The river card syndrome

[PrayingMantis]

This is my first post here. I usualy post at the SNG's forum, or the tournies, but I have this thought for a while now, and decided to post it here. I apologize for my English, I hope you won't find it too rigid.

I play poker mainly on stars, and I've noticed that people there have this strange feeling about the river card. I guess it is common everywhere, on other sites and in poker-rooms. For example: let's say 2 players are all-in. One with AK, other with 55. Now, if one of the flop-cards will be A, (for the AK to beat 55), nobody will say anything. But if the RIVER will be A, often somebody will say something about the river, how bad or good the river cards are today. Statistically there's no different if it's the turn or the river, but the psychological effect of the A on the river is much stronger.

(Attention, bad beat story ahead /images/graemlins/smile.gif)

In my last SNG I lost twice: first time with TT vs. 44 (river: 4), survived, and when I was HU, lost with JQ vs.92, board: J256 (pushed here) river: 9, to give my opponent 2 pairs. Now, these are only two bad beat anecdotes, but I know I'm much more inclined to tell them (or remember them) because it was the RIVER card that busted me (or my opponent, it doesn't matter).

I'm saying that something about the river cards make people see them as completely different entity than other board-cards. Some people feel they have "river-curse", others feel the river cards love them . Again, people at stars call this site "river-stars", and of course there's nothing special about the river cards on stars, but there's this FEELING, and the feeling gets into people and when it happens (like in the aforementioned SNG anecdotes), you do feel there is something in it, that river cards have this way of behaving… As I don't know anybody who feels that the turn cards love him today, or hate him today.

Just a thought.

BTW, I know that by definition bad-beats usualy occure on the river, but I think there's something more in this than just this statistical fact. That's why I'm posting it here...



PrayingMantis

[SevenStuda]

Thanks for boring me to death.

[andyfox]

I think the explanation is indeed partly psychological. It's like losing a ballgame in the 9th inning when you were leading after 8. It doesn't matter when the runs score, only who scores more, but it does hurt more when you only have one more inning to go.

Ditto in hold 'em. There was the pre-flop action and then the flop and then the double stakes on the turn. The pot is pretty big by now and you feel you have the best hand all you need is for the odds to work in your favor; there are usually just a few cards that will beat you. And then BOOM. There it is and you lose. How could that guy hit his flush when you've missed fity-three of them in a row?

[Nate tha' Great]

[ QUOTE ]
I think the explanation is indeed partly psychological. It's like losing a ballgame in the 9th inning when you were leading after 8.

[/ QUOTE ]

You should ask Joe Tall about this.

[PrayingMantis]

[ QUOTE ]
Thanks for boring me to death.

[/ QUOTE ]

This is another interesting psychological phenomena, one can find on these boards. I've noticed that poeple who reply repeatedly only with one-liner belittling posts, usualy don't ever post anything more than those one-liner reply posts (afraid to be thread-commited?), and almost never post any original post, to open a new thread with, never ask any questions, never elaborate on their thoughts or reasons for anything. I wonder why.


So, thanks for replying while dead.

Hope you'll resurrect soon /images/graemlins/smile.gif.


PrayingMantis

[Joe Tall]

Click Here (http://www.riveredagain.com/articles.htm#Tall_Enjoy_a_Bad_Beat)

Peace,
Joe Tall

[PrayingMantis]

I liked your article. the whole site looks like an interesting place. I'm not sure I was specifically thinking about the emotional aspects of bad-beats (in my post), but rather about the fascination people have with the river cards, whether they save them, or break them.

However, I have a question regarding your article.

[ QUOTE ]
The bad player just announced to the table that they are here to pay you off next time. Granted it cost you a few bets to find this out but that player will be folding on the river or calling with worse hands more often than they’ll be dragging the pot

[/ QUOTE ]

You talk about how one should enjoy his bad beats. I tend to agree this is quite possible in a ring game. But how can anyone really enjoy it in a multi-table tourney, when a 4 outer bad-beat bust him on the bubble?

Of course you "need" these bad-beats in tournies as in ring-games, you want bad players to chase you and call your all-in with their gutshots, but I suspect it is quite impossible to treat it as in a ring game, at least for one important reason: you won't be able to "enjoy" this weak player anymore, at least not now, because you're out.

Do You have any mathematical suggestions for dealing with *this* kind of agony?


PrayingMantis

[Joe Tall]

[ QUOTE ]
you won't be able to "enjoy" this weak player anymore, at least not now, because you're out.

[/ QUOTE ]

Yes, short term gratification is impossible when you are snapped off in a tournament. However, you like to play tournaments, correct? You play them frequently and will have 100s more to play in the future, correct?

Well if all those bad players stop catching those long-shots, they may never be another tournament to play in. It's just a longer run in tournament play.

I guess you are a fallen soldier but will still win the war in the end.

Peace,
Joe Tall

[bigpooch]

I was especially amused by "Business as usual at the Mirage"
and am looking forward to browsing the rest of the site!

[CrisBrown]

Hiya P.M.,

I think it's partly a matter of expectation and partly a matter of control.

Regarding expectation, by the time the river card comes off, a player has built an expectation about the hand in play. I'm not talking about the $ expectation, but the emotions invested in an expected outcome.

E.g.: T.J. Cloutier vs. Dot-Com in the Legends of Poker tournament this year. T.J. gets his opponent all in; T.J. has JJ, and his opponent has 77. T.J. cracks a smile. Flop is blanks. T.J.'s face starts to brighten. Turn is blank. T.J.'s face shows his expectation ... he'll be heads up with Mel Judah for a shot at his third LoP title. River ... 7. BOOM ... that expectation gets gutted.

If the 7 had come on the flop, T.J. would not have invested any more (emotionally) into that hand. But with each blank that fell, his emotional investment grew. And that's one reason why the river beats hurt worse.

As for control, most of the time the betting is over (or practically over) by the river card. You no longer have control over the hand; that control now resides in the dealer and the deck. Even if you do still have chips to bet, if the river card is one that obviously killed your hand (e.g.: you had QQ and an Ace falls on the river; your opponent pushes all-in ahead of you) you've no choice but to fold. You're helpless, and most of us don't like to feel helpless.

Put the two together and I think that's why river beats hurt so much more than others.

Cris

[PDosterM]

One reason the river often provides a beat is that the number of five card poker hands dramatically increases as the hand progresses. Specifically, there is one five card poker hand after the flop (his two cards and the three on the board); there are six at the turn (take each of the six cards away individually to leave six five card hands); and there are fully twenty-one at the river. If someone stays in until the river (as happens all in), he will make his best hand on the river fifteen times out of twenty-one.

So people are noticing what is actually a real effect.

[Toro]

Hence the over general cliche "all in always wins".

[J_V]

If I see another "enjoy a bad beat" post, I'm gonna yack over my keyboard.

[CrisBrown]

Hiya PDosterM,

Thank you so much for clarifying an obvious (but only in retrospect, of course) point. I'm not being sarcastic; this is one of those things that once you see it, you're left wondering why you hadn't seen it before. But it will help me in coping with the river beat syndrome!

Cris

[glen]

This guy is the most worthless poster I've ever seen. Everything you said is true. . . some people provide comedy or at least raise interesting and worthy issues out of their extreme views, but that is not the case with this cat. . .

[Al Schoonmaker]

I'm embarrassed to admit that I hardly ever thought of the issue you just raised, and I never did the "computations."
Thanks,
Al

[Dov]

This is why it's important to punish people who limp in with garbage early in the hand. They are much less likely to make a hand until the river.

[PrayingMantis]

That's a very interesting point.

However, you write:

[ QUOTE ]
If someone stays in until the river (as happens all in), he will make his best hand on the river fifteen times out of twenty-one.


[/ QUOTE ]

This has more to do with the probability forum, but can you explain why this sentence is true?

On the flop there's 1 possible hand, on the turn 6, and on the river 21, which is 15 "new" possible hands. But I'm not sure that the spread of "best hands" is equal for all streets - I will assume that reasonable players will have their "best hand" earlier, and *that* will diminish the probability of "making the best hand on the river" from 15/21 (that you state) to a lower number.

The 15/21 probability will be relevant to "random hands", played from PF to the river all-in.

Am I missing something here?


PrayingMantis

[PDosterM]

Praying Mantis,

No, you did not miss anything. Clearly the play of the hand affects whether someone stays to the river or not. The original post hypothesized two people all in, and that is the question I addressed.

But if you do see the river, you will make your best 5-card poker hand there 15 of 21 times. Sometimes it doesn’t matter much. You might improve AAKK7 to AAKK8 by getting an eight on the river. It’s not quite true that “reasonable players will have their ‘best’ hand early.” What is true is that reasonable players will have an adequate hand in order to continue.

This is the psychology forum, and my post was meant to simply point out that a large fraction of hands are actually made on the river, hence creating the (correct) perception that you get beat by the river a bunch.

(If this was the mathematics forum, I would have found a better term than “bunch.”) /images/graemlins/smile.gif

[colgin]

JT,

You can't link to your excellent piece enough times. Thanks once again. Eventually everyobody here will read it and we will get to stop reading "bad beat" stories.

Colgi

[TripDuck]

[ QUOTE ]
Click Here (http://www.riveredagain.com/articles.htm#Tall_Enjoy_a_Bad_Beat)

Peace,
Joe Tall

[/ QUOTE ]Nice article, Mr. Tall. Thanks.

[PrayingMantis]

This is maybe getting still deeper into the mathematic side of the matter, but I rather enjoy dealing with it here, without the mathematic jargon (I liked your use of "bunch", for example /images/graemlins/smile.gif).

Anyway, I'll try to make it a bit more complicated. And you're right, I misudsed the word "best", thinking only of what "matters" to the player.

[ QUOTE ]
You might improve AAKK7 to AAKK8 by getting an eight on the river.

[/ QUOTE ]

Let's say you are all-in, against one opponent. After the turn you have your best hand of XXXXX. On the river there are 44 cards to come. With an even spread of them, and without taking in calculation any relevant "outs", 22 cards will make your hand "better", 22 will not make it better. So, rougly speaking, only half of the time your hand will become "best" on the river. Out of 21 possible hands, that's only 10.5.

If so, the probability of making your best hand on the river is only 1/2, which is less than 15/21. And still, this is obviously much more than the probability of making your best hand on any other specific street.

What am I missing now? /images/graemlins/confused.gif /images/graemlins/smile.gif


PrayingMantis

[PDosterM]

Praying Mantis,

I believe your logic error is here: [ QUOTE ]
On the river there are 44 cards to come. With an even spread of them, and without taking in calculation any relevant "outs," 22 cards will make your hand "better," 22 will not make it better.

[/ QUOTE ]

I know of no reason why this should be true. (A proof would be interesting if it is.) For example, consider hole cards of 2/images/graemlins/spade.gif 3/images/graemlins/diamond.gif and a board of 4/images/graemlins/club.gif 5/images/graemlins/spade.gif 7/images/graemlins/heart.gif 8/images/graemlins/diamond.gif. Every remaining card in the deck improves this holding. I think if you get out a deck and try several random 6-card holdings, you will find that substantially more than half the remaining cards improve the current best five card poker hand.

I tried 10 random trials and got the following: (Note at the river there are 46 cards left – you can’t count the two in your opponent’s hand because they are just as unknown as the ones in the remaining deck.)

Better Not Better
34........12
42..........4
32........14
27........19
46..........0
37..........9
34........12
30........16
37..........9
14........30

In my (admittedly small) sample, the hands improved 72.39% on the river. Note that 15/21=0.7143. (Scary how close that was and honest, I didn’t cheat.)

Look at this as just a simple combinatorics problem. With seven cards, there are 21 5-card hands. One is best and there is no particular bias for it to be anywhere in the list. So how many hands use the last card? The answer is 15.

Hope this helps.

[spike]

Another aspect of this River card syndrome is like this...

Midway through a Pokerstars tournament and an EP player pushes all-in pre-flop. I have him well covered and I have AA so I reraise to get him heads-up and in this I'm successful.

Cards are shown since there's no more money to be bet and he has 77.

Flop contains a 7 giving him a set and I get that sinking feeling. But the river is an Ace and he's out.

He then hangs around on the rail to whine about how I rivered him and how lucky I got.

Hmmm... AA beats 77. I was pretty damned lucky that's true.

I love it when the losers in these online tournaments hang around as observers to whine about their bad luck and the bad play of their antagonists :O)

[PrayingMantis]

PDosterM,

Thanks for taking the time to answer and do the simulations. But I'm sorry, I'm still not completely convinced. I hope you'll understand why.

[ QUOTE ]
For example, consider hole cards of 2 3 and a board of 4 5 7 8. Every remaining card in the deck improves this holding.

[/ QUOTE ]

That's true, but you can take a contrary example. With hole cards of AK, and a board of 9TJQ (no flush possibility), NONE of the cards in the deck will improve this holding. (BTW, I agree that you can use 46 instead of 44 remaining cards in our "calculation". Actualy, you can use any random number of remaining cards, because you're not dealing with pot-odds here).

Regarding your simulation. I think that if you choose only 10 hole-cards and boards, they will probably be skewd significantly towards one side or the other (whether MANY river cards improve them, or only few). But your experiment is interesting.

I've tried one simulation myself. I dealt 2 hole cards, 4 board cards, and a river, to see if it improves my hand or not. Then I shuffled and dealt again. I took my time and did it 200 times, each time with a different hole cards, board, and river. These were actually 200 regular holdem hands, played to the river. It's a microscopic sample, but I was only trying to "feel" the statistics here.

The results are these: 61% of the time the river made the best hand. 39% of the time the hand didn't improve. The results were very similar for the first and second 100 trials (about 60-40 on both sequences). And I use "best hand" the way you did: AAKK7 to AAKK8, is improvement to best hand.

I know you cannot tell much by that, but even with this small sample, the difference of 10% from what you say, is siginificant, IMHO. I'm sure it wouldn't be difficult to try and make a serious simulation here, with ten thousands and more of hands. Any volunteers? /images/graemlins/smile.gif

(Of course, my last assumption of 50% improvement on the river desn't look too good now, But that's another story.)

[ QUOTE ]
Look at this as just a simple combinatorics problem. With seven cards, there are 21 5-card hands. One is best and there is no particular bias for it to be anywhere in the list. So how many hands use the last card? The answer is 15.


[/ QUOTE ]

I completely understand what you mean by that. It's just that I feel this is not quite "a simple combinatorics problem". At least for one reason: the probability of the river card improving the hand, is dependent by the cards already out. Our 15 new "river hands" have to "beat" one of the six hands we already have, and if higher cards are already dealt, this diminish the probability of our "new hands" to do so. In some ways, this situation resembles cards-counting problems in Blackjack.

That's it. And I know I could be absolutely wrong here, but I'm taking my chance... /images/graemlins/wink.gif.

PrayingMantis

[PDosterM]

Praying Mantis,

I’m only trying to make two points here.

1) The first answers the original post: The river creates more hands than the flop or the turn so you do tend to get “rivered” more than you get “turned.” (One of our local players has been known to exclaim, “Oh no! You rivered me on the turn.”)

2) Your gut feel that 22 of 44 (corrected now to 23 of 46) cards improves is incorrect. I agree that you can specify a 6-card combination that can’t be improved, but the number of such non-improvable combinations is far fewer than the number of 6-card combinations that can be improved with all remaining cards – for example any combination resulting in the high hand being no pair and which also contains a deuce and a trey. (The proof of this statement is left as an exercise for the student.)

So I stick to my original thesis that people are observing a real phenomenon.

Your observation: [ QUOTE ]
the probability of the river card improving the hand is dependent on the cards already out.

[/ QUOTE ] is true but leads you in the wrong direction. You must consider all 6-card combinations – some favor improvement, some don’t – and you will find that they will be biased to being more likely to improve. It will settle in at our 71% value.

[PrayingMantis]

PDosterM,

Fair enough, I'll accept the 71% (at least until I find a different way to solve it, or think about it /images/graemlins/grin.gif).

Thanks for the discussion, it was really interesting,

PrayingMantis

[PrayingMantis]

I'm revisiting this old thread, to share some new thoughts in the subject. (The subject was why people tend to see the river card as having more "powers" than any other board card in HE, and why they feel they're often get outdrawn on it. There were some very interesting replies here, specifically by PDosterM)

This has to do with some probablity calculation, so I'm cross-posting this in the probability forum too.

Assuming player A holds AA, and player B holds 22. They are both all-in pre-flop. 22 will outdraw AA a little less than 20% of the time.

I'm doing here a really rough calculation, *without redraws*, not to complicate it. So, I assume 22 beat AA by hitting his set card.

Now, looking backwards, on what card of the board was it more probable that player B would hit his set? (I'm calculating the outs from a 48-cards-deck to begin with, since we are accounted for 4 known cards)

First card: 2/48 = ~0.04167

Second card: 2/47 = ~0.04255

Third card: 2/46 = ~0.04347

Turn card: 2/45 = ~0.04444

River Card: 2/44 = ~0.04545

It is clear that the chances player B outdrew player A by hitting his set *on the river*, are bigger than the chances he hit it on any other specific board card. Not by much, but the difference is there. I assume this kind of small difference will be there for any draw, against any made hand.

This is a very simplistic calculation, but I believe it sheds some interesting light on this "river card syndrom".

Any thoughts?

[TomCollins]

You are forgetting something basic. Let's change the game to make it 100% rock solid and not having to worry about redraws. Player A is given a 2, Player B is given an A.
A deck of 10 cards exists, one of which is a 2. The other cards are blank.

So we turn over the cards in order, which brings us several cases.

1) The first card is turned over and is a 2. The second card is obviously a blank. (1/10)
2a) The first card is turned over and is not a 2. The second card is not a 2 as well (9/10)*(8/9)= 8/10
2b) The first card is turned over and is not a 2. The second card IS a 2. (9/10)*(1/9)= 1/10

So with this case, since there is only one 2, the second card clearly has an equal chance as being the 2nd.

But, according to your logic, the first card has a chance of 1/10, and the second card is 1/9. This is incorrect because you assume the first card is not a 2 (9/10 chance), so we must multiply the two together.

Hope this helps.

[PrayingMantis]

[ QUOTE ]
You are forgetting something basic. Let's change the game to make it 100% rock solid and not having to worry about redraws. Player A is given a 2, Player B is given an A.
A deck of 10 cards exists, one of which is a 2. The other cards are blank.

So we turn over the cards in order, which brings us several cases.

1) The first card is turned over and is a 2. The second card is obviously a blank. (1/10)
2a) The first card is turned over and is not a 2. The second card is not a 2 as well (9/10)*(8/9)= 8/10
2b) The first card is turned over and is not a 2. The second card IS a 2. (9/10)*(1/9)= 1/10

So with this case, since there is only one 2, the second card clearly has an equal chance as being the 2nd.

But, according to your logic, the first card has a chance of 1/10, and the second card is 1/9. This is incorrect because you assume the first card is not a 2 (9/10 chance), so we must multiply the two together.

Hope this helps.

[/ QUOTE ]

Thanks for replying. No, I'm not forgetting anything, I'm only looking at it from a different perspective.

First, I would suggest reading my last post in the probability forum, this is a clarification of my original post:

internal probability and river card syndrom (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=623279&page=0&view=ex panded&sb=5&o=14&fpart=1)

Now, I will take your example and try to show what I mean.

We have a 10 cards deck, one of the cards is a 2. We have a player who's waiting for this 2 to come. (That's all we need in this example, to make it even more simple). We are dealing the cards one after the other.

The prob. the 2 is the first card: 1/10 (no problem here).

The prob. the 2 is the second card: (9/10)*(1/9)=1/10 (as you said). From an external view, it is indeed the same. and so on for any other card that will be dealt.

HOWEVER, in the perspective of the player who's waiting for the 2, after it didn't show as the first card, it is already clear that the 2 didn't show on the first card. Otherwise, he woudln't be wating for it NOW. But if we look at the probability that the 2 will show as the 2nd card, which means NOW, it's obviously 1/9, since we know (and the player knows) that it didn't show on the first card.

So, from an "interanl" point of view, our player will be much more ready to see the 2 come now, than he was before the first card was dealt. Actually, it is (1/9)/(1/10)=(10/9)=1.1111 times more "probable" that it will show now.

As more and more cards are dealt, and the 2 havn't shown yet, the probability that he'll show on the next card (from an "internal" view) is P(n+1)/n, while n is the cards left in the deck now, and P is the probability of the 2 falling on the previous deal.

In your example, after 9 cards were dealt, our player KNOWS that the next card will be the 2. The probability is, then, 1.

That was my point. To look at it from another angle, more "psycological", take player A from my original example, the one who holds AA against player B, who holds BB.

Player A is pessimistic is his nature. He has a feeling that player B will outdraw him by hitting his set. They are both all-in, so there's nothing player A can do, but to watch the cards fall, one by one, and talk to himself.

Before the first card falls, he tells himself: "the 2 will come NOW". If it didn't, he'll say the same thing before the next card falls, and so on, up until the river.

From an "internal" point of view, he'll be right about his pessimistic prophecy more times ON THE RIVER (or JUST BEFORE the river, actually), than on any other specific card (see my original post, and the link above to see the simple calculation). By a small margin, true, but still. Hence, the river card syndrom.

I hope this is more clear now. I'm ready to read more thoughts and criticism.

[Paul2432]

22 will beat AA by sometimes making a straight or flush on the river when the board shows a four card straight or flush.

This cannot happen on the flop and is much less likely to happen on the turn. I think this would account for much of the discrepancy.

Paul

[PrayingMantis]

[ QUOTE ]
22 will beat AA by sometimes making a straight or flush on the river when the board shows a four card straight or flush.

This cannot happen on the flop and is much less likely to happen on the turn. I think this would account for much of the discrepancy.

Paul

[/ QUOTE ]

That's a good point, but it has more to do with the fact that on the river you are more likely to have your best hand than on the turn or flop. See some of PDosterM posts in this thread, about this.

However, I'm refering here to a different "phenomena", that has more to do with the fact that when you're waiting to the river card to fall, and your (or your opponent's) miracle card or cards *havn't appeared yet*, it's more probable that it will appear now, than on any other specific street (I'm talking about "internal probability", probability at the point of action, i.e., right before the actual next card falls) since you know that the deck is *smaller* now, but your miracle card is still out there.

[Gonzoman]

Just FYI... the 'internal probability' concept you have here is called conditional probability, i.e. the probability of something happening given that something else has already happened.

[PrayingMantis]

[ QUOTE ]
Just FYI... the 'internal probability' concept you have here is called conditional probability, i.e. the probability of something happening given that something else has already happened.

[/ QUOTE ]

Yes, I'm aware, of course, to this term. But I wanted to use a different title, that marks the difference between an "exterior" point of view (what we know should happen without being "part" of the evolving occurence), and an "internal" one, that expiriences the occurence (the dealing of the cards), from within.

But essentially you are right, and whether you call it "conditional" or "internal", I just wanted to show that it might be a better perspective to understand how people react to random events, than the "non-conditional" probability perspective.

[JNash]

I agree with those that have commented that losing on the river hurts more because the build-up of expectations makes the let-down worse. I'd like to add a couple more thoughts...

Because of "selective memory", you tend to really remember the bad beats. When you're the favorite and win the hand, everything is as it should be with the world. But when the long-shot beats you, something "unusual" has happened, which is therefore more memorable.

The other aspect is that on the flop there is less money in the pot, but on the river the stakes are higher, so it hurts more.

[3rdEye]

That's a pretty interesting way of looking at it. Also, part of it is definitely due to the fact that the turn card will often significantly increase the number of outs available to the underdog, increasing the probability that the "river" card completes the suckout (which happened to me a while ago when I had KK against A8...the guy hit running 8s on the turn and the river).

[3rdEye]

The number of cards that can improve your 5-card hand is not necessarily equal to the number of cards that don't help you. If you have KQ and the flop comes KKQ, the only card that will improve your hand is the one remaining K.