I recently had a brief conversation with a young player which got me thinking how to explain the need for multiple opponents in order to play small pairs. (Not that I have any intention of explaining how to play to any of my opponents!)

The explanation I came up with is the following: given that the odds of flopping a set are 7.5:1, if you play a small set for one small bet 68 times you will fold on the flop 60 times for a loss of 60 small bets. 8 times you will flop a set and play on. Assuming you win 75% of the time you flop a set you will probably lose an average of ~8 small bets the 2 times you flop a set and lose (your opponent will raise you with a bigger set or a straight/flush at some point.) Therefore, the 6 times you flop a set and win you have to win an average of 76/6 = 13 small bets to break even. This is difficult to do w/o at least 4-5 opponents seeing the flop.

What do you think?

Can't imagine you'd get set over setted 1/4 of the time. You might not win 100% of the time, but an underset is (and should be) expensive for you. I'd guess a flopped set on a decent board wins more like 85%-90% of the time. If you saw an overset 1/20th of the time, it would be sad. Would guess small/mid sets lose to straights and flushes much more often than to other pocket pairs.

The thing about smaller sets is that you tend to have a strong hand that is well hidden. You want action when you hit, and sets can play well out of position. This is where sets do well in games that are aggressive post flop. Connectors tend not to love this as much -- some of their draws are to gutshots and they don't like wild flop/turn action. This is where you see soft game advice for games that feature passive multiway action preflop.

If you have a set of 4's on a T94 board, when the 8 hits the turn and you get action, you have some idea that proceeding carefully is good.

The rule of thumb I used to have was that I wanted to think I'd make ~10:1 on my preflop action to play pairs for sets. 13:1 is a bigger ask, but sure, wanting mulitway action to play hands for set value is the correct concept.

There is some danger in learning to play for sets in soft games. You get habits that you have to unlearn in tougher games. You're just not going to play 33 in EP or MP very often at 20/40+. If you're going to move up, you have to understand that it can be expensive to add in limping hands to your ranges and then find out that every time you try it in a 30 game you get isolated and then the guy who iso-raised you gets 3 bet. In tougher games, pairs get to showdown in heads up pots and starting with a pair gives you other options, you steal, play well post flop, and have a hand that starts with showdown value.

You have the right general idea. If you're playing small pairs for set value, you're playing for implied odds, which means that you are hoping to get paid off down the line when you hit your set. So all of those times preflop where you call and miss need to be made up for when you call and hit.

But to echo Doug's sentiments, you're probably undervaluing the win frequency of sets. At some level, if you're saying that sets are beat 25% of the time, you're saying that 25% of the time your opponents have straights or better. That would be something like two straights or better PER ORBIT.

But your sets will lose sometimes, and that needs to be taken into account in your estimates.

Set mining in a 5-handed pot (4 opponents) is often on the wrong side of the line for me. Position matters (because this is poker), the rank of the pair matters (because hand strength still matters), and how loose and/or aggressive players are postflop also matters (because implied odds improve with aggression), but if you told me in a vacuum that there would only ever be 4 opponents when I limped with a pocket pair, I'd decline to play. I might be able to be convinced if I were on the button, but it would take a bit of data to convince me.

sometimes you'll win unimproved with your pocket pair though

This. All pocket pairs are not created equal.

Example, in typical live low limit games, you should probably be open-raising 99+ from any position and folding 22-55 in EP,

88-66 depends on position and specific table dynamics. But raising these for LP also gives you 2 ways to win post flop.

Playing pocket pairs is not solely about set value.

I'll bring attention to the thread title, which specifically indicates small pairs.

Doug hit on other ways that small pairs can have value at the end of his post.

Thanks for the comments. Looks like we're pretty much all on the same page. Regarding win rates for small flopped sets: I used 75% because I seem to lose quite often when I flop a small set. In my games there are many players who call on the flop with as little as a back door flush/straight. With four/five people seeing the turn, a straight or flush often ends up the winner. Set over set is rare, of course, but painful when it occurs!

There is some danger in learning to play for sets in soft games. You get habits that you have to unlearn in tougher games. You're just not going to play 33 in EP or MP very often at 20/40+. If you're going to move up, you have to understand that it can be expensive to add in limping hands to your ranges and then find out that every time you try it in a 30 game you get isolated and then the guy who iso-raised you gets 3 bet. In tougher games, pairs get to showdown in heads up pots and starting with a pair gives you other options, you steal, play well post flop, and have a hand that starts with showdown value.[/QUOTE]

You should know how to play in both types of games! "habits you have to unlearn" lmao. Get in the habit of playing good poker! You should know when someone is trying to isolate you...PLAY OFF OF IT! You should know difference between a tough game and a loose good game..AT ANY LEVEL! and should know how to deal with each. You should know how to handle a maniac, a nit, a pro. Until you do...ur just getting lucky when you win.

You should do some record keeping for yourself. The closer you can bring your estimates to the true value, the better off you'll be when making such estimates. Even in very loose games, 75% seems quite low.

How often is often in the bolded sentence? With ranges as wide as you seem to indicate, there should be tons of one pair hands floating in the ranges as well as drawing hands that *don't* get there. It all seems extremely pessimistic.

Good suggestion! Starting tomorrow, I'm going to keep a record of the results every time I flop a set. Will take a while until I have definitive results.

Depending on how many notes you want to be taking, you could also develop a proxy measure and just start keeping track of the strength of hands at showdown. It's an imperfect measure, but you'll get data faster.

Another X factor to consider is how often we win the bad beat jackpot w our small pairs. Like for example, if we limp 33 from the cutoff instead of rfi, the SB is now able to complete w something like 66. It’s not a strategy I’d always recommend, but the higher the bbjp, the lower the pair I’ll vpip with, and at a higher frequency (I have a system)

If the board runs out Q63 36, my first instinct would be to get upset w myself for calling the 4th bet on the river w the worst hand. But something tells me my frown would very quickly be turned upside down once I realized that I was getting “max value” w my river call. And instead of stiffing the dealer for the rest of the month, they would be getting a little overtime pay if u know what I mean lol. That’s the best part - everybody wins.

Also, my sets have been holding up 83.3% of the time so I’d agree w others that 75% might be a tad low. But again, this isn’t necessarily proper strategy. It’s just what’s worked for me. Gl!

Had me at first and then I looked at the post count. Nice level.

i think the obvious that's being unstated is having multiple opponents does drastically increase the frequency a lone unimproved pp loses and that you'll be outset or outdrawn when you do hit the set

this kind of makes it all a useless exercise unless you really get into the lab and crunch the numbers in each specific instance and all the ranges

it's easier to just know, you need good implied odds otherwise it's a losing proposition in the long run

I developed an implied odds model that includes the possibility of a hitting the draw but losing – reverse implied odds. When applied to set mining I found that the required 15 or 20 to 1 implied odds often cited is quite reasonable for a number of cases I looked at. The details can be found in the following blog:

http://holdemmathology.tumblr.com/po...t-2-set-mining

If the statman can do it, so can you. I'm the statman.

Seriously thanks for that stat; I knew the simple 7.5-1 and knew you had to account for RIO, but wasn't sure what to peg the needed odds at.

It's worth pointing out that you are not folding every time you miss a set.

55 is not folding for one bet in a limit game on a flop of 346.

The fact that you sometimes make a straight, and sometimes win a huge pot with a full house vs a straight or flush at least partially makes up for the fact that sometimes you make a set and lose.

Regarding the implied odds of set mining, I failed to note that in fixed limit, you probably don't get the needed odds because of the bet size limitations unless there are a number of players in the hand.

You're correct, but in live LHE, unless you're at high limits (over 20/40) where a high percentage of pots are HU, you'll get the right odds.

Example: You're in the BB with 55. 3 limpers to the BTN who raises, SB folds. There are now 6 sb in the pot (assuming the folded .5 sb is the rake), so you're getting 6:1 to call.

Not enough to set mine? It actually is since unless the limpers are idiots they will call, so true immediate pot odds are 8:1.

The above is a pretty midrange scenario in low limit LHE.

Post flop, unlike in NL, when you flop your set you'll likely get c-bet by the original raiser and if you just call, you'll get overcalls. Also unlike NL, normally betting, or even raising OTF and/or OTT will not usually fold out everybody.

In limit, you don't make your implied odds by taking one opponent's stack, you make implied odds by taking a few bets from more than one stack, and you often have immediate pot odds to see the flop.

That's a bad example because in bb defense you have to think of things in terms of equity as well. I think with any pair, you'll have the equity to call one extra bet out of the bb no matter how many ways it is.

True enough. I'm thinking about the 4/8 games I play where HU pots are few and far between.

If I was in a 4/8 game where there was frequent bb defense I would get up and leave. lol

*in Asian accent*

"Y U fold pahket pear?!"