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

[MarkD]

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.

[Spicymoose]

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]

[MarkD]

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.

[etizzle]

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.

[MarkD]

[ 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.

[krishanleong]

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

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

[Surfbullet]

[ 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

[MarkD]

[ 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.

[Wynton]

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?