my reads more. If my reads are wrong, so be it, at least I will be using them.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

I'm going to use this thread as an opportunity to repeat a question I haven't yet been able to elicit an answer for: how do we know what the "correct" number is for folding at the river?

Is the concensus view simply based on the numbers respected players have generated, or is there any mathematical basis for the opinions about how often (or how rarely) one should fold at the river?

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

I guess the reason we say call because the pot is big is because very rarely can we be so sure of our "reads" online, a 4% difference is very difficult to really identify. Given the very random nature of many peoples play makes it difficult to accurately pick a number that really is our pot odds for calling on the river, and Ed and Sklansky's idea is that generally for this reason it's better to call than fold because it's more often correct (which I think we know it is). Also for metagame reasons that I think are difficult to quantify many people have built a game around not folding much on the river.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

[ QUOTE ]
I'm going to use this thread as an opportunity to repeat a question I haven't yet been able to elicit an answer for: how do we know what the "correct" number is for folding at the river?

Is the concensus view simply based on the numbers respected players have generated, or is there any mathematical basis for the opinions about how often (or how rarely) one should fold at the river?

[/ QUOTE ]

from my understanding of it this stems from a "look at him, he's good, wins alot, and folds xx%. that's probably best"-type thing. certainly FRB should be lower at 6max than full ring b/c we are folding less in general, but your playstyle weighs heavily on this.

Players like Josh who check behind on the turn to call river bets in aggressive games will have a much lower FRB than someone like me who fires again often, so if i'm faced with river aggression it's usually a c/r or a donkbet after a free SD raise which I can usually confidently fold to. Reads change this pretty significantly, as do the games you play in...the party 20/40 i fold much less than I do at UB 10/20.

Surf

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

.33 BB is a huge mistake. river decisions are the most important in a hand, by far, imo.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

[ QUOTE ]
.33 BB is a huge mistake. river decisions are the most important in a hand, by far, imo.

[/ QUOTE ]

You're right, of course. That is another thing that this chart illustrates - just how important good river decisions are. You don't have to be off by very much percentage in either direction before you are making a significant mistake.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

[ QUOTE ]
I guess the reason we say call because the pot is big is because very rarely can we be so sure of our "reads" online, a 4% difference is very difficult to really identify. Given the very random nature of many peoples play makes it difficult to accurately pick a number that really is our pot odds for calling on the river, and Ed and Sklansky's idea is that generally for this reason it's better to call than fold because it's more often correct (which I think we know it is). Also for metagame reasons that I think are difficult to quantify many people have built a game around not folding much on the river.

[/ QUOTE ]

I agree with this, and that Ed Miller's idea of calling "because the pot is big" is a pretty good reason. Obviously there are times where a fold is easy. But looking at the chart, its very very hard to calculate with certainty your exact chances of winning the pot to make the correct +EV decision. Since it will often be close, it is always better to err on the side of calling. This is because if opponents see you folding many rivers, it encourages them to bluff at you when for example they missed a draw they have been playing stronly. The increased chances of your opponents bluffing makes it even harder to calculate your exact winning %, which causes us to make even more mistakes.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

[ QUOTE ]
[ QUOTE ]
I guess the reason we say call because the pot is big is because very rarely can we be so sure of our "reads" online, a 4% difference is very difficult to really identify. Given the very random nature of many peoples play makes it difficult to accurately pick a number that really is our pot odds for calling on the river, and Ed and Sklansky's idea is that generally for this reason it's better to call than fold because it's more often correct (which I think we know it is). Also for metagame reasons that I think are difficult to quantify many people have built a game around not folding much on the river.

[/ QUOTE ]

I agree with this, and that Ed Miller's idea of calling "because the pot is big" is a pretty good reason. Obviously there are times where a fold is easy. But looking at the chart, its very very hard to calculate with certainty your exact chances of winning the pot to make the correct +EV decision. Since it will often be close, it is always better to err on the side of calling. This is because if opponents see you folding many rivers, it encourages them to bluff at you when for example they missed a draw they have been playing stronly. The increased chances of your opponents bluffing makes it even harder to calculate your exact winning %, which causes us to make even more mistakes.

[/ QUOTE ]

Exactly.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

[ QUOTE ]
[ QUOTE ]
I guess the reason we say call because the pot is big is because very rarely can we be so sure of our "reads" online, a 4% difference is very difficult to really identify. Given the very random nature of many peoples play makes it difficult to accurately pick a number that really is our pot odds for calling on the river, and Ed and Sklansky's idea is that generally for this reason it's better to call than fold because it's more often correct (which I think we know it is). Also for metagame reasons that I think are difficult to quantify many people have built a game around not folding much on the river.

[/ QUOTE ]

I agree with this, and that Ed Miller's idea of calling "because the pot is big" is a pretty good reason. Obviously there are times where a fold is easy. But looking at the chart, its very very hard to calculate with certainty your exact chances of winning the pot to make the correct +EV decision. Since it will often be close, it is always better to err on the side of calling. This is because if opponents see you folding many rivers, it encourages them to bluff at you when for example they missed a draw they have been playing stronly. The increased chances of your opponents bluffing makes it even harder to calculate your exact winning %, which causes us to make even more mistakes.

[/ QUOTE ]

IMO this is more of an argument for a showdown-oriented game than for not folding on the river... I think players here(and everywhere!) pay off river raises far too lightly for "metagame" reasons, when pure bluff-raises or bluff-3bets on the river are in actuality quite rare... and writing it off to "metagame" is not a good excuse for lax hand-reading and proper estimation of the %age that we are behind given the aciton + the board.

Surf

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

i'm saying the same thing as baronzeus. obviously theres no such thing as a 1bb mistake unless the cards are turned over, and similarly you can never make a mistake that "costs you the pot" unless you have the nuts and openfold the river. I would think these EV calc results would be obvious.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

Hi Mark,

This provides some excellent insight and thank you for your work on it. A couple of things. First, I'm sure it was just an oversight and this in no way changes the spirit of the discussion, but if an opponent's bet brings the pot to 20BB for instance (there were 19BB after the turn betting and he bets the river), we must be good 1 time in 21 for calling to break even--not 1 time in 20. The easiest way for me to think of it is that if we are getting x to 1 odds, we need to be good 1/(x+1) of the time to break even.

This is the reason why when you tested a departure of 1.7% in both directions from what you thought was the required 5% to breakeven, you got different magnitudes for the two mistakes. The actual required probability of winning to break even in a 20BB pot is 1/21 = .0476. You can try any departure from that number in both directions and you will find the magnitude of each mistake to be identical.

One interesting change occurs when we the pot gets very large and our resulting required probability of winning to make calling breakeven becomes very small. The definition of very large varies according to the skill of the player making the estimation. For instance, lets say the pot has 19BB in it. The required probability of winning to breakeven is only 5%. I am certainly capable of misestimating this probability by more than 5% as I suspect most players are. So let's say I estimate that my probability of winning is exactly 5%. If my margin for error is +/- 6% for example, that means that I "know" my true probability of winning is could be as high as 11% and as low as zero. In this situation, I must call because the proximity of zero to my estimated probability of winning actually makes the potential mistake of folding incorrectly worse than the potential mistake of calling incorrectly. Zero has basically ruined the symmetry of the respective mistakes because although it is possible that I underestimated our probability of winning by as much as 6%, the worst possible overestimation I can make is 5% (because there is no such thing as a -1% probability).

To put it another way, if my estimate of our probability of winning is 5% but our true probability is 11%, then folding is a 1.2BB mistake. But if I estimate our probability of winning is 5% and it is actually zero, then calling is only a 1BB mistake. The less skilled a player is at estimating these probabilities, the more inclined he should be to call in a big pot when in his estimation the decision is very close.

Cartman

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

that's pretty interesting!

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

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

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

Wow, excellent post. Good things to think about.

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

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?

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

[ 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.

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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.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

[ 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

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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]

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

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On the river you need to use your judgement.

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The best part of the post by far.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

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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

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

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]

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

[ 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.

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

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

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!

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

[ QUOTE ]
[ 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.

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

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I didn't fold because of the chart - it was because of the board and betting sequence.

But you are absolutely righ.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

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I'm asking because up until now I've been using a heuristic approach that considers the above factors, but is not really precise.

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It will never be precise. Even if you could pause and go run pokerstove and excel for hours, you will still only be as good as your subjective estimates are. The fact that you can't do these indepth calculations at the table make it even more imprecise. When people talk about a player being a good hand reader or being experienced, I think it is situations like this one that we are referring to in large part. Obviously the better you get, the closer your estimates in these spots will be to the "truth".

Cartman

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

One question for Cartman about his 'Zero Philosophy' shifting the judgment towards a call. For that to be true, doesn't it assume a flat distribution? I would imagine that even in a situation like that where we need to be good 5% and we're +/- 6%, the distribution may be a bit bottom heavy to make up for the lack of range the zero creates.

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

[ QUOTE ]
One question for Cartman about his 'Zero Philosophy' shifting the judgment towards a call. For that to be true, doesn't it assume a flat distribution? I would imagine that even in a situation like that where we need to be good 5% and we're +/- 6%, the distribution may be a bit bottom heavy to make up for the lack of range the zero creates.

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Hi Moozh,

Maybe I am misunderstanding your question. My "zero philosophy" assertion did assume that we are equally likely to be off by x% in both directions. Since our estimate of how often we are good is a subjective estimate, unless the player has a natural bias toward folding or calling, it seems that this is a valid assumption. So I would expect a player's true probability of winning to be a normal distribution centered around his estimate.

I don't understand in what you mean by the distribution being bottom-heavy in this context. Can you elaborate?

Thanks,
Cartman

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

So now it's time for a new book called the "Complete Theory of Limit Hold'em" [img]/images/graemlins/wink.gif[/img]

Re: Chart - EV of Calling on the River... (is folding as bad as we thi
 

Ok, I think I'm being nitty here, but maybe these pictures will help.

I gathered that your agument said lean towards a call in those close decisions because assuming a flat or normal distribution around your estimation of how often you'll win, it's possible that the actual likelyhood of winning is a lot higher than you think, but can only be a little lower because it can't be lower than zero. (That was a mouthful)

What I wanted to consider is that you can't assume an even normal distribution around your guess.

I made these two graphs by freehand in Paint, so be nice.

http://www.geocities.com/moozh6/poker/bellgraph.GIF

In graph A, you think need to be good 5% to call profitably. Since the distribution is even, there's more area under the curve to the right since the left side is cut off. Thus, you're more likely to be better off more often than worse off. This would lead towards a call.

In graph B, the distribution isn't normal. Notice that the zero cutoff on the left has caused the bell curve to 'bunch' on that side. Thus, the areas under the curve on each side are fairly close and thus you can't necessarily lean one way or the other. I would think that graph B is a more accurate representation of the way things are when dealing with small percentages.

Did that make any sense and did it have anything at all to do with what you were saying? I think I'm just making things more confusing.