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

[imitation]

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.

[Surfbullet]

[ 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

[baronzeus]

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

[MarkD]

[ 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.

[ 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.

[imitation]

[ 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.

[Surfbullet]

[ 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

[etizzle]

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.

[cartman]

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

[Lmn55d]

that's pretty interesting!