I was pretty sure that looking at all the postflop stuff would be good, but I also thought there wasn’t a whole lot of discussion about why we choose the hands we choose preflop, so this post will cover both aspects of the game. The preflop stuff is mostly mathematical with some reads, and the postflop stuff is mostly reads with some math…any surprises there? There shouldn’t be!!
Preflop
So…what’s a drawing hand? Basically, it’s a hand that you don’t rate to be the best right now, but has the potential to become something huge later. To be fair, any hand has the potential to become something huge, so let’s take a look at some hand-types and see how likely each of those is! This first set deals with sitting with any two unpaired cards and we’ll consider “huge” to be 2pair plus.
If we have two random, unpaired cards:
flopping EXACTLY two pair by pairing EACH of your hole cards 2.02%
flopping EXACTLY trips by flopping two cards to one hole card 1.347%
flopping EXACTLY a full house, trips of 1 hole card and pairing the other 0.092%
flopping EXACTLY four of a kind, three cards to one of your hole cards 0.01%
flopping four to a flush 2.245%
If we have any 2 suited cards, we figure the first 4 plus:
flopping a flush (including the slight chance of a straight flush in some cases) 0.842%
flopping four to a flush 10.944%
If we have connectors:
flopping a straight (including the slight chance of a straight flush in some cases) 1.306%
flopping an 8 out straight draw* 10.449%
If we have one-gappers:
flopping a straight (including the slight chance of a straight flush in some cases) 0.980%
flopping an 8 out straight draw* 8.08%
If we have a pair:
flopping EXACTLY two pair by pairing the board 16.163%
flopping EXACTLY trips by flopping a set for your pocket pair 10.775%
flopping EXACTLY a full house, a set to your hole pair + pairing the board 0.735%
flopping EXACTLY a full house, by the board tripping up 0.245%
flopping EXACTLY four of a kind, two cards to your hole pair 0.245%
Dealing with SC’s is HIGHLY math intensive…fortunately, this amazing thread has done it.
http://archives1.twoplustwo.com/show...0&fpart=1&vc=1
This is a lot of info to take in, but the general idea is that while any two cards can flop a huge hand, the likelihood of flopping something big with 27o is much lower than with 55 or 67s. Think about it. With 78s we can hit all the same types of hands that 27o can hit, but also hit straights (and straight draws), flushes (and flush draws) and occasionally straight flushes. Looking at it from an equity standpoint:
Text results appended to pokerstove.txt
41,095,296 games 0.016 secs 2,568,456,000 games/sec
Board:
Dead:
equity win tie pots won pots tied
Hand 0: 22.475% 22.29% 00.18% 9161616 74394.00 { 76s }
Hand 1: 77.525% 77.34% 00.18% 31784892 74394.00 { AA }
---
123,285,888 games 0.016 secs 7,705,368,000 games/sec
Board:
Dead:
equity win tie pots won pots tied
Hand 0: 11.800% 11.59% 00.21% 14288040 260154.00 { 72o }
Hand 1: 88.200% 87.99% 00.21% 108477540 260154.00 { AA }
It shouldn’t be much of a surprise that a suited connector holds up much more often than 27o, but realize that a HUGE percentage of this difference is from the draws (mainly because they’re both 7-high hands, so the high-card value is nearly the same. For those of you who are interested, 56s has 22.5% equity vs AA and in terms of sole high-card value, 72>56).
Why does any of this matter?
Well, assuming we’re going to play straight-forward (meaning that we’re folding if we totally miss), we’re going to need to make a good deal of money when we do hit (in order to counter the losses we incur when we miss). The amount of money we need to earn can be roughly calculated by:
Money made > preflop investment x (100\percent chance of hitting).
If you’ve heard of the 5 and 10 rule, or the 3 and 6 rule, this equation is where those rules came from. Let’s look at each aspect of this equation.
Money Made
So…what determines how much money we can make?
a) Stack sizes: Obviously, the maximum we can win is the villain’s (or villains’) stacks.
b) Villain range: The stronger the villain’s range, the more likely he is to be willing to put the monies in!
c) Villain tendency: Some villains don’t like to fold…some fold a whole lot. Those that fold less will give us more money (assuming we’re playing straight-forward)
d) Board texture: If the board looks really scary, our villain may find a reason to fold. If it looks safe, he may be more likely to pay us off.
e) Our image: If we look really tight/nitty, an observant player will fold to us more often than if we’re raising and betting all over the place.
Preflop Investment:
What do I mean by “preflop investment”? Basically, I mean the amount of money you put in preflop. (Whether you’re calling a raise, or limping in). It should make sense that the equation is easier to satisfy as our preflop investment goes down. In fact, some hands that are highly profitable to play for a small investment, are worthless when the “price of poker” gets too high. Note that this is also directly related to the effective stack size. Let’s look at a couple of situations.
Pokerstars $1/$2 (assume all other players are 100BB deep)
Villain ($ 120) (UTG)
Hero ($120) (BTN)
Hero has 6h 6d
Villain raises to $xx
Hero…?
If we look at our equation, then money made needs to be > investment x (100/10.8)
Investment x (9.26)
Since the cap on the money made is $120 (assuming everyone folds), then the most we should be willing to invest is $12.96. Of course, this assumes that villain is stacking off on every flop (which isn’t the case) so, it should actually be less than that. (The rule of 5/10 says we should be willing to pay $12 max, given good reads). In essence, if the villain raises to $13 or more, we should be folding now if our plan is to fold the flop if we miss.
However, if the stacks are $250, we can call a much larger raise and still be able to make monies!
Percent Chance of Hitting:
We’ve covered that, pretty much! Feel free to take a look back for some percentages, or…..
CLIFF NOTES (rougly)!
Hitting with jank: 5.714%
Hitting a straight or straight draw with connectors: 11.85%
Hitting a set with a PP: 10.8%
Hitting a flush or flush draw with sooted cards: 11.85%
Flopping sexy with a SC (sd, fd, combo draw, or made hand: roughly 25%
Note: Flopping sexy is not my term, but it’s awesome.
Last edited by RapidEvolution; 05-04-2009 at 12:45 PM.