An answer, or maybe just confirming what we already know

[rtrombone]

huzitup2 brought up a great point in response to my thread on no fold 'em hold 'em games. While the addition of each chaser reduces the leader's chances of winning the pot, it also makes the pot larger should the leader win it. The question then becomes, is the extra money a chaser contributes worth the threat that he represents?

When the leader's hand is TPTK, the answer is no.

I ran a bunch of simulations on twodimes. It's a common scenario: our hero picks up big slick suited UTG and raises. He flops TPTK and bets the whole way. If a chaser catches up, he will put in a raise--but not until the end, for simplicity's sake. I don't think this assumption is unrealistic, either, because the chaser may want to get some overcalls at the turn before going upstairs at the river. And of course in those instances where the chaser gets there at the river, that's when he's going to raise.

So in the first scenario our hero raises UTG with A /forums/images/icons/spade.gif K /forums/images/icons/spade.gif , a fish cold calls with Q /forums/images/icons/spade.gif 8 /forums/images/icons/spade.gif , blinds fold. The flop is A /forums/images/icons/club.gif 8 /forums/images/icons/diamond.gif 2 /forums/images/icons/heart.gif . Hero's expected winning percentage is 81.6%, and when he wins he will collect 4.5BB from the chaser (assuming the chaser calls the whole way, including at the river). Hero's expected losing percentage is 18.4%, and when he loses he will lose 4.5BB because the chaser will raise him on the river and hero will pay him off. (BBs won and lost are equal because of the dead blind money. I've rounded up, assuming a 2/3 SB small blind.) Hero's EV for this hand is 2.844 BB.

I continued adding chasers to the hand, each time figuring out the hero's EV. No surprise, it drops with each chaser. Consider this extreme example:

Hero: A /forums/images/icons/spade.gif K /forums/images/icons/spade.gif
Chaser 1: Q /forums/images/icons/spade.gif 8 /forums/images/icons/spade.gif
Chaser 2: 6 /forums/images/icons/spade.gif 2 /forums/images/icons/spade.gif
Chaser 3: A /forums/images/icons/heart.gif 10 /forums/images/icons/club.gif
Chaser 4: J /forums/images/icons/heart.gif 8 /forums/images/icons/club.gif
Chaser 5: 3 /forums/images/icons/club.gif 3 /forums/images/icons/diamond.gif
Chaser 6: 7 /forums/images/icons/diamond.gif 7 /forums/images/icons/heart.gif

Same flop, A /forums/images/icons/club.gif 8 /forums/images/icons/diamond.gif 2 /forums/images/icons/heart.gif .

In this hand, our hero's expected winning percentage is 25.3%, and he will collect 16 BB from the field when he wins. His expected losing percentage is 74.7%. He will lose 4.5BB when he loses, just like in the first scenario. His EV for this hand is 0.6865 BB!!

So clearly, in loose passive games with everyone and their mama trying to chase you down, your EV goes way down when you try to win with TPTK. Granted, this is a worst case scenario where everyone is drawing live, but I think that even if some of the chasers hold each other's outs or are drawing dead, TPTK's EV still drops with the addition of each chaser.

This is kind of disturbing to me. Is it even worth it to try to win with TPTK? I guess it is, but it's far less valuable than in a normal game.

Clearly, you have to adjust. Anytime you are drawing to the nut straight or nut flush or flop a set, you are getting tremendous odds when you ram and jam. I submit, however, that even the poorest players recognize a flop that hits them well, and will know to do this.

If everyone knows how to play properly in these games, doesn't this necessarily mean that the good player's edge is smaller?

[rtrombone]

You will get overcalls occasionally with poor players. Maybe I should have assumed an average of 1 overcall. I don't think this has too much of an effect, though.

[Dynasty]

Doing a quick caculation, you've given these six opponents, 19 outs to outdraw the hero. That just seems like way too many outs even for the whole field. If so, that's distorting your results and causing you to draw an incorrect conclusion.

Don't just focus on how many opponents you're up against. Focus on how many outs they have. Try the same scenario (6 opponents) but give them just 15 outs. Then try it with 11 outs. Try changing the # of players but keeping the outs the same (19,15,11).

[andyfox]

In the second situation, hero will only win 25.3% of the time if everyone stays until the river. Very unlikely the pocket 7s or 3s will do that. In fact, when hero bets, and A-T raises, it will more often than not become head up, and then hero is in great shape.

[huzitup2]

Top pair/good(top) kicker is one of the few hands that DOES go down in value when there is a large number of players trying to "run him down".

In general, big unsuited cards go down in valus in multi-way pots.

However, there is a big difference between "going down in value" and "becoming a -ev hand".

AK/off will lose value if 6+ players are seeing the flop, BUT, I have never seen a game where this hand does not show a profit if played correctly.

Look at it this way; you are in a "no-foldem" game and are dealt AK/off every hand - how do you think you would wind up after (let's say) 100 hours ?

My guess is that you would not be able to close your wallet /forums/images/icons/smirk.gif.

No matter the "type" of game, all premium hands retain their value.

In some games, less than premium hands go up (or become) playable but the premium hands - AK/off included - ALWAYS remain valuable - they simply lose SOME of their "ev".

I am just back from a cocktail party at which I indulged my semi-annual thirst so I'll elaborate further tomorrow.

- AK (suited or off) is a good hand in any game; it won't win many monster pots in loose games, and it will get run down more than in a "normal" game, but it is always playable and it will (again, if properly played) show a profit in any game you will ever find yourself in.

Best wishes,

- Chris

[rtrombone]

Dynasty is right that the 6-chaser hand I laid out is an extreme scenario. Many times, at least some of the people will be drawing very thin. But I don't think it is an unrealistic hand. The problem is that I don't know how these people think. How many of us have inadvertently seen the cards of the guy next to us and then been stunned by the calls he made? I've seen people call with nothing but a backdoor draw. I've seen them call with a single overcard. I've seen them call with nothing, I mean absolutely nothing. It's as if they're hoping to pick up a pair at the turn.

I would include a backdoor straight draw and a backdoor flush draw in the interest of completeness, but this complicates things because these chasers will give it up at the turn (you would think) if they don't improve to a 4-flush or 4-straight.

And in response to andyfox, when was the last time you played at a table of chasers? (Ok, so sometimes the 40-80 at Hollywood Park resembles a 3-6 game.) This bet call call call call call action is not uncommon. Especially if the person doing the betting is considered a "solid" player. They all know he has at least top pair, and are just hoping to hit at the turn or river. In the 9-18 game I described in my other post, I would see a bet and 4 calls at the turn when there was no flush or straight draw to be seen.

We don't have to use the 6-chaser hand to prove my point. As I said, I ran simulations with 1, 2, 3, 4 and 5 chasers as well. To recoup, when the hero with A /forums/images/icons/spade.gif K /forums/images/icons/spade.gif was against only one chaser with Q /forums/images/icons/spade.gif 8 /forums/images/icons/spade.gif , his EV for the hand was 2.844 BB. (Remember, the flop was A /forums/images/icons/club.gif 8 /forums/images/icons/diamond.gif 2 /forums/images/icons/heart.gif .) Add another chaser holding 6 /forums/images/icons/spade.gif 2 /forums/images/icons/spade.gif . Then the hero's EV drops to 2.397 BB. This is a significant drop, almost half a big bet a hand.

Now, if you replace the 6 deuce guy with someone drawing less live, say, someone with A /forums/images/icons/heart.gif T /forums/images/icons/club.gif , the hero's EV DOES increase--to 3.1823 BB.

To complete the comparison, let's try a chaser with 4 outs at the flop, with 4 /forums/images/icons/spade.gif 5 /forums/images/icons/spade.gif . In this situation, the hero's EV is 2.29735 BB, again, a significant drop from the heads up hand. Curiously, the 4-outer guy hurts the hero even more than the 5-outer guy. This must be because he may pick up a pair at the turn to go with his inside straight draw.

My conclusion is that compared to being heads up against a guy with 5 outs, the introduction of another live 5-outer chaser or a guy chasing an inside straight HURTS the player with TPTK. TPTK PREFERS to play heads up. Who wants the other chaser in the hand? Chaser #1 (Q /forums/images/icons/spade.gif 8 /forums/images/icons/spade.gif ). Because his chances of winning if heads up with TPTK are about 18.4%. His chances of winning if you introduce the chaser with 6 /forums/images/icons/spade.gif 2 /forums/images/icons/spade.gif don't change much. They go to 19.38% (don't ask me how they increased, ask twodimes). But the pot gets bigger for him.

As I've maintained all along, chasers benefit from each other's presence. Who gets hurt? The guy in the lead.

It looks like in truly loose games, the best hands to have are draws to the nuts. Because you're getting tremendous odds, and your hand is very safe if you make it.

But again, it seems like these hands are easier to play (just pump it), and with the playing field thus leveled, the good player loses some edge.

[Jimbo]

As I've maintained all along, chasers benefit from each other's presence. Who gets hurt? The guy in the lead.

Just wondering how you can continue to forget that although you will win less often you will win much larger pots with more chasers. As I have said before but not quite so explicitly; Would you rather win a $100 pot 22.9% of the time or a $150 pot 19.3% of the time? To me this is a no-brainer!!

[rtrombone]

Jimbo, this is exactly the question I sought to answer through simulations. Does the slightly bigger pot make up for the fact that the chaser can suck out on you?

When the person in the lead has only top pair, the answer is a resounding no.

Your EV with only one guy trying to hit a 5-outer is higher than if you have two guys trying to hit two different 5-outers. I'll put in terms of pots.

Say the limits are 15-30. You raise before the flop with A /forums/images/icons/spade.gif K /forums/images/icons/spade.gif . One opponent cold calls with Q /forums/images/icons/spade.gif 8 /forums/images/icons/spade.gif . Both blinds fold. $85 in the pot. Flop is A /forums/images/icons/club.gif 8 /forums/images/icons/diamond.gif 2 /forums/images/icons/heart.gif . You bet the whole way, he calls the whole way. If he doesn't catch up, you win a $235 pot. More importantly, you're $130 richer than before the hand. According to twodimes, this will happen 81.62% of the time.

If he hits a Q or an 8 and puts a raise in there, and you pay him off, you will have lost $135 on the hand. This will happen 18.38% of the time.

$130(81.62%) - $135(18.38%) = EV of $81.29

Say there's another chaser, someone with 4 /forums/images/icons/spade.gif 5 /forums/images/icons/spade.gif . Everything's the same as in the prior hand; the guy with middle pair calls to keep you honest at the end. You will win 61.79% of the time and drag a $310 pot. More importantly, when you win you will be $205 richer than before the hand.

38.2% of the time, one of the chasers will get there. For simplicity's sake, I assume that he raises at the river and you pay him off. When this happens, you will lose $135 on the hand.

$205(61.79%) - $135(38.2%) = EV of $75.10

So you see, you win a bigger pot because of the chaser, true, but this plus is outweighed by the times when he gets there and sucks out on you.

THIS is a no-brainer.

[Jimbo]

Here is your problem. First you are paying off on the river to a raise by a known chaser. If you do this regularly you are too weak to win in the first place so the discussion is moot. Next you created a contrived example to prove your point with a specific board that shows what you want it to show. Try changing the 2 /forums/images/icons/heart.gif in your scenario to the 9 /forums/images/icons/heart.gif and see what happens. Better yet just run two-dimes and let all the boards run out, you only win 46% of the time but that assumes they and you go to the river every time. You will not but they will more often since as you said they are chasers. Therefore you will win more often and bigger pots. Also you are ignoring blinds and other dead money in the pot for your computations making your example innacurate at best and useless in reality.

The only reason a superior player wins at poker is because they know when to call, raise, fold, semi-bluff, and checkraise. Not because they always get better cards or win everytime their hand is the best preflop. You are not accounting for superior play in your calculations and examples. In fact calling river raises from loose chasers/calling stations is far from superior.

Lastly your examples demonstrate the top pair top kicker scenarios. Previously you asserted even better hands than this (such as AA preflop against 7 chasers) lost money. At the very least you should renounce this assertion before narrowing your examples to Top Pair Top kicker (TPTK) scenarios.

I believe everyone here knew beforehand that with TPTK your hand loses value the more opponents you are up against. This is where your skill in maximazing your gains and limiting your losses comes into play. It is not some remarkable revelation that has been overlooked by poker authors and poker players for the last century.

[ACPlayer]

Very interesting analysis.

The analysis argues quite persuasively in my opinion that betting the river when unimproved in a No Foldem game is not a good idea as you are rewarding the chaser with 2BB and have a small EV on that bet.

This also supports S&M's view that AQo should not be raised pre-flop in these games, which would give more of the opponents are getting the odds to chase.

The analysis is completely consistent with S&M when they state that in very loose games to routinely throw away AJo type hands when many players have limped in but raise with Ax suited hands.

Skillful players still have a big edge in these games as they will adjust when the pots have few opponents; will know when to go for a flop check raise (and set it up in they have AK type hands in the blinds for example) to thin the field; and perhaps fold on the river when the bozo hits a gut shot 4 liner or "know" that the unexpected bet from the SB means he has just hit 2 pairs.

Note that is also appears (and I need to analyze this further) that the situation may be worse for an overpair as it cannot easily improve when all the 2 pair cards are covered by the opponents.

[rtrombone]

You didn't read my post carefully. I did assume that the blinds had folded to the UTG raise, and calculated the pots accordingly.

You bring up a good point with regard to calling the river raise. But you cannot go your entire life folding to these raises, even if you're sure you're beat. Maybe your opponent is not observant enough to notice you betting what figures to be top pair and folding to a river raise. If he is, he will surely put in a raise with garbage at some point and steal the pot from you. Just because a player likes to chase doesn't mean he's a complete idiot (although admittedly, the two usually go hand in hand). You are right that you can't call every river raise. But you most definitely cannot fold every time, either. This is straight out of HPFAP.

I used the particular board I did for a reason. I didn't want there to be any flush or straight draws, or backdoor flush or straight draws, for that matter. I wanted to be able to control the number of outs each chaser had. I wanted them to be drawing as thin as reasonably possible. Live 5-outers are very common chase hands. You don't think that changing the deuce to a 9 will help the chaser holding Q /forums/images/icons/spade.gif 8 /forums/images/icons/spade.gif ? Doing this will lower the hero's EV even more.

I can run simulations where the hero holds an overpair rather than TPTK, but I am certain the results will be the same. It's not difficult to understand why. Think of it this way. If you are holding the nut flush draw and there is a bet to your right, it is technically correct to call because you want everyone else to call behind you. You are an underdog at this point, and you want to maximize the odds the pot is offering you. If a raise will get you heads-up with the bettor (and you can't bluff him out of the pot down the road), this is a very bad play to make.

Say that a bunch of people do call behind you. You're happy! You don't care what hand they're trying to make, because if you get there, you figure to win the pot. You are making money off of their calls. But if you're making money off of their calls, who is losing money? The leader (if he has top pair or an overpair). This, too, is straight out of HPFAP.

All the chasers in my simulations are in the same situation as the nut flush draw guy above. They call, hoping for overcalls, because if they're drawing live, they'll win the pot, and each additional caller means more money for them at the end. The chaser loves when another chaser calls. But if the chaser loves it, someone has to dislike it, right? Someone does--the leader.

The question I was trying to answer with my first post was whether it's possible that too many loose chasing players can actually hurt a good player. Everyone kept saying that they would much rather play in a game with 8 bad players than 3 bad players, 3 decent players and 2 good players. I can't deny the simple logic of this. The more bad players there are, the more mistakes they are going to make, and the more likely they will be putting money in the pot when they are getting so much the worst of it that it's almost like free money.

But, as you said, hands like TPTK go down in value the more people there are trying to run you down. We are in agreement here, yet you also say that this is where skill comes in. Can skill overcome the lower EV that each additional chaser represents? I don't believe any amount of skill can overcome a mathematical truth. Sure, there will be times when you can raise and check-raise to cut down the odds a chaser is getting. But there are other times when all you can do is bet, and all they will do is call. They will do this with top pair, fearing an overpair or a better kicker. They will do it with trips, again fearing a better kicker.

I ran some more simulations, this time with the hero holding A /forums/images/icons/diamond.gif A /forums/images/icons/club.gif . The flop comes Q /forums/images/icons/club.gif 7 /forums/images/icons/heart.gif 2 /forums/images/icons/spade.gif . Chaser 1 has Q /forums/images/icons/diamond.gif 8 /forums/images/icons/diamond.gif . Chaser 2 has 2 /forums/images/icons/diamond.gif 3 /forums/images/icons/diamond.gif . Hero has raised UTG, chasers call two cold. Blinds fold.

Interesting results. Again, if you assume just one river call and the hero paying off a river raise, his EV goes down with the addition of chaser 2, from 2.8458 BB to 2.7082 BB. However, if you assume the hero folds to a river raise, his EV goes up with the addition of chaser 2, from 3.0296 BB to 3.0814 BB. Similarly, if you assume both that no chaser calls at the river and that the hero folds to a river raise, his EV goes up with the addition of chaser 2, from 2.2134 BB to 2.4546 BB. I didn't try it assuming that the hero gets no river calls but pays off a river raise, but clearly his EV will go down with the addition of chaser 2 under these assumptions.

So it looks like if you pay off every river raise, you are clearly hurt by each 5-out chaser. Clearly you cannot fold to every river raise, so the solution is to pay them off only sometimes. If you do this, you will be very close to breaking even from the presence of additional chasers.

At the very least, I hope it's become clear that more chasers is NOT necessarily a good thing.

[Philuva]

You are overlooking a critical point. Every time you raise and get 2 chasers or 3 chasers calling you pre-flop, they will not hit their hand on the flop.

If I raise with AA and I get someone calling me with Q8s and 23s, I am in heaven. If another person calls me with 56, even better. I gurantee you my EV is not going down with the additional caller with a 56 in his hand. Your assumptions are based on the fact that each of these players will make one-pair on the flop, and thus each will have at least 5 outs. Most of the time they will hit nothing, your simulations do not account for the times you win this dead money right on the flop.

It is very rare to have 3 or 4 callers and all of them drawing to 5 line outs after the flop. Of course when those situations occur, it is going to hurt your EV, but those situations don't occur that often.

[rtrombone]

I'm only considering EV issues post-flop. Bad pre-flop calls, though, is a factor definitely supporting the more "loose players = good" position. These bad calls and cold calls HAVE to be +EV for a good player.

[Jimbo]

I'm only considering EV issues post-flop.

Sorry Rtrombone but when you wrote this I felt I wrote several hundred words in three seperate posts all for naught. If you do not include preflop action with good flops for your hand what does it matter?

Since I'm already here I will address a couple of things in your last response to me. /forums/images/icons/smile.gif

I used the particular board I did for a reason. I didn't want there to be any flush or straight draws, or backdoor flush or straight draws, for that matter. In that case you did a poor job, the 4/5 suited flopped a gutbuster straight draw. I wanted to be able to control the number of outs each chaser had. You missed on that note. I wanted them to be drawing as thin as reasonably possible. Not too bad there but they had more outs than you computed. Live 5-outers are very common chase hands. Debatable but acceptable however they had more outs.
You don't think that changing the deuce to a 9 will help the chaser holding Q 8 ? Not as much as it hurts the 4 5 , use two dimes and find out, I did. Doing this will lower the hero's EV even more. Not at all, in fact just the opposite. See what I meant about contriving an example that suited your supposition?

You are right that you can't call every river raise. But you most definitely cannot fold every time, either. Using your calculations I can, and should. You cannot have your cake and eat it too. If you based your profit on them never river bluff-raising you (which you did) you cannot exclude that profit while including the losses when you call their river raise every single time. You must allow yourself to fold at a proper frequency to still show an edge. Again for your examples this frequency will be 100% of the time since you never allowed our hero with TPTK to profit by catching a bluff. (Aditionally you never allowed a chaser to fold before the river and ocassionally missing one of his outs) It can be summed up by stating that "If the chasers called bets that did not correspond to their pot odds they lost and you gained". Sound familiar? Is this clear?

The last point for this post that I will address (although there are many more to chose from) is this one:

Can skill overcome the lower EV that each additional chaser represents? Of course or else why would you ever play poker? I don't believe any amount of skill can overcome a mathematical truth. The problem is that you created a mathematical fallacy and called it a truth. Big difference, great discussion but this sleeping dog needs to take a break from the lunacy! /forums/images/icons/smile.gif

Best regards,

[rtrombone]

I added the inside straight draw after first running simulations with 5-outers only. Of course I knew what I was doing here. If you will recall, I had just computed the EV from an additional player trying to hit a 3-outer, so I wanted to see what the EV was from a guy trying to hit a 4-outer, for purposes of comparison. Remember the curious result? TPTK actually prefers to have a guy chasing 5 outs rather than 4, presumably because the 4-out guy can pick up a pair at the turn, thereby increasing his outs significantly.

I used a board of A82 because I didn't want to give Q8 guy a backdoor straight draw, which clearly helps him, as you can see below.

pokenum -h as ks - qs 8s -- ac 8d 2h
Holdem Hi: 990 enumerated boards containing Ac 8d 2h
cards win %win lose %lose tie %tie EV
As Ks 808 81.62 182 18.38 0 0.00 0.816
Qs 8s 182 18.38 808 81.62 0 0.00 0.184

pokenum -h as ks - qs 8s -- ac 8d 9h
Holdem Hi: 990 enumerated boards containing Ac 8d 9h
cards win %win lose %lose tie %tie EV
As Ks 792 80.00 198 20.00 0 0.00 0.800
Qs 8s 198 20.00 792 80.00 0 0.00 0.200


As for your argument that changing the 2 to a 9 hurts someone holding 45, of course it does, but a guy holding 45 has nothing to chase on such a board. If they're going to call with absolutely nothing, clearly that is +EV for everyone else in the hand. This proves nothing.

You repeat my point that at the river, you cannot call every raise nor fold every time. The proper frequency lies somewhere in the middle. And excluding bluffs at the river is not unreasonable, in my opinion. These people are chasers. They chase chase chase and give up if they don't get there.

The gist of everything we have talked about is this. This is the question to which I am still seeking an answer. You are in the lead. You bet. Somebody calls. He is trying to draw out on you. Now, another person calls. He is also trying to draw out on you. The first chaser clearly likes the fact that someone else has called, because it improves the odds that he is getting to draw out on you. The second chaser is likewise happy that someone has called already, because he is getting better odds than if it were just him and you. Both players' EV is higher than if the hand were heads up.

How can it be that the first caller's EV has increased, and yours has increased as well?! Isn't EV a zero-sum game? My calculations seemed to indicate that if you fold at the right frequency at the river, you can break even in terms of EV from an additional caller. Even so, how can the introduction of another chaser result in positive EV for one player and have no effect on the other player's EV...

[DKNY]

Rt, thought you were busy. Interesting stuff and very nice data to support it.

Some of you missed the point by saying stuff like, if your opponents missed on the flop they will fold and so on so your EV blah blah blah. Think about it, ideally you don't want them to fold now do you? you want them to continue. If you have AA, flop is Q 9 2r and your opponent has 54, would you rather have your opponent calling or folding?


You're right about the EV in your TPTK situation against any random hands. It's obvious your EV goes down when you're in the lead against more chasers. There's no argument, and it's a fact, if you're in the lead, the more people chasing you, the lower your EV would be.

Thing is, that's only half the picture of these passive loose games. There are going to be times where you have TPTK but then there would times where you'll be the one drawing and not in the lead and these bad players will now help you and increase your EV.

So the question is, does the positive EV you get when you are drawing and not in the lead outweigh the EV you lose when you're in the lead? If you can do some simulation for that, that'll answer your question. I think it does, because you are more likely to flop a draw than a big hand.

D