Texas Hold'em Hand Strength, Visualized | Hacker News Reader

Texas Hold'em Hand Strength, Visualized

chrisbeaumont.org

179 pointsalexcasalboni62 comments

Looks like you used heads up hand strengths, and then full-table hand frequencies, and computed weighted hand strenghts based on that--which is a mistake, of course.

Could you expand on this please.

Yeah, so he's using heads-up hand strengths. So how well QQ fares vs all other hands, for instance, but only one hand at a time. (It's not QQ in a pot with 9 other hands.)

Then he computing weighted hand strengths based on frequency of opponents playing a hand. So now QQ doesn't win as often, given that the opponent doesn't play 27o very often so you don't actually get to win hands vs 27o (they don't occur).

BUT to determine how often an opponent plays a given hand, he's using the IRC poker database, which is full-table hands. So we see that people play K7 infrequently, for instance, which is true at a full ring game. But in a heads-up match, K7 is played very, very frequently. 85%+ I'd say, but easily 75%. [1]

[1] I played heads-up poker professionally for a few years. I logged millions of hands.

Hand strength isn't all that matters - you also need to account for "expected winnings". A-9 has a strong hand strength, but in a real game you'll probably win small pots with that and lose large ones. 9-10 has a middling hand strength but when you win, you'll probably win big.

That's not what this blog post was about at all, and certainly not what GP asked me to expand upon.

You're not wrong, it's just off-topic, essentially.

You could say that you need to account for talent, too--but at some point you're going beyond what can be analyzed, at least currently. NLHUHE is not a solved game.

I'm just saying, if you simply used these results to guide your bidding process, any halfway-decent player would take all your money.

These charts are nothing more than starting hand strengths. There's no mention of 'bidding process' on any street.

I'm not even sure how you could extrapolate a betting strategy from the post. It doesn't even mention money, let alone stack sizes, position, or any of the thousands of variables you might factor into an entire strategy.

The post talks about "which hand is more likely to win". All I'm saying is that you don't care about how many hands you win, you care about how much money you win. It would be like measuring programmer productivity using number of lines of code written. This is obviously not an issue for someone who already understands poker, but if you didn't and you tried to use this table to scale your bets according to your overall likelihood of winning with a particular hand, then you wouldn't do well.

I think you're in violent agreement with defen. You're probably so entrenched in Texas Hold'em thinking that it didn't even occur to you that a naive player may see this and think, "This hand is great! I'm going to bet it all!" defen is just pointing out that is a terrible idea, which I think you agree with, but it probably didn't occur to you that anyone could be so naive to even try.

I am in violent agreement with defen, however I'm not with you.

Given a very naive player with a hand they've seen on the chart is great, I'd advise them to bet it all (early/preflop) rather than try to play a hand out. I think they'll be more profitable on average, particularly against a solid player, which defen mentioned.

I'd love to do this with play-raise-fold frequencies by number of people at table. Are there relatively untainted public poker hand datasets? WSOP tournament data maybe?

There's a piece of software out there called PokerTracker that allows a user to gather hand data for real-time statistical analysis. There are users out there who have very large databases (Billions of hands) and some users who will buy/sell/exchange these databases.

You can buy huge databases from other players, yes. They're full data sets, not "tainted," and have far more hands than have ever been played in the WSOP.

It's considered bad form in the poker world, and generally against site TOS, if you're a player using the data to have a read on a player before you've ever played him.

If you're just doing research, nobody cares at all. They might even give you the datasets, if they actually believe you. Or perhaps if you let them anonymize them?

Unless I've misunderstood you, it's really not considered bad form at all. It's considered pretty standard amongst professional poker players that most everyone (at least the professionals) are all using some form of HUD (heads-up display) that will overlay stats next to each opponent's name, detailing all sorts of useful information about the player's tendencies. It's almost mandatory to use a HUD if you like to multi-table more than 4 tables at once.

Collecting and mining hands you play\see is fine but its the buying and selling of other people's datasets that is bad form / banned. In the small circles of nose-bleed games, it is resembles collusion when a team shares data to undermine a single target across a set of games.

It's still pretty standard to mine hands that you didn't personally participate in. Lots of players mine nonstop. You're right that you're probably crossing the line when you buy/share other people's datasets, as you'll get information that your opponent can't possibly get without also sharing/buying datasets. That being said, of the nose-bleed players I personally knew it was still the norm to share data with your friends. I think at that level you just have to assume that all of your previously played hands are visible to all your opponents and adjust accordingly.

I think I played a little over a million hands online and probably have a dataset with millions more on top of that. If you want it, I can probably find it and send it to you. Email is in my profile.

Here are (correct?) preflop odds according to number of players: http://www.natesholdem.com/pre-flop-odds.php

And then, what's interesting is that with 2 players ak win at 67% and jj win at 77.5% (ak < jj)

But at 10 players, ak wins at 20% and jj wins at 19.3% (ak > jj)

Illustrating the number of players changes the hand strength

That's still not weighted for how often a player plays a given hand. It assumes the opponent will play every hand equally as often.

I don't mean to be OT, but does anybody play online anymore? I paid my (cheap) rent in college playing on FullTilt and PokerStars, but the (unreasonable) gov't crackdown seems to have put an end to online play. Or is there a secret I'm not in on?

The shutdown was only in the United States. You could cross the border to play freely. Inside the US, there's a couple of states that have legalized within-state play; other than that there are a few minor online venues (several hundred to a couple of thousand players online at any given time). I believe that r/poker has an updated list if you're interested.

Online poker for real money is still strong outside the USA, and there are a few state-specific enterprises (for example, wsop.com and--until recently--the unfortunately named Ultimate Poker in Nevada) starting for USA states that have specifically legalized online poker.

There's a couple of sites where you can still play, however there's not much action and you essentially can't cash out.

I have a buddy with ~200k on some network, I think merge, and he has a pending cashout for 2k (the max) that has been pending for months. He can't initiate another until the last has been resolved.

Until about a year ago (post-black-friday, of course) he was able to remove about 12-14k/year, given the wait time per check and the maximum of 2k per check.

You need to move or play in a casino.

bovada... not nearly as many players as there used to be when it operated as bodog, but it'll still scratch your itch.

Seals With Clubs. Deposit bitcoin. Play with bitcoin. Withdraw bitcoin. Probably not legal in the U.S. but it's a great site (and they don't check your IP origin afaik, though you could probably get in with TOR or a proxy anyway).

Seals With Clubs shut down three days ago: http://forumserver.twoplustwo.com/29/news-views-gossip/seals...

You can try Bovada. Fairly soft site with decent deposit and withdrawal options.

Online poker is very much alive. You can check it out for yourself twitch.tv

I personally recommend pokerstaples stream. He's a very math based MTT player.

Repost of my reddit rant about UX issues in this visualization:

This is interesting, but the layout is pretty confusing for somebody who studies poker.

Every other hand chart has AA in the top left, like these from Poker Stove: http://i.imgur.com/cvgvh.png

Also, yours have duplicate information. As2d and 2dAs are both displayed, when in fact they are equal in poker. Most charts split up suited and offsuit hands, like the ones above or this one from Equilab which lists out every combo separately like you do: http://i.imgur.com/BqS1iht.png

Your input format is also confusing. On your site, users have to type '6C 6D' but everywhere else on the internet, that would be written '6c6d'

OP here. Your points about the convention for lowercase and aces on the upper-left are fair. However, the duplicated information in these grids was intentional. I was less interested in building a standard suited/off suited odds table (those are readily available) or a strategy tool, and more interested in a visually clear way to explore the "probability landscape". I find these grids with duplicate information easier to grasp on first viewing. I also like seeing how subtle suit-based patterns in panel 1 cancel out when you average all slices into panel 2. You can't show that unless you retain all suit information

This doesn't consider the post-flop strategy though. Since heads-up limit holdem has been solved, it would be interesting to look at the EV of the hand with the optimal play. I would think hands like 22 should have been weaker than show down value suggested..

Good luck with that decision tree for 1.3 trillion hands!

Actually this EV is the by-product of solving the game. U of Alberta must save it somewhere.. only if we can access it..

weakly solved. What was shown is essentially a optimal solution for playing against itself. Not an abitrary villain of unknown tendencies.

Besides, limit is dead.

This is mostly untrue, to my understanding.

It was not solved to maximally exploit a bad villain, but it was solved to be unexploitable, and therefore unbeatable.

It would make mountains of chips vs 99%+ of players, probably at 80%+ of the possible rate.

No, it's a solution that loses very slowly vs. an opponent that plays optimally against its strategy. Meaning bluffs and calls at optimal percentages KNOWING the percentages of the program.

It reminds me the "Temperature Maps" by Sho Sengoku in backgammon [1]. For a given move, it syntheses the equities (somehow probability of winning) for each possible dice roll of the opponent on next turn. It allows among other thing to see how dependent of luck you be after a move (by looking at the contrast between squares).

[1] http://www.bkgm.com/articles/Sengoku/TemperatureMap/index.ht...

Fascinating. I've seen a few remarkable showdowns between AQ and KK, I never would have guessed the odds were quite so tilted in KK's favour.

AQ vs KK is no different than A10 or AJ vs KK. Even middling Aces like A7 or A8 aren't much worse off because of the lost straight possibilities due to two K's being taken.

I haven't looked at the numbers but I would bet that A2-A5 are better off against KK than AQ.

The numbers have arrived -- thanks to www.sliceeq.com -- and your hunch is right. After 100,000 Monte Carlo simulations, Slice declares that winning odds are as follows

KK (70.9%) vs AQsuited or AQoffsuit (29.1%)

KK (69.2%) vs A5suited or A5offsuit (30.8%)

The reason why the seemingly inferior hand of A5 does better is that it has about a 4.6% chance of making a straight. (Usually A2345, but conceivably something else) The AQ hand has only about a 2.7% chance of making a straight, because the deck is depleted of Kings, making the desired AKQJT straight hard to catch.

In general, Slice is a wonderful -- and free -- tool for testing various hand outcomes, particularly against likely ranges that an opponent might have.

NOTE: The simulation percentages above will vary slightly each time Slice goes hunting for 100,000 random hands. But the disparity between AQ and A5 generally is somewhere between 1.5 and 2 percentage points.

Additionally, if AQ has made a straight with a K, KK now has a redraw to a full house. If the flop was KJT, KK still has a 34% chance to win the hand.

Yup, it's a classic poker situation referred to as a "race".

Interesting visualization!

AQ v KK is not a race, it's a rout.

Right. AQ vs. JJ would be a race.

Right you are, my mistake.

Everything that's wrong with poker as a game can be exhibited in the fact that 70-30 is considered a rout. It's slightly better than 2 to 1, you lose almost 1/3rd of the time. AQ vs KK preflop is roughly like leading 1-0 in a baseball game.

What I think you're saying is "everything that's wrong with poker" is exactly what I find makes poker great.

So much incomplete information combined with luck obscures the best strategy. If it weren't for these traits, it's likely poker would have been relegated to the likes of checkers by now. Solved and not fun for competent players.

The luck keeps people coming back.

Anyway, I can't agree with what you're saying, which is really just an opinion.

Go does not have any luck, but it's an incredibly elegant and deep game with basically 3 rules. Computers still don't win against the top pros. (But that'll probably change over the next 5-10 years.)

So you don't need luck to make it an attractive spectator sport. But I suppose it might be very different from poker if there wasn't luck involved.

Mostly I mean that people think it's absolutely unbelievable that 70-30 gets beat and whine like it was an actual rout when it happens, then tell stories about it for years.

if I got it in 70-30 every time I'd be a very rich man

usually you're getting it in 65-35 with your strong hands or worse (overpair vs. a strong draw)

AQ, AJ and A10 are all deceptively okay hands (not exceptional like AA, AK, KK, not quite mediocre like J10, QJ) because of the Ace.

You might be surprised to hear that 95% of poker players do not consider JT mediocre.

(I'm not among the 95%!)

In Australia we call JTss the 'Greek flag'. It is a very powerful hand in the Manila variant of poker - which is popular with Greeks - and thus extremely popular in holdem also. Note that every two card straight it makes is the nuts.

Note that it's rarely worth playing in a raised NLHE pot.

I know it's good when it's good, but it can be easy to read, it splits a lot of the pots because the board goes four paint or whatever, it gets tricked into dumping money with top pair no kicker, etc.

Plenty of guys are flatting two raises OOP and hoping to hit a flop and that's a recipe for dumping chips.

It's a great hand to play anytime 76s would be a great hand.

I enjoyed this analysis, I went through something similar when designing a bridge hand 'strength' estimator as part of an automated bidding program. I'm going to have to go back and see if I can borrow some of these ideas :-)

I thougt that a 2 and a 7 were the worst, but here a 2 and 3 has -35.4% win%-lose% while 2 and 7 has a slightly better -30.8% win%-lose% (second diagram). Any idea what the difference is?

Not a poker expert by far, but this could be because 2/3 can only participate in three straight draws (A2345,23456,34567) whereas 2/7 can be in seven straight hands. (A2345, 23456, 34567, 45678, 56789, 6789T, 789TJ)

But you need 4 cards on the board vs using both in your hand for all those 2-7 "straights"

Suffice it to say that no, that's not the reason.

The reason is entirely high-card strength vs all the hands including cards less than 7, like 65, 64, etc.

EDIT: And the value of pairing the 7 vs pairing the 3, again where high card strength matters--6X pairing the 6 won't matter as often.

Given there's only two hands, they are somewhat likely to showdown unimproved, not making a pair or better. If you analyzed ten handed tables, 2-7 fares the worst.

72 offsuit is the worst hand against a table of opponents because it is the lowest hand that has no straight or flush opportunities (using both hole cards)

23 offsuit is the worst hand against a single opponent because the likelihood of needing a straight or flush to win the hand decreases and the penalty for having a lower highcard is higher.

27 has high card value compared to 23 vs all other hands. Vs a hand someone would actually play, like JT, you don't have any high card value.

I'm going to guess that, after you enumerate all possible opposing hands along with all possible table cards, that the 7 gets paired up for a win more often than the straight lines up for a win. Also, due to their low card value, a 2-3 will pretty much automatically lose with no pairings, straights, or flushes. (And even then, it's a weak flush.)

If you look at the final diagram, they are almost equal in average expected payout, with the 2-7 dropping value much more than the 2-3. I would expect this is due to the paired 7 not being very strong against more commonly played hands with higher average card value. (In other words, 7 doesn't mean as much when the average opponent has cards higher than a 7.)

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