Any two suited cards revisited - some calculations

If we reject the notion of playing any two suited cards under most but not all circumstances, where do we draw the line between playable and unplayable suited hands? Attempting to judge from experience doesn't strike me as good enough because expectation is a very long-term proposition. So I've put together one approach to considering this question, and I'm interested in comments/reactions - is it totally naive? Does anyone have a better suggestion?


OK, here goes:


Having read in some of Mason Malmuth's essays that he considers Qxs to be playable against many limpers in an unraised pot--for example, as happens in a very loose passive game--but not ever coming across a reference to Jxs being okay in the same situation, I decided arbitrarily that this might be where Mason and others believe the dividing line lies between playable and unplayable.


Using Poker Proke, I then ran Q3s vs. 9 random hands and J3s vs. the same, for 10,000 hands (a small number, but all of this is ballpark anyway). This gave me a crude count of wins vs. losses. I threw out all the two-pair, trips, etc. wins and losses and stuck with flushes, which is the reason you're playing this hand to begin with. (Anyway the results say that most of the time you will lose with a two-pair based on something like Q3s.)


Let's say our equation for expected value is something like:


Cost to draw in an unraised pot, then fold

when the flop doesn't present a flush draw,

multiplied by Prob. of this event

+

Cost of making your flush and losing,

multiplied by Prob of this event

=

Profit when you make your flush and win,

multiplied by Prob of this event


... where we are solving for the profit we need to at least break even, on the right side of the equation. We have somewhat understated our costs, since now and then we'll get raised before the flop. In addition, we must estimate an average cost for losing when we make our flush - I arbitrarily set this at 6 small bets.


Solving with the values from the run of hands in Poker Probe, I get that you need to make a profit of 20.77 small bets for each pot you win just to break even with Q3s. For J3s, you need to make a profit of 23 small bets. So we might say that Qxs is about two small bets better than Jxs.


This begins to look like you'd prefer a bare minimum of a 7-way pot (i.e. 6 opponents) to play Q3s, so as to get enough small bets into the pots you win (especially in a low-limit game where you have to contend with the rake). And it looks like Jxs might be playable if you got an 8-way unraised pot or better.


As a side note, it seems to me that the above calculations don't necessarily apply to playing two suited cards from the big blind in a raised pot with fewer players. I'd want to do a separate exercise for such cases.


Comments? A pointless exercise? A better way to do it?

I threw out all the two-pair, trips, etc. wins and losses and stuck with flushes...


Why would you do that?


Anyway the results say that most of the time you will lose with a two-pair based on something like Q3s.


Should I throw away AA in a 10 handed pot because it will lose most of the time anyway?


Your analysis is flawed.

Are you taking into consideration the rake when you are determining the profitability of a hand? I'm sure there are lots of hands that could be profitable that will never beat the rake.

I threw out the two pair because you will quite often lose to someone with a Q and a better kicker. That's basic poker logic, which the simulation backs up--as does the advice of nearly everyone reputable on this subject, e.g. Slansky, Malmuth, etc. Similar reasoning applies to the other hands like trips, etc. Before you are so quick to dismiss the analysis, think about it a bit harder.

Calculations are BEFORE the rake, just to keep things eaiser. But you are quite right that this affects the profitability of any hand, especially marginal hands like Q3s and J3s.

What I meant to say is, if you have something like Q3s and make your two pair, someone with a Queen and a good kicker isn't going to be discouraged; they're going to hang around and if the board pairs or they spike their kicker you're done. Whether this is the reason or not, the simulation still indicates that you lose more with your two pair than you win when playing a hand like Q3s. If someone would like to crunch some numbers or demonstrate some logic as why this isn't so, I'd be happy to listen; but just saying "the analysis is flawed" without explaining in detail an alternate analysis isn't good enough.

I show on the Wilson software hand analyzer using a tough lineup the breaking point is between QTs and Q9s. And between Q9s & Q8s using a loose player lineup that pretty much agrees with Krieger and most other tables for drawing suited hands.

So... let me make sure I understand what you are saying... your claim is that if you have Q3s and you hit two pair on the flop, that you are now in a -EV situation and should fold? This is what I understand when you say, "you lose more money with your two pair than you win."

That's what the simulation result is: 221 wins to 1707 losses, which is pretty staggering.


The question is, why would this be the case? It may be that in real life, two-pair wins would be much higher because a human won't go all-in with them, as opposed to the computer--we'd pick our spots to bet the two pair or fold, based on the board, how our opponents are betting, etc.


However another answer might be that this was a 10-player simulation. The more players in a hand, the more likely that the winning hand will be the nuts or close to it--a flush, a straight, what have you. So 2-pair in such a circumstance may not hold up as much as it would if, say, 3 players see the flop. Given that you're likely to play Q3s with many players seeing the pot rather than just a few (unless you're in the blinds), I think it's more realistic to assume that two pair will in fact not be a winner very often.


I'd be glad to listen to arguments to the contrary...

I don't have any of his books. Which one is it? I'd like to take a look.

Fewer players, more wins for two pair - esp. the better your cards.


KQs versus two other random hands, run it for 10,000 all-in games: 1362 wins, 799 losses. Same hand but versus four other random hands this time: 934 wins, 1123 losses.


This is only an indication, since the computer is going all-in with all the hands and that's not how real games are played ... but I think it does show the trend that the more players, the less often two pair will win. And that backs up how you will tend to win with something like Q3s and many players in the pot.

I will not post to Some Gun as I found his first reply to me insulting.


You are correct. As you add additional players, the % of hands you win goes down. This happens for ALL starting hands. Of course, as you add players the greater the odds you are receiving for your hand.


To exclude all hands besides a made flush is foolhardy. If I run an all in sim with a hand containg Qc6c, a board of Qh6d, against 9 other random hands my hand will hold up 50% of the time. 26% of that is with unimproved 2-pair, 21% from a full house (yes, 2 pair turns into full houses), and the remaining from other hands. This does not sound insignificant to me.

If I ran a simulation that led me to the conclusion that I should unconditionally fold two pair on the flop, instead of questioning the value of two pair, I would question the value of my simulation.


A good place to start is with the assumptions you've made in your simulation. It sounds to me like you have ten hands playing to the showdown in your simulation. Think about how appropriate this assumption is.

Some Gun and Turbidino both focused on the number of hands won and lost. In poker, we do not count the number of hands won and lost... we count the amount of money won and lost.

I could rerun it with eight hands or seven, if that's what you're saying. That doesn't seem so impolite to me.

Right, but I guess Some Gun's point (however insulting he was) was that sometimes you make your desired hand and lose, and you must figure that into your EV.

Okay, Q3s versus six random hands - all-in for 10,000 plays. Two pair wins 367 times, loses 1674 times.


Now we know the computer didn't do anything wrong - it just ran an all-in simulation and got these results. The question is how to interpret the results.


So please tell me how you would adjust these numbers to come up with what you believe to be a more nearly correct number of wins and losses for two pair that might be added into an expectation equation. I'm looking for a useful answer here, not to win an argument.

Right, but I guess Some Gun's point (however insulting he was) was that sometimes you make your desired hand and lose, and you must figure that into your EV.


Some Gun wrote "I threw out all the two-pair, trips, etc. wins and losses and stuck with flushes..."


I stated this was incorrect, and therefore the analysis is flawed.

majorkong's point was very inportant. Dismissing it is a significant mistake.


I think the problem with your analysis is that you're using a simulator. I don't think a simulator is a very good tool for this type of analysis.


I think the first step in your analysis should be How often will I get a good flop with Q3s? The rest of your analysis should be built from that point.


I'll get you started. There are 19,600 possible flop.s When holding Q3s, you will flop:


A four flush: 2,145/19,600

A flush: 165/19,600

Two pairs: (Q's and 3's): 396/19,600

Trips: 264/19,600

Full House: 18/19,600

Quads: 2/19,600


Total Good Flops: 2,990/19,600 (15.25%)

To add to the 15.25% "good flops" with a hand such as Q3's you still might not win the money in the pot. I think that many experts have already considered these plays and have written many essays on why mostly suckers play these hands.

My point is that all-in simulations aren't worth a whole lot, because that isn't the way poker is played. It should be suspicious that the difference between expert players and novices in poker is in their decisions to raise, call, or fold; in an all-in simulation, there are no such decisions.


If I have two pair on the flop, I'm going to protect it, because as you have noticed, it is a vulnerable hand. If I think the likely bettor is on my right and I am in early position, I might check-raise to force gutshots to call two flop bets (at horrible odds) to draw out on me. An all-in simulation can't capture that.


If you are serious about simulations, I would pick up Wilson's Turbo Texas Holdem software. While it is far from perfect (poker is a very difficult game to get a computer to play even passably) it will give you much more accurate results if you craft your simulations cleverly. All-in-all, however, I feel the value of simulations in determining strategy is limited.

the results. I just wish the casino would let us put $20 each in the pot and deal five cards face up and push the pot to the high hand. Actually I don not wish this.


You must understand that poker is much more complex that this and your findings simply do not take into account that there are betting rounds and checking, calling, raising, and folding. Right now, an all-in simulation is about as worthless as tits on a boar. Read the Theory of Poker carefully if you want to know why this is true.

Thanks, Dynasty, for posting something constructive.


However my problem with approaching it the way you suggest is that I don't think basic combinations/probabilities/odds by themselves address the problems with making your hand and losing in a multiway pot. I know you're a fan of Mike Petriv's book (I think I remember you posting this a while back), so you'll probably be familiar with pages 70-76 where he tries to do a manual calculation for a very simple matchup (pocket Kings versus pocket Queens) and basically gives up. In his words, "It is impractical to caculate multi-hand probabilities and come up with all the situations and numbers. The computer and program are king in this area."


I think what would work best is a combination of a lot of experience plus a simulation. Someone who has played an enormous amount of hold'em (which I haven't) could look at the raw numbers spit out by Poker Probe and say, "well, this two-pair figure is wrong because of X, Y, and Z; try adjusting it on the basis of experience to something more like this." This is essentially what someone like Mason Malmuth does in some of his essays where he criticizes simulations. It doesn't mean simulations are the wrong approach for a complex, multi-hand problem such as the one here; it just means they can't be blindly applied. My initial figures may be too crude because I didn't adjust, but I think it's the right way to start off at least. Starting off with just basic odds isn't powerful enough for this level of problem, as Petriv states.


I know you don't have time for this, so I won't ask you - but in my opinion with your fairly reliable experience you'd have a good head start on making such adjustments. For example, if the computer consistently shows 2 pair loses much more than it wins in multiway pots with Qxs or even a much stronger hand like QJ, how would you suggest a ballpark adjustment to this to get a more nearly correct win/loss ratio? In other words what is the computer doing "wrong" with its all-in simulation that we should correct for?

Sure, all-in is not how poker is really played. My only basis for using the figures is that it's somewhere to start. How else could we solve a question like whether Qxs is positive or negative expectation in the very long run?


1) By keeping detailed records of how it does when played by a good player. Note that this rules out the expectation figures posted by online poker rooms for various hands, since we can assume that an enormous amount of misplayed hands are included in these figures, and that's not what we're interested in. Now, I don't know of anyone who keeps detailed records of every hand they play, and anyway, if Qxs is a marginal hand you're not going to get the chance to play it often enough to accumulate statistically meaningful rescords. So this option is out as far as I can see.


2) Running a Turbo simulation, as Abdul Jalib has done. This would be my own next step.


3) Trying to attack it via Dynasty's suggestion of looking at "good flops." The problem is that this approach doesn't provide a figure for how often you'll make your "good hand" and lose. As I posted to Dynasty, Mike Petriv, an amateur mathematician who has written a very detailed book on calculating odds, has rejected this approach as utterly inadequate. I think it MIGHT be okay in the hands of someone who had really thought about it and worked on it a lot - but it has many problems.


So I'm left that thinking all-in simulations, IF properly adjusted, are the best way to go to get a very rough estimate of a longshot hand's playability, i.e. can you collect enough bets when you do win to compensate for the times you don't? The key is, how do you adjust the all-in figures to get something realistic? If it can't be done, then it can't; but no one has convinced me of that yet.

You may be right that it's too hard to adjust an all-in figure - but I'm going to give it a try anyway. The Turbo idea is my next shot - I have Turbo, but it's a lot of work to set it up for a decent simulation. And as you say those are somewhat suspect too - mostly because we can't get at the assumptions built into the computer opponents.


I think the value here has to do with computing long-term expectation for marginal hands. If you don't at least attempt this, then you wind up on a slippery slope where you may well be negative expectation without realizing it. Human beings aren't built to keep track of very small incremental amounts, which is what you're dealing with when you play a longshot hand like Qxs or Jxs. And as I've stated elsewhere, in your entire poker-playing lifetime you are unlikely to have the chance to play Qxs or Jxs often enough to compile a statistically valid record as to whether these are PE hands or not. So what's left? Got to do some figurin' if we're to escape playing in the dark.

It's very crude, but with Turbo set for a very passive game and with the player holding the test hand on the button being a modified Advisor (but probably still pretty lousy), the results show Q3s holding its own with about 66 cents worth of PE - but J3s losing, with about 27 cents worth of negative expectation. I doubt these numbers mean very much - except to reinforce my conviction that big-little suited and similar hands are NOT automatically playable even with many limpers. Somewhere there is almost certainly a dividing line between positive and negative expectation, though whether it lies at J3s or lower (or higher) is open to debate.


Anyone who continues to contend that suited trash is always worth paying a single bet for if you can get enough limpers needs to show something to back this up. A general assertion isn't good enough. How many times did you limp with your suited trash and fold upon seeing the flop? Have you counted? How many times did you play it and lose? How much did you lose upon those occasions? How big were the pots when you made your hand and won? Have you kept track? If you don't keep track, how the hell do you know? It's easy with bigger & better hands to show they have PE - but with marginal hands, it ain't so easy. Making broad assertions about initial pot odds and "good flops" isn't going to do it. Better to clutch your copy of HPFAP to your chest and repeat the starting hand tables to yourself like a mantra ... Sklansky/Mason don't list J3s anywhere in those tables, nor do they list 72s or other suited trash, and maybe there's a reason why. Unless you're willing to do more work than they already did and compile new starting tables that include your additional suited trash hands, you're better off falling back on what they have to say.

In other words what is the computer doing "wrong" with its all-in simulation that we should correct for?


Here's an example of an error in the computer results which are giving you poor results.


You've got Qs3s


The flop is: Kh,Qd,7s


Someone bets (representing top pair), some callers, and you call with middle pair and a backoor flush draw.


The turn is: Kh,Qd,7s,7c


Same person bets. You must fold in this spot.


The river is: Kh,Qd,7s,7c,X


A player in a live game would have folded on the turn since almost all his outs are gone. But, the computer simulation shows you losing with two pair.

For example, if the computer consistently shows 2 pair loses much more than it wins in multiway pots with Qxs or even a much stronger hand like QJ, how would you suggest a ballpark adjustment to this to get a more nearly correct win/loss ratio


When you are trying to make two-pair with Q3s, it must be an uncounterfeited two-pair. Two-pair on a board of K,Q,7,7,3 is no good. However, two-pair on a board of K,Q,7,3,2 will win a good share of it's pots.


Try this.


Run a simulation where you hold Qs3s and the board is pre-determined to be:


Kh,Qd,3c,7h,2s


This may give you a number which allows you to estimate how often an uncounterfeited two-pair will win the pot.


Then, you need to figure out how often your bottom pair of 3's will be counterfeited.

Anyone who continues to contend that suited trash is always worth paying a single bet for if you can get enough limpers needs to show something to back this up


The origninal debate was about calling a raise out of the big blind when you were getting 9:1.


I rarely play these hands on the button. I think I would need six limpers ahead of me giving me 7.5:1 and position.

... even then I wonder. I know Sklanksy/Malmuth, Abdul Jalib and others all say to call with very weak hands indeed under such circumstances - but I would like someday to see how Sklansky in particular works out his expectation for marginal hands/circumstances. I'm sure he's got a ton of paper somewhere covered with scribbles, but he's never explicated this to my knowledge. Maybe in that 600 page book he's never going to write...

Why would you want to play Q3s -- this is a hand that rarely, if ever, will drive the betting. Perhaps from late position, if everyone has passed, this could be to steal the blinds, but, in the vast majority of situations, playing hands like this will cost a lot.

In fact, even though many books recommend playing middle suited connectors (78s, 67s, 56s), only very solid players can achieve a positive EV playing these hands.

Since, in most games, you will get paid off on your bigs hands, why waste time (and potentially a stack of checks) playing hands that will lose so often?

You flop top pair -- overcards will stay in. You flop a flush -- there are potentially 2 higher flushes out there (and someone could be drawing to a full house). You flop 2 pair -- now you have a chance to win some money, if the turn and river are kind.

Kxs has a decent chance to make a winner; Axs also has a decent chance (both from late position, either because there are a lot of loose, passive players already in, or because they can steal the blinds), but playing Qxs will cost money. At least a suited connector has a chance to hit a straight (and it might be the nut straight, which can drive the betting and win a bigger pot).


Another flaw in the calculations for this hand is that there are times when you will flop a gut-shot draw at the nut straight -- most players will stick around for this draw. Often, if you hit, you will split the pot. Usually, this will cost you money. But on occasion, this might account for some wins.


Qxs is just a bad hand -- there are so many opportunities to play good hands that can drive the betting that playing Qxs, Jxs and the like sounds like a real leak.

I don't think you've grasped the situation that Some Gun describes. The idea is that if it's a very loose passive game, you can play certain big-little suited combinations because you're getting good enough pot odds to draw to what will be a very strong flush (ignoring for now the debate over other possible hands you might make). You would only play such hands - for example K6s - in late position with many in, or possibly in early position if the game is such that limping will attract many behind you without a raise.


As for your fear that a bigger flush will be out there - with Kxs and Qxs, this is very unlikely; as other posters have pointed out, this is an overblown fear. Put it this way: if a solid player can play something like JTs and like a four-flush on the flop, why is it wrong to like a four-flush with a higher suited card such as a Q or K?


Go read some of Mason Malmuth's essays on this topic, if I haven't convinced you. Plus look again at HPFAP - they cover hands like Kxs in the discussion that amplifies the hand tables.