Calling a pre-flop raise with the smaller pair

*Last edited by Fnord on Wed, 07 Dec 2005, 5:22am; edited 1 time in total*

Since this has come up a couple times on this board... Please correct any errors, I only have the equivalent of a minor in math. There are a lot of factors not included in this simplistic analysis such as straits, quads, flushes, other pair on board and bluffing.

Situation: You hold a small pair (lets say 22) and another player comes out with a pre-flop raise. You put him on a likely larger pair.

Your plan: Call his pre-flop bet and look for a set. Go nuclear if you get it, otherwise fold.

How much money needs to be left in both of your stacks for this to be profitable, assuming you can hit him up for lots of additional chips if you hit your set? Also assume you can't make the lay down if he makes his set too.

Odds of you not flopping a set if your opponent doesn't have one of your cards (safe assumption if you have 88 or lower)
46/48 = 0.95833333333333333333333333333333
45/47 = 0.95744680851063829787234042553191
44/46 = 0.95652173913043478260869565217391
=
0.87765957446808510638297872340227

Inverse to get odds of flopping a set
1 - 0.87765957446808510638297872340227 =
0.122340425531914893617021276598

or
1 in 8.1739130434782608695652173911537

Odds he doesn't get his set if you do.
45/47 = 0.95744680851063829787234042553191
44/46 = 0.95652173913043478260869565217391
0.91581868640148011100832562442008

Flopping a set and not losing to a better set on the turn + river (doesn't factor in your draw to quads)
43/45 = 0.95555555555555555555555555555556
42/44 = 0.95454545454545454545454545454545
0.91212121212121212121212121212068

Algebra time.
Let:
X is pre-flop betting
Y is post-flop betting
Z is the pot size = 2(X + Y)
we'll assume blinds and limpers cover the rake...

Cost for getting and playing that set is:
8.17 X + Y

You'll pay X for the flop 8.17 times to get your set, then pay Y to get showdown.

Profit on a win:
(0.916) * (0.912) * Z =
0.835 * Z

Odds of them not flopping a set times odds of not getting beat on the turn or river.

Which yields this equation to determine our break even point.
-8.17 X - Y + 0.835 Z = 0
8.17 X + Y = 0.835 Z
8.17 X + Y = 0.835 * 2(X + Y)
8.17 X + Y = 1.670(X + Y)
8.17 X + Y = 1.670 X + 1.670 Y
8.17 X = 1.670 X + 0.670 Y
6.5 X = 0.670 Y
6.5 X = 0.670 Y
9.7 X = Y

Adding in some room for profit and fuge factor, you need at least 10x the pre-flop raise worth of chips in BOTH stacks that you think you can get in the pot if you hit your set to call that bet. You probably can subtract a little for each additional caller, but not quite 1x because of the additional chance of a better 3 of a kind, flush or straight.

I don't know.

It all is situational to me. It depends on who is raising, how good they are, their position, how strong my pair is and how many callers there are. Set hands tend to be very profitbale, especially when an Ace flops with your set (say I have 66 and the flop is A,J,6). Also, if the raise is kind of high, like $2.50 or so, but 3 players call, I will take a chance with a hand like 33 or 44 on the chance of a big payout if it hits.

I get your point with the odds, but as I said, it depends on thet table, the players and position. For instance, more often than not at PokerStars, I would lay down 88 or lower against solid raises, mostly because the player pool is smaller and I tend to have a good idea whether or not I'm beat.

At PartyPoker, there seems to be more maniac players and just flat out bad players overall. I'm calling it a day at PP right now, and after 2 days I'm up $95 with maybe 4-5 hours of play total in. I won with sets at least 6 times, all of them 10,10 or lower. My tables consisted of mostly bad players, raising with hands like K10 suited, QJ suited, A9 offsuit, etc.

All of this data is based on $25 NL. At higher stakes, such as $50NL or $100 NL, I'm playing more conservative of course.

If I'm near the bottom half of the tournament standings, there's around a 66% chance they have High Connectors. Since a small pair has an advantage over any High Connector, at this point barring extraordinary circumstances I would go All-In. 66% of the time I have the advantage, and sometimes they'll fold giving me free money.

Fnord good point here. I want to have even deeper stacks because more often than not they only have 2 big cards and you will not play for stacks. Also QQ will not play for stacks when A pops. This all when you will fold if you dont hit, if you feel you have a read good enough you can also try to win the pot without hitting the set but that is a whole another story. Also, if you want to get paid the fullest, have a big stack. reloaaaaddd. (I hate short stacks)

Iconoclastic: 22 vs T9s ~= 46.2 vs 53.8
22 vs T9o ~= 48.6 vs 51.4

Wow this is so weird reading what I wrote a year and a half ago. Anyways Pingviini you're correct but I was talking about tournaments (not sure why I did that at the time) and rarely do people raise with T9 in tourneys, more likely something like AQ you know what I mean? Besides, even fewer would call an AI with T9o.

man am I taking alot of grief over this one post. What I wrote was just a single hand guys not an overall strategy. I made a good read pushed ran a bluff and pulled it off and its like some people are questioning my intelligence. As far as all that math at the beggining of this post. Thats good info but for figuring it out that far im sorry but I know the general odds for me to hit or draw something but numbers arnt everthing.sometimes you have to throw out the numbers go with youre reads or youre instnicts and just go for it. thats why its called gambling

Does your equation take into account redraws? For example i hit top set but my opponent can redraw by hiting a flush because he has the king of clubs and all 3 cards are clubs.

You are totally leaving out the fact that you can also out play your opponent after the flop. Real simple for me, if it cost me 10 dollars to see the flop and my opponent has 120 dollars or more I am calling . I need no other callers. I believe the math is important in NL but it doesn’t have to be exact. Because outplaying you opponent can not be overlooked. There is a lot of value in that.

I like the algebra equations up there... I understood those thanks for the help..

I like to call the pre flop raise when i do have a low pocket pair and just hope for that 3 of a kind..

thanks..

Reading this thread makes my head hurt.

Not sure why this isn't stickied:
Changing 10x rule to 20x rule

In my opinion you by pass all this bull chit 1.003458675 odds freakin donkey crap. Because lets face it we know who and how many is at are table and we know what the betting patterens have been and it doesent take a rocket scientist to figure out that you are going to have to get lucky to hit your set of quack quacks and if you do its all about getting paid..... Chances are if you hit your set on flop you are going to have best hand and if it looks like it is dangerous waters after you hit your set, such as, suited and or all connected flop then you better either pushem out of pot or hope you dont get split. Me, especially on dangerous flop like that I am going all in, if my opponent wants to risk his stack on the come , so be it, im committed! I know it is nice to know the odds,but it is nicer to know your cards and who you are up against. Then you throw in your math and I wish upon a star my 2&2 trips! LOL! Wink

seems to my having 10X the raise is pretty standerd. Thats like having 20 in a nL 50 game (st pf raise being 2.0)

I think we're all agreed that 10x is not enough (unless they always have AA and always felt it). The thread that swig linked earlier is a good discussion and has some good posts from Lukie in it : http://www.flopturnriver.com/phpBB2/forum/poker-31291.htm

What if the guy is raising with 57 suited and bluffs you out every time you miss your set and gives you no action when you hit?

or

You have 66, the flop is A96 and the guy had KK? how much do you make here?

You need a very good board or a very dumb opponent to double up, I think it's very easy to overestimate our implied odds with small pockets.

Stack-size is important. Of course I'm not often gonna play a medium, or low pair against the very tight/min buyin/all-iner who has just unexpectedly made an out-of-position move.

I almost exclusively play NL short-handed cash game holdem. Any pocket pair is a powerful hand.

You said initially that your calculations excluded bluffing. That's why the calculations don't work.

In practice your opponents will often bluff and if they don't show any strength (or even if they do), you should often bluff, or play back.

----

If the point of the post is, that it not profitable to call medium/small pocket-pair's with the intention of setting, or folding; then I agree entirely.

However, pocket pairs should be profitable. Preflop raise, pressure the flop. Hit sets occasionally / fold from time-to-time.

thats pretty deep dude.if I could remember all them numbers,I wouldn't even play poker.But thanks for the info.

thanks

Stack-size is important. Of course I'm not often gonna play a medium, or low pair against the very tight/min buyin/all-iner who has just unexpectedly made an out-of-position move.

this is a great post, i just had a discussion the other day with a couple of friends and i was telling them that i thought that i had read somewhere that it was about 9%. i am glad to see that i had retained the information and that i was right.

are they deep i.e starting stack or higher....am i deep...similar.....how good/bad are they sets can be over rated unless someone gets there themselves so u have to be careful particular out of postion

HOWEVER if you have postion then there are so many other factors to take into consideration if it comes unfriendly flop

example

you got 44 call in postion from lets say unknown player

flop AS 10C 9C

now u dont got any of this whatsever but but depedning at what level u play most player will c bet an aces so i often that i will normal will call here....i love to float on an a high board cause if you consider its the flop the most c betting will occur with no hand then it usually end up profitable....also if the player has no ace its unlikley he willl fire the turn out of postion so its often a great chance to take it away....alot of the time i will even raise a turn bet in postion cause i find in deep stacj cash games player are relunctant to go broke with just an ace....particular if you are playing slight;ly higher....most importantly though its importasnt not to go to deep into....if someone does bet the turn i will often just reaise just above the min if they call this they will almost never fire the river....the river bet is tricky if i know the player is good but not to good i will bet big on the end....if hes rubbish i will check alway.... if he is very good i will check....if hes average or i dont know it depends if a draw gets there i will always bet big if i cant sell that my hand has got better on the end i will check....

great post....ive learned something usefull....thanks

your very welcome

reading this posts kindly made my head spin when seeing all the endless possibilites to contemplate as a rule I dont like low pairs unless can limp in just too easy to get outdrawed with them

i like to call alot of hands preflop with the small pair most of the time your a favoriot after the flop but you just dont know it so alot of time like if im a 3 to 1 chip lead on the person ill just push them in hope for the coin flip

lol ease up on the numbers rely on psychology

multiply them together or otherwise written (46*45*44)/(48*47*46)

Thanks for the odds,Fnord
I will keep them in mind when I gaze at my low pair.
In early position I would probably raise. But in late position I call or even fold (depending on te situation on the table).
Maybe it´s all up to what you are willing to pay to see the flop.
So if I simplify you calculation. It pays 1 to 8.2 to see the flop.
After that there are to much factors. Cool

I think knowing your player and what he preflop raises on is the key but if i call and do not hit on flop i fold

i dont know the numbers that well in poker but those tits that are 20 posts before this one are 38 DD and as far as betting you better hope he's not on a bigger set or your ass is sunk because its all in or fold at that point................RUFF

im gald i found this post....ill have it in mind on tomorrow's tourney =D

.....i think 10x isn't enough tho

i thought we needed 15x the raise left in stacks just to set mine against a random hand.

We have a 1 in 8 chance of hitting a set and we basically double it for implied odds, and we have a 1 in 10 chance of our low pair, flopping a set and holding up against a higher pair (from what i understand from above), then i would have thought we'd need to double it for similar reasons, maybe even triple it becuase so many hands can beat a low pair.

So it would become the 30x rule for me, that is until we get an uber genious to solve this.

But generally if i have a low pair and there is heavy action then i'm out without a second thought, but this is just my 2nl thoughts here

regards
dh

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Calling a pre-flop raise with the smaller pair