Help with a bet on poker odds please!

Factual Questions
1

My friend and I are stuck on a bet and I am pleading with the Straight Dopers to help us with this one. It is about poker and which hand is better than another. So here we go…

It is said that in Texas Hold’em a 2 and a 7 in the hole are the worst cards to have. Here is a quick reference as to why…

My friend disagrees with this and believes a 2 and 7 are better than a 2 and 3,4,5,6. His reasoning is that since a 7 is higher than a 6,5,4 or 3 you are more likely to win. He does not believe that the possibility of a straight helps the odds of a 2 and 3,4,5 or 6 winning a hand.

His resolution to the bet was to do heads up, best of 10 hands with me holding 2 and anything under 7 versus him holding 2 and 7. Without getting to philosophical, i disagreed with this and felt that this was the wrong approach. In essence my argument is that a 2 and 3-6 have better odds of winning versus an unknown hand than a 2 and 7 versus an unknown hand. My thought is that the odds difference between the hands will only show itself over a VERY long period of time and must be against other random hands and NOT versus each other.

So what do the dopers think? I eagerly await…

-n

2

Play around with this simulator. I assume it’s using the correct math.

Preflop, 7-2 vs. 7-6. I made them both suited. 7-2 wins 24%, 7-6 46% of the time, the rest are ties.

7-2 vs. 7-3 suited is closer, 25% vs 32%. In either case, 7-2 loses. That’s not quite the same as 7-2 vs x-x compared to 7-3 compared to x-x, but I don’t see a way to do that. Try putting poker odds simulator into Google, there were lots of others I didn’t explore.

…now I did. http://www.pokercalculatoronline.com/ looks good. It gives the odds of 7-2 unsuited as 31% to win in headsup play. 7-3 unsuited is 33.6%, 7-6 unsuited is 39.5% of win.

3

Not only does 7-2 win less often, but in a real game it is a MUCH less powerful hand, for the simple reason that when you win with just a pair, it’s likely to be a very small pot. It’s very hard to bet the hand, because there is either going to be an overcard to your 7 on the board, or a potential made straight. If you flop the best hand, it’s very easy to get run down. On the other hand, if you have 53s, you can make a straight that will catch your opponent off guard and trap him for his entire stack.

Now, you can win with two pair, or with a flop like 77K. But that’s true for any hand. What’s different here is that if you flop 77K and anyone else has a seven, your kicker is no good so you’re playing for at best a tie.

Small hands like 34s or 76s are not played to flop a pair. Most of the time, if you flop a pair with these hands you should still fold unless you have other outs. in fact, in real live play these hands aren’t really profitable at all - you only play them to mix up your game and prevent people from running all over you when a flop comes up 456 or something. Or as I said earlier, in a no-limit game you can play these hands sparingly in an attempt to trap someone when you make a straight or a flush.

Played perfectly, these hands can make a small profit over time. A very small profit. The bulk of your profit in poker comes from the premium hands like AA, KK, QQ, AK, etc. But that brings us to the other problem wth a hand like 72 - it’s a very difficult hand to play. There are never any easy calls with this hand. You’re always having to use your superior judgment to figure out where you stand. This means that even the occasional playing error would wipe out any profit you might otherwise make (assuming the hand could even be played for a profit over time, and in this case it can’t).

A hand like 56s is easy to play. You either flop a straight draw, or a flush draw, or a miracle flop like 552, or you throw your hand away.

For all these reasons, small suited connectors are not just a little bit better than 72 - they are a LOT better. But even being a lot better, they’re still not great hands, and if you are playing against clueless opponents who don’t modify their play based on your patterns, you wouldn’t be giving up anything if you never played them at all.

4

The number of hands being played matters. 7-2 is the worst in a multi-player game but heads-up, it’s 2-3,4,5,6.

5

Here’s the bit he’s missing: even if you do pair your 7, the chances are very low that it’s the best hand.

IOW: chance of making a pair- decent; chance of making a straight- low. Chance of winning with pair (of 7s) - low; chance of winning with straight: very high.

6

The circumstances of the bet are not clear, but if you are talking heads-up play, 7-2 v 2-[3-6], 7-2 is the better hand. The straight possibility does not add enough to the expected value. This does not constitute a particuarly good argument that 7-2 is the better hand in hold-em poker, however, for reasons that Sam and others mention.

Typical strategy I’ve read involves playing low suited connectors (like 2-3) when there are a lot of people in the pot. This is because it is safe to assume that most others are holding AA, KK, AK, 10’s, etc, so your suited connector aiming at a flush/straight draw has a decent expected value. That is to say, given normal poker strategy, playing something like a 7-2 sucks big time. This doesn’t mean it is the worst hand in heads-up play here both parties are playing through to the river with no betting.

It is the wrong approach. Generally you’d either attempt to calculate the odds directly or run a large number of simulations.

7

Bolding mine

At my regular game we call AK “Anna Kournikova” because it looks good but it never wins. (Obviously, it wins sometimes, but it just seems like not as often as it “should”.)

8

Among the ‘premium’ hands, there are standouts. AA wins far more than the next best hand, KK. AK is profitable, and a premium hand, but you’d much, much rather have AA.

AK also requires more skill to play. To maximize your profit with it, you have to be good at knowing when it’s the best hand even if it doesn’t improve. You have to know how to get off it cheaply if you miss, and when to use it as a good semi-bluffing hand.

9

Not really. Odds of winning a given ring game (10 players) hand with A-A: 34%
Odds with K-K: 30%

Odds of winning a heads up hand with A-A: 88%
Odds of winning a heads up hand with K-K: 85%

Obviously, 3/4% is a big deal over 1,000 hands- but all but insignificant for a single hand.

10

That of course assumes staying in to the showdown every time, and against random hands. Not very likely in the actual world. Sure if you’re going all-in before the flop, K-K is nearly as good as A-A.

But if you have to make a decision any point after the flop, A-A is much better. When an A comes on the flop (or turn or river), it’s much, much harder to call a bet with K-K (because you’re not against a random hand; you’re up against hands that haven’t folded pre-flop, which means a much higher chance of there being an A in your opponent’s hand). So K-K will fold the winning hand much more often.

11

Where’d you get those numbers from? I’ve been looking for a table that has all the numbers; the best I’ve found is one that ranks them from 0-8.

12

My one, and only, time at a cash table in Las Vegas a couple years ago; I had a lot of lousy hands and finally saw A-K. The flop comes A-K-7. I don’t remember the exact betting, but one other guy stayed in the hand and he was betting and I was raising or calling. Rags on the turn and the river. I turn over my A-K, and he shows trip-sevens.

13

http://cardgamerules.homestead.com/Poker_Odds.html

Scroll down a bit.

14

All this does is show the limitations of using simulations to determine the value of poker hands. In the real world, AA is much more profitable than KK.

15

Yep, see, Anna looks good, but never wins!

16

Thanks, Really Not All That Bright.

I always heard the saying as, “Anna Kournikova; looks good, but doesn’t play very well.” It flows a bit better, and makes a bit more sense. YMMV.

17

No, it isn’t.

18

I wouldn’t butt heads with Sam over poker knowledge. He’s right, in this case.

You seem to be working under the assumption is that the only relevant data is how often each hand wins against random hands after all the cards are out. This isn’t all that useful. The way poker coverage on TV centers around late stage tournaments skews the public perception on how poker is actually played.

In actual poker, you’re not playing random hands, and you’re not making one decision. You’re playing hands that, given that they called a bet/raise preflop, are more likely to contain an ace than random hands, and you’re also facing 3 more betting round decisions after the preflop betting rounds, where at any point you may be forced to act against a bet or a raise. In the event that an ace is on the board (a significant portion of the time), against typical opponents in a typical game KK will generally be thrown away. For that reason alone KK has significantly less value than AA. Other issues are that having two kings in your hands versus aces leaves fewer situations where other people can hit a king giving them top pair and you an overpair, you’ll generally lose the AA vs KK situations that happen frequently enough and tend to be big pots, etc.

As to the OP: “2-7 is the worst hand in poker” isn’t really a useful statement. It’s situational. The way they (the WPT?) came up with this little gem was probably simply to simulate 10 random hands showing down - I can believe 2-7o is the worst hand in that case, but there are no useful lessons to be learned from that really, it doesn’t resemble any actual poker scenario. In that same scenario with only 2 players, 23o would be your worst hand.

19

See this link; it is a compilation of average real-world outcomes of various hold’em starting hands over millions of deals. AA winds up being about 39% more profitable than KK in real play.

20

Cite?

My evidence is that I’ve seen AA v KK several times in televised poker tournaments.
The commentators always say “This is a cold deck”, the money goes in and AA wins most of the time (as you’d expect).