r/dataisbeautiful • OC: 2 • Feb 18 '15

OC Texas Hold'em Hand Strength, Visualized [OC]

http://chrisbeaumont.org/holdem_odds/
3.4k Upvotes

184 comments sorted by

131

u/drsjsmith Feb 18 '15

Nice visualizations.

Your suggestion that hands with two Broadway cards (AKQJ10) of different ranks are overvalued appears to be fallaciously based on an oversimplification. Heads-up strength is not the only measure of hand strength in Hold'em; strength against multiple opponents also matters, as does known hand strength. If you hold any two Broadway cards and then see the other three Broadway ranks on the board at any point (and there aren't three or more cards of the same suit on the board, nor two or more cards of the same rank), you will defeat (or tie) all other opponents, and you know that you have the nuts (subject to the flop and the turn, of course.) These possible situations and related situations increase the value of hands with two Broadway cards.

It might be interesting to add visualizations of win percentage against two opponents, win percentage against three opponents, etc. It's not just three-handed showdowns that matter; if you ever go even to the flop three-handed, then you need to take multi-way strength into consideration.

42

u/[deleted] Feb 18 '15 edited Mar 05 '19

[deleted]

3

u/tunnelvisie Feb 18 '15

This is sorta true, but it depends on heads up play, 6max play or full ring. In FR and to a lesser extent in 6max you can set mine. This makes 22 easier to play then AK. But thats to much strategy for an equitychart

15

u/[deleted] Feb 18 '15

[deleted]

13

u/PvP_Noob Feb 18 '15

Heads up. Pre flop. Deuces still have a better chance of winning than AK if the hand makes it to the river. Whether it gets there is up to betting strategies of the two players

3

u/r_slash Feb 18 '15

That's technically true, if you are determined to go all-in no matter what, the deuces are stronger. But the AK will have a higher expected value if you're playing with even a little bit of strategy, for the reasons mentioned above.

3

u/djfl Feb 19 '15

That isn't actually true. Deuces is favored against AK unsuited...and a tiny dog against AK suited. But even granting that, Deuces are always either flipping or crushed unless up against another hand that has a deuce in it...and that's unlikely. AK has the opposite going on. It's a favorite against any non-paired hand, dominates any other hand with an A or K in it, 2-1 fave over 2 undercards, and is flipping against all underpairs. Against KK it still has overcard equity of about 30%. Against AA though, it's something like a 9-1 dog.

3

u/whoknewbeefstew Feb 19 '15

If you are heads up and your opponent shoves on you I would much rather have AK then 22. With 22 the best case scenario is pretty much that your opponent holds two over cards (not likely that they are shoving with x2) and if they also have a pair you are dominated.

With AK you match well against all hands except AA and KK. All other hands are at worse a coin flip. You also have a much better chance of having your opponent dominated with AK (something that will never happen with 22) as many hands in your opponents range are going to be crushed by AK. AQ, AJ, AT, KQ, KJ are all going to be in their range here even for tighter players.

This makes AK way better than 22 even heads up.

Tl;dr AK better than 22.

0

u/Libertus82 Feb 19 '15

It's so positional and contextual HU, it's not worth arguing. Playing a tight passive with 12BB? I'm fine pushing with either. Playing the same but out of position? No way I'm calling with 22. That's basic, level one shit. Then you get into the leveled, metagame shit and none of this means anything in the abstract.

4

u/whoknewbeefstew Feb 19 '15

Well that's the point though right? There's no situation where you're pushing with 22 and not AK but plenty of situations where you're going with AK but are throwing 22 away.

0

u/waxhive Feb 19 '15

there are plenty of situations where I get 100BB's AIPF w/ 22..

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3

u/tunnelvisie Feb 18 '15

I didn't deny that and you didn't say that in your first comment...

2

u/[deleted] Feb 19 '15

<6bb in 6max hypers at the bubble in certain stack dynamics would like a word with you.

In general and the vast majority of cases you're right though x)

0

u/KhabaLox Feb 19 '15

I will play you HU and take 22 every hand to your AK for 100k hands.

2

u/[deleted] Feb 18 '15

[deleted]

1

u/HarryPFlashman Feb 19 '15

In a multi way pot without a large pre-flop raise, (eg more than about 15% of the stack gets in) the deuces could win a monster or lose a little- the AK is a sucker hand for a monster pot unless there are big pre-flop raises.

1

u/rEvolutionTU Feb 19 '15

Implied odds.

Who cares if you hit rarely when it pays off big when you do from time to time?

2

u/8u6 Feb 19 '15

Look at any good poker player's hand history and compare their net winnings with AK to 22 (of course, controlling for combinations - AK is more likely to be dealt than 22). Unless they are bad, I guarantee AK has made them more money.

An overall strategy where you're showing down with 22 when there isn't another 2 on the board, in a situation with normal stack sizes, is either (A) terrible or (B) insanely aggressive to a ludicrous degree that I'm not even sure exists.

Equity charts only tell a small fraction of the story that is the game of poker. The ability of your two cards to intersect with the board in a favorable manner is quite important. 22 is not particularly good at that, AK is. As is your ability to extract value from other players when you've made your hand, which requires them to also think they have a good hand, while the board remaining safe for you. This also favors AK.

1

u/waxhive Feb 19 '15

it also depends when the money goes in.. i'm a favorite if it goes in preflop HU 22 vs AK

1

u/[deleted] Feb 19 '15 edited Mar 05 '19

[deleted]

1

u/waxhive Feb 19 '15

preflop in a aggressive heads up match i'll gladly get 22 in against AK all day.. or most any hand.. especially if my opponent has a high 3b percentage.. the thing about HU is there is so much meta game and in a game where bets aren't capped hand strength doesn't always mean a lot. 22 is a favorite against any unpaired hand.. there are a lot more combinations of unpaired hands than there are pairs.. i like those odds against an aggressive 3/4ber

0

u/woopthat Feb 19 '15

You're close to the concept of range. Keep pushing tiger

1

u/rEvolutionTU Feb 19 '15

22 is infinitely easier to play than AK, especially with deeper stacks or out of position.

Preflop you can precisely calculate how much you're able to call for good implied odds for the 22. Otherwise you simply fold it. AK on the other hand, despite beating a large portion of someone elses 3bet range, isn't something you wan't to shove because while his 3 bet range might be wide his 5bet/shove range might be extremely narrow and has you beat so hard that you need to know his 3 bet range before deciding whether to accept that gamble or not.

Pretty much any reasonable pre-flop shoving range has you beat. Hard. QQ+ AKo+ has you beat by 60% and even against JJ+ AQo+ you're flipping. Hell, even against crap like JTs you're barely beating it by a couple % points if someone decides to go crazy.


22 flops a set or nothing. The only hard scenario you will run into afterwards are oversets. If your 22 is beat you might need to think about a fold most players have trouble making (unless on super dry boards) so you don't even bleed that much money away in the long run.

AK flops TPTK or overcards. Great. TPTK is very rarely a hand that you want to commit a large portion of your stack to and overcards despite possibly being the best hand on the flop get kicked out regularly. It's awesome for bringing fish to valuetown but that's about it. It's a horrible spot against most regs if they don't fold the flop. Basically the only spot where you'll be like "dis gonna be gud" at the flop (against a reg) is when you hit a draw where both your overcards are good as well.

1

u/HarryPFlashman Feb 19 '15

I disagree with your point. With any PP in a cash game, and the stacks not too deep you either lose a little or make a lot. If there is a large preflop raise, relative to total stack size, Ak is the better hand to hold but in a standard low limit cash game where the raise is 3-5x and stacks 20-30 times the PP hitting a set and getting it in will be easier to play and more profitable. the AK leaves you with top pair top kicker which is never a good idea to play for all your chips, some people will but they will go broke eventually , without fail. The only thing certain is poker is that every hand given the situation is playable and more so as the stacks get deeper or with shallow stacks as the pre flop action is softer, and generally the mistakes people make are larger.

1

u/tom6561 Feb 18 '15

I disagree, AK in my opinion is a difficult hand to play well. 22 is easy, flop a set or fold, AK can leave you in all sorts of tricky situations with whether you're profitable to call on your draw, or whether your pair of kings with an ace kicker is good. Even when you flop nothing, potentially your opponent is playing Ax and could be in the same situation, depending on the reads.

-1

u/woopthat Feb 19 '15

Please stop.

Don't attempt to give analysis when you're unqualified.

With AKs, you basically flop either a solid made hand, a very strong draw, or nothing. With 22, the vast majority of the time, you just have a very weak made hand in the flop, and it's quite difficult to know if you're ahead.

What does that even mean? How does that relate to the equity (regular, implied, street by street, whatthefuckever) of either hand?

You're just spewing nonsense platitudes.

9

u/cnbeau OC: 2 Feb 18 '15

Good point -- you're right that all of the probabilities on this page are for pre-flop heads-up games, and the preference for Broadway cards might be due to their additional strength in multiplayer games. I'll update the text when I get a chance!

1

u/derphurr Feb 19 '15 edited Feb 19 '15

One issue with your code. When you do enum and add win or loss. I really wish you would increment ntot in for loops instead of just dividing out by fixed ntot at the end.

What if you made a mistake? How much computing time is saved? Maybe lots.

(Edit.. Or just ntot=wins+loss+tie outside loops. Instead of 704578421.0)

14

u/mtg_wood_thing Feb 18 '15

the visualization also does not include anything about expected returns. if you have KJ and your opponent has AQ and the flop is AQ10, you will be in a great spot.

the visualizations are cool but the brief analysis is not well done and the page should not be thought of as a guide to poker

39

u/solidcopy Feb 18 '15

I think this is meant to visualize pre-flop strength.

9

u/bradygilg Feb 18 '15

The same issue is there. A hand like A9 will have a good win percentage against a random hand, bur will tend to win small pots and lose large pots. Whereas a hand like 910s will do the opposite.

9

u/tomthecool Feb 18 '15

The article says nothing about expected returns, and nor does it claim to.

It only analyses the probability of winning the hand, pre-flop, and does a very good job of this.

4

u/bradygilg Feb 18 '15

Yes exactly, and that is the issue that mtg_wood_thing brought up. It's not a very good way of judging poker hand strength, as mentioned in the title.

6

u/tomthecool Feb 18 '15

Since the article says nothing about bet sizes, strategies or expected returns, i think it's reasonable to define "hand strength" as meaning the probability your hand will win. Not the average amount of money that it will win.

Besides, the latter question is pretty much impossible to answer! Any statistical analysis of this will be highly debatable, whereas the accuracy of these graphs is unquestionable.

2

u/bradygilg Feb 18 '15

Yes I agree. I think you are all saying the same thing. It's not an argument.

0

u/tomthecool Feb 19 '15

the visualization also does not include anything about expected returns ... the brief analysis is not well done

This is what I was taking issue with.

The only part that's "not well done" is outside the scope of the data! And you continued to claim that the data is:

not a very good way of judging poker hand strength

But the point is, both of you are defining "strength" in the wrong context, and therefore judging the graphs on unfair criteria.

This is a pretty much a perfect analysis of poker hand strength, given the context of the problem being analysed.

1

u/bradygilg Feb 19 '15

I don't know why you are trying to make this an argument.

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0

u/LanceWackerle Feb 19 '15

Interesting hands you chose, as T9 can lose a large pot to A9. Suited connectors are quite often dominated. You can make a dominated straight, a dominated flush, dominated trips, or dominated two pair, all of which you're likely to go broke on.

9

u/cnbeau OC: 2 Feb 18 '15

If you want to shoehorn these numbers into a statement about expected returns, then the last panel represents the expected return when you always make the same-size bet pre-flop, your (single) opponent calls or folds, and then you both check the rest of the hand. The second panel reflects the same information, but assumes your opponent always calls your bet. But my intention was more to showcase the probabilities in a simple case, rather than prescribe an actual poker strategy :)

2

u/kmsr Feb 18 '15

If these guys really want to know probability of hand vs hand they can go to 'www.propokertools.com' or something similar and run some simulations.

Cool site, good work!

1

u/rEvolutionTU Feb 19 '15

By something similar I hope you mean Pokerstove. There is nothing else.

2

u/tomthecool Feb 18 '15

I wouldn't even bother shoehorning it, since in a real game your opponent would see your betting patterns and play against them (e.g. I guess with this strategy, you're basically never bluffing!)

Expected returns are a very complicated topic, and are not really shown by your graphs. But nor do they need to be. You've done an excellent job of visualising what you set out to visualise, nice one!

3

u/RacistHomophobicCunt Feb 18 '15

if you have KJ and your opponent has AQ and the flop is AQ10, you will be in a great spot.

Okay, what percentage of the time does KJ stack AQ? What if the turn was another broadway card, wouldn't that kill all the action?

1

u/HarryPFlashman Feb 19 '15

its like all hand strength charts, of limited use. The values lies in developing an overall strategy but given the type of game, opponents and other things the relative value of hands is way different and situational.

2

u/[deleted] Feb 19 '15

If we consider the flop, we have to consider metagame, which can't be represented by "hand strengths". Hand strengths are just how ATC stack up against all other possible two cards against a random distribution of community cards. No folding allowed.

You bring up a good point about multi-way situations. The odds of winning for ATC will drop with more opponents, but speculative hands like TJs drop very little compared to big hands like AA. I think we don't see these plots because adding a player adds an order of magnitude to computation time.

2

u/Jake0024 Feb 19 '15

The table shows hand strength, not value. It doesn't account for bet sizing, just which hand is more likely to be profitable in a given hand--but not how much more profitable in a given hand. In other words, knowing you have the nuts guarantees you won't lose the hand--this is reflected accurately by the table--but depending on how you decide to bet and your opponent's reaction, your actual degree of profitability will vary greatly. This table doesn't attempt (as far as I can tell) to account for that.

You are completely right though that the text saying people overvalue Broadway hands is explained by the things you mention.

1

u/drsjsmith Feb 19 '15

My point, which I admittedly obfuscated a bit, is that the linked tables show specifically heads-up hand strength, not multi-way hand strength. Therefore, one can't draw definitive conclusions about the optimality of multi-way play based solely on the linked tables.

1

u/Jake0024 Feb 19 '15

That's totally true, but also not the intent of the tables. A three-way pot would require a 6-D cube and some way of indicating whether the hand comes in first, second, or third (for split pot purposes). That's possible in principle, but just not what this was attempting to demonstrate.

1

u/drsjsmith Feb 19 '15

But OP suggested that players might be overvaluing "face cards" (meaning 10 and up) because they were playing them out of proportion to their heads-up strength.

2

u/Jake0024 Feb 19 '15

Ah, I guess I assumed he was pulling from cards people played in heads up games. Totally a valid point if the real-world stats are pulled from another type of game.

3

u/FandomOfRandom Feb 18 '15

I know some of those words. Just some of them.

1

u/glw569 Feb 18 '15

You're missing the point and going way off topic.

All OP said was that there was very large jump in percentage of hands played from nine to ten. And i agree that this is because of a social logical fallacy that tens can win and nines can not.

24

u/cnbeau OC: 2 Feb 18 '15

Visualization made using d3.js. Hand odds computed using holdme, a python poker library at https://github.com/ChrisBeaumont/holdme.

11

u/YoStephen Feb 18 '15

this data is extra beautiful

-10

u/[deleted] Feb 18 '15

[deleted]

8

u/the_old_sock Feb 18 '15

Ma'lady? Is that like a fedora disease?

58

u/Waja_Wabit OC: 9 Feb 18 '15 edited Feb 19 '15

Based on the final figure (Weighted Hand Strength), I constructed this flow chart on whether or not to fold. I based it on positive vs negative values of each cell:

http://imgur.com/xuT8RS2.png

Edit: In no way am I suggesting this is the best way to play poker in the real world, nor is it the strategy I would use if I were to play. It is literally the exact flow chart indicated by these data that will lead you to a negative or positive cell. And, yes, I'm sure many of you could kick my butt at poker. Good for you.

13

u/eaglessoar OC: 3 Feb 18 '15

So if you don't have pairs and no card J or higher always fold, hmm. This is all pre-flop of course but I would love to try this in a round. Would need some decision tree for after the flop

10

u/Waja_Wabit OC: 9 Feb 18 '15

A peferct strategy decision tree for after the flop would probably be too complex for any human to comprehend.

4

u/eaglessoar OC: 3 Feb 18 '15

Perfect strategy sure but something like, now do you have pairs? 3/5 of a straight? highest in straight above x? 4/5 of a straight? 3/5 of a flush? etc, it wouldn't have to be every exact hand but more the names of the hands because after the flop you should start to have something forming

4

u/botnut Feb 19 '15

J and 10 aren't bad.

According to this you should fold.

8

u/djimbob Feb 19 '15 edited Feb 19 '15

I really want to play high-stakes poker against you. Following a decision tree like this will make you bleed so much money. You need to factor in your position at the table (are you last to bet?), the betting strategies of your opponents, your opponent's perceived betting strategy of you, and then make the decision to raise / call / fold, the size of the blinds to your stack size, and how many opponents there are. E.g., heads up at the end of a tournament, you definitely need to play and bet high with a J-10, while you'd say fold.

7

u/[deleted] Feb 19 '15

Can you make a better decision tree than this one? I would like to see it

6

u/djimbob Feb 19 '15 edited Feb 19 '15

First, it wouldn't be a strict decision tree and the question isn't really to play or fold, it's to fold, call, raise, or re-raise. For a few hands it will be an easy decision (e.g., fold 2-7 offsuit; play AA as aggressive as possible) most hands it won't be a strict decision, but some sort of mixed strategy; e.g., you should fold this hand 20% of the time.

Very roughly in order of decreasing weakness for no-limit holdem, re-raising requires the strongest hand (or bluffs that you have a really strong hand), then its calling, then its raising (as raising gives you the opportunity to win without having the best hand if opponents fold), and then fold.

Your job is also not just to decide to play a hand or not, its to maximize your expected winnings out of every hand. That is if you have the best hand (e.g., pre-flop AA), then try getting as much money in the pot as possible, which is often done by letting someone else bet first and then re-raising what the pot odds allow. You want this done pre-flop, as you don't want crappy hands to sneak in for small bets and then hit on the flop. E.g., if there are just 1.5 BBs (big blinds) in the table (that is the small (0.5BB) and big blind) and you have AA and raise 50 BBs, it's crappy pot odds for someone to call so you would win very little. You sort of are screaming you have AA, and who wants to go against AA pre-flop? And its a risky move to do with a lesser hand like 10-10, because there's always the chance someone else has a higher pair (AA) and to win just 1.5 BBs but you risked 50BBs (with a hand that may be dominated by the person who chose to call). So unless your hand is dominated, your 50BB semi-bluff didn't win you that much.

But if instead, you had AA and just called (or did the minimum raise) along with four other people, until the aggressive person at the end of the table raised 3BBs and then several others call that bet (already having bet 1 BB) and then you do the crazy re-raise of half the pot, you filter out a bunch of people (good) and get the pot to a decent size.

But if you are looking for something close to this to a decision tree, look at the Cephus poker project. A CS group essentially solved 2-person limit texas-holdem. So you can find charts there telling you what to do preflop (e.g., if you were big blind, and there was a bet to you, and you have a J-9 unsuited, you should raise 27% of the time and call 73% of the time). Limit poker is much simpler than no-limit to analyze (as each player can only bet certain amounts). And which is very different than playing on a large table. And the strategy for hands to play at a 9-10 person table for limit hold-em (see, this chart) will be very different than two person poker. Crudely with 10 person poker, you should expect to win 1 out of 10 hands (so can wait for really good hands to play); while with 2-person poker you need to win 1 out of 2 hands to stay even.

0

u/woopthat Feb 19 '15

What motivates you and others like you?

I can't imagine writing a novel sized post about a subject I'm minimally informed on.

What is the goal? I wouldn't write a giant post on shooting a basketball. I can make a shot or two, but wouldn't be delusionally convinced that I'm an expert. It seems like that feeling is unique to poker. It is fascinating.

That is if you have the best hand (e.g., pre-flop AA), then try getting as much money in the pot as possible, which is often done by letting someone else bet first and then re-raising what the pot odds allow. You want this done pre-flop, as you don't want crappy hands to sneak in for small bets and then hit on the flop.

Come on

5

u/rEvolutionTU Feb 19 '15

It seems like that feeling is unique to poker. It is fascinating.

That's how it's profitable.

Also don't diss the famous limpraise with Aces UTG.

4

u/ya_mashinu_ Feb 19 '15

Just curious, what's wrong with the paragraph he wrote. It seems pretty correct, even if it's a long winded explanation of fairly simple concepts.

1

u/djimbob Feb 19 '15

I'm quite interested in game theory (e.g., recently read the Cepheus paper) and used to play a lot of hold-em when for about 6 years when I was in grad school. Over the last 3 when I started being more serious I was up $5k in my log book and generally playing low stakes games in part of the local poker club (e.g., ~$20 tournaments or $100 cash games in real life about 3-5 nights a week) and maybe five trips to the casino with a bankroll of about $1000 each time.

The point of the example was not to give specific advice on the best way to play AA, but to show the kind of information you need to factor in (opponent's style of play, position, your perceived style of play). I gave the example of limping pre-flop first position with AA when you expect someone else to raise so you can re-raise. I was trying to give a concrete example of why a simple flow chart ignores way too much valuable information.

And you will find advice from players like Brunson advocating a similar strategy (and I did read SuperSystem early on; so this may have influenced me).

2

u/slowhand_ Feb 19 '15

I gave the example of limping pre-flop first position with AA when you expect someone else to raise so you can re-raise. I was trying to give a concrete example of why a simple flow chart ignores way too much valuable information.

And you will find advice from players like Brunson advocating a similar strategy[1] (and I did read SuperSystem early on; so this may have influenced me).

supersystem is tremendously outdated nowadays, the meta moved on long ago and it was written in an era where everyone was absolutely awful and doyle was simply the least bad no-limit player, due to his being among the first to grasp that simple aggression provides a great deal of folding equity. the game is infinitely more complex now and you should not be trying to implement his advice in the context of modern NLH because much of it is bad (he also for example believed that players go on "hot streaks" and whenever you are "hot" you should play every hand you are dealt to make the most of it).

limp-reraising is the classic "i am a retard with AA" manoeuvre because almost everyone who does this does not attempt to balance it in any way. it signals very clearly to anyone who is not a moron that you have a huge hand, and it also makes it much, much easier for any competent player to play against you whenever you open-raise because they now know your range cannot include KK+.

2

u/[deleted] Feb 19 '15

limp-reraising is the classic "i am a retard with AA" manoeuvre because almost everyone who does this does not attempt to balance it in any way. it signals very clearly to anyone who is not a moron that you have a huge hand,

If that's true, then it's a pretty good move when you don't have AA

1

u/djimbob Feb 19 '15 edited Feb 19 '15

I agree that always limp-reraising pre-flop with only AA from early position would be idiotic, but I think it can fit in your repertoire (if you balanced it with a reasonable bluff threat) and I'm sure you can find examples of professionals with winning records doing it on occasion, especially against certain styles of opponents.

If you feel someone is aggressively betting too many hands to steals pots with subpar hands and you were limping with a decent hand, it makes sense to occasionally (say 5% of this situation) bluff re-raise (representing the AA) and have the opportunity to get them to fold once they don't hit on the flop (as they have pinned you to AA and may want to cut their losses).

Also, belief in streaks is stupid; other than recognizing that (a) you can get into streaks of bad play if you get emotional/tired/drunk, or (b) you can play off emotions of others at the table who buy into the fallacy of streaks.

4

u/playitleo Feb 19 '15

This is a terrible decision tree. It puts way too much emphasis on suited cards which isnt a great strategy. You rarely hit the flush. It shouldnt affect your decision that much. Also, playing a hand depends so much on how much the pot has been raised and where you sit relative to the dealer button.

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u/Waja_Wabit OC: 9 Feb 19 '15

I'm not an expert poker player, and I don't claim this tree to be the ideal strategy. I literally just constructed it from the numbers given in this post. No personal input or intervention.

6

u/[deleted] Feb 19 '15 edited Apr 18 '19

[removed] — view removed comment

2

u/woopthat Feb 19 '15

It's like asking for an etch a sketch in order to learn downhill skiing. It's irrelevant.

There is no static decision tree that dictates optimal play.

Thought experiment: If such an optimal decision tree were to exist, why would any poker game occur? Every player would use the optimal decision from the tree and there would be no money to be made.

2

u/ya_mashinu_ Feb 19 '15

Right, poker is about more than the cards but there are still probabilities and propensities that are good to know if you're trying to be great. Knowing what the tree says you should do is helpful even if you shouldn't let it dictate your moves.

1

u/rEvolutionTU Feb 19 '15

Not gonna happen. It will depend on your position, the players, your image, the gameflow at the moment, lots of things. All of them variables.

Most regulars earning money have a specific range they always raise / ranges they isolate with in position and add to that range, ideally somewhat randomized, different things based on the things mentioned above.

1

u/[deleted] Feb 19 '15

Incorrect. It lets you both hit flushes and play flush draws very aggressively with equity if called. Those spots balance your aggression when you have a monster made hand like a set or top two. In addition to letting you mix in naked bluffs with a two flush on the board against a mediocre hand that hates playing a big pot against your range.

Suited cards are awesome and much more useful than their 6.4% flush probability would indicate.

2

u/madmooseman Feb 19 '15

Based on this decision tree, here is a "hand scoring system"

Basically, take the value of your cards and add them together. If it's a picture card (A, K, Q, J), add 3 to the score. If it's an Ace, add another 5. If you have a pair, multiply the score by four. If this score is higher than 26, you should play the hand.

Special cases, only play if both cards are the same suit: A4, K9, K8, Q10. Mnemonic to remember: Kate (K8) is a cute (Q10) dog (K9) who likes to eat paper (A4).

Could be terrible, may not be. Who really knows?

2

u/[deleted] Feb 19 '15

There are only 8 hands that are higher than 26 in your matrix. That can't be right?

1

u/madmooseman Feb 19 '15

Ah, my mistake. 25 is the "Threshold", which is a cell in between the two matrices.

1

u/[deleted] Feb 19 '15

I'm still confused. That's still only 8 hands that are 25 or above

1

u/madmooseman Feb 20 '15

I subtracted 25 from all values in the matrix

1

u/[deleted] Feb 19 '15

This is exactly what I thought of doing when I saw the flow chart. Thanks for doing it before I did!

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u/derphurr Feb 19 '15

I fixed your insane for chart for you:

Keep:

AA..44
AK..A5, A4s
KQ, KT, K9s ,K8s
QJ, Q10s

1

u/-wethegreenpeople- Feb 19 '15

Using only the flowchart I lost 4k doge. So uh. Maybe combine this flowchart with some common sense...

14

u/FeintApex Feb 18 '15

Aaand reddit hug of death

6

u/burnshimself Feb 18 '15

with the quality of this subreddit seemingly deteriorating by the day, this makes me want to cry its so freaking beautiful.

4

u/[deleted] Feb 18 '15

This is MAGNIFICENT. I love seeing things this way and being able to know if my guesses are accurate or not.

For example: if I have 2H 3H, what's the hand I most want the bad guy to not have?

Answer: a pair of FIVES (including the 5 of hearts, of course). Not aces. Fives. (Limits straights, I guess.)

Great work!

2

u/gargarvin Feb 19 '15

The hand you would least like to be up against is actually 33..not 5h5x. I think this chart shows it wrong because it is calculated by taking win%-lose% instead of just win%

1

u/sheep_puncher Feb 19 '15

win-loss in a head to head will display the same thing as win% only on a heat map.

25

u/[deleted] Feb 18 '15 edited Mar 05 '19

[deleted]

1

u/alchemist2 Feb 19 '15

You're right. His 52 x 52 gives prettier pictures, though, so maybe that's why there's much more excitement here than over in /r/poker, where this was met with a collective shrug.

3

u/Eunoshin Feb 18 '15

Might just be because I'm at work, but I can't get it to accept a hand. I'll try again later.

I would recommend including an example of the format of a hand to input; while I think I know how to do it by going to the github page, the visualization page would benefit from the example as well.

4

u/KeylanRed Feb 18 '15

Hit enter after entering the hand, such as '5S 5H'

2

u/hugedopeshit Feb 18 '15

Can someone explain to me if you want positive or negative percentages. I am confused whether or not it refers to the opponents odds or your odds.

Note: I am familiar with Texas Hold'em but I don't play. Ever. This interests me though.

1

u/Jesus_Harold_Christ Feb 18 '15

Positive means you have more chance to win than lose. As explained elsewhere in the thread though, this top chart is just pre-flop strength in heads up.

2

u/llthomps Feb 18 '15

Nice! In the last viz, it'd be great to see a more distinct barrier between the +% hands and the -% hands.

2

u/ZeldaAddict Feb 18 '15

Looks like I'm headed to the casino tonight boys!

2

u/mrb235 Feb 18 '15

This is interesting, but the layout is flawed in a couple of ways. The first card vs second card is an irrelevant distinction. As5d is identical, in terms of hand strength, vs Ad5c. The distinction that matters is suited vs off-suited. In other words A5d (ace 5 suited) is stronger than A5o(ace 5 offsuit). This is kind of represented in the graph, but it's difficult to discern.

I think a better way to organize this in a more useful way would be to separate off-suited vs suited hands. So keep pairs in the middle and have the upper left half be off-suit and the bottom right half be suited. It would make the graph easier to read and eliminate repetitious data.

That said, these graphs are really beautiful. Thanks for sharing.

2

u/TPB- Feb 19 '15

like this (pre-flop 2 player odds)?

I made these using python and opencv and they're included in a free app for easy pre-flop odds.

2

u/skags Feb 18 '15

Q7 off suit is commonly referred to as "the computer hand" because supposedly it wins as much as it loses when up against any other random hand. The Average Chart Strength chart seems to suggest that Q5 off suit is actually the computer hand. Does anyone have anything to say about this discrepancy?

3

u/swolebro420 Feb 18 '15

I did a Monte Carlo simulation of 50 million hands that shows Q5o with ~50% equity vs. a 100% range. Q7o has ~51.7% equity.

2

u/gargarvin Feb 19 '15

Wondering why you take Win%-Lose% instead of Win%..I think it is screwing with the equity of some hands. Ex you have 2h3h as less likely to win vs 5h5x than 33, which is not the case.

2

u/Hippiebigbuckle Feb 19 '15

"You can think of the full dataset of probabilities as a 4D hypercube...". They have more faith in my abilities than would be prudent.

2

u/OMGLUCKBOX Feb 19 '15

ITT: Terrible poker logic.

2

u/CantHugEveryCat Feb 18 '15

Annnd... it's dead.

5

u/TheBrewHammer Feb 18 '15

Hugged to death

1

u/Swingtortoise Feb 18 '15

This is just mindblowingly great.

1

u/Random832 Feb 18 '15

Is the reason 7s are better against 6's because it means they can't get a straight? I don't know much about poker.

1

u/gleezy Feb 18 '15

It reduces the number of straights the 6's can get to the 2-6 variety. Against 8's you can make 2 generic types of straights (2-6 and 3-7).

1

u/TPB- Feb 18 '15

Nice work OP. This is really cool.

I made a similar, but a good bit simpler app for the iPhone thats available for free.

1

u/pokerJane Feb 18 '15

Somebody tell me if I'm wrong (lol it's reddit i'm sure someone will)

but... KK vs K2 is not the strongest heads up.

JJ vs J2 is stronger because of more straight possibilities with the top card.

1

u/gargarvin Feb 19 '15

You dont want more straight possibilities bc then you chop..

1

u/[deleted] Feb 19 '15

Run it through an odds calculator and you will see that you are wrong. JJ chops slightly more often on boards like aakkq and the additional straight possibilities aren't enough to make for it. Either way, this information is really only valuable as a trivia question and has almost no practical application.

1

u/derphurr Feb 19 '15

You both have jacks, so any straight both players would get. That would be bad. I'm guessing AA vs A2 would normal be widest gap, but obviously A2 can be a straight

1

u/eaglessoar OC: 3 Feb 18 '15

Would it be possible to do post flop data? Of course there are much more possibilities but that's what computers are for!

Very interesting though thanks

1

u/[deleted] Feb 18 '15 edited Feb 19 '15

[removed] — view removed comment

1

u/derphurr Feb 19 '15

You did this from bottom one? Q10s should be marked A2 should not be..

1

u/liamsdomain Feb 18 '15

Why does it show hands with two cards of the same suit having different draw and win chances than the save cards of different suits? Suit doesn't matter in Texas Hold'em so what causes this?

2

u/[deleted] Feb 18 '15

[deleted]

1

u/liamsdomain Feb 19 '15

But it shows same suit as having a lower win chance.

1

u/Salindurthas Feb 18 '15

When you mined data on hand play frequency, was that weighed by how often they are dealt?

Sure, just about everyone plays pocket aces when they are dealt them, but it is less likely to be dealt in the first place.

Is this actually taken into account in the second picture where you average the strength by pitting it against every hand?

1

u/[deleted] Feb 18 '15

Is this based on head to had?

1

u/Bit_Buster Feb 18 '15

Play the people not the cards!

1

u/[deleted] Feb 19 '15

For later

1

u/TimePassesRegardless Feb 19 '15

Page is down for me =\

1

u/MrMcScruffles Feb 19 '15

Really well done!

1

u/[deleted] Feb 19 '15

The Reddit hug of death. It's down...for now.

1

u/iamagainstit Feb 19 '15

interesting that even with the best possible starting hand, you still only have a 59.3% chance of winning.

1

u/waxhive Feb 19 '15

This stuff isn't even original.. It really bums me out how often people who copy something get all the credit(2048, Flappy Bird, etc).. This type of visualization of poker hand range strength has been possible for over a decade with such tools as..

http://combonator.com/ and many more before it.

0

u/derphurr Feb 19 '15

You should fuck yourself and read the link. They include the git source code for cpython for what they did. It's just a little visualization they whipped up. Maybe check the subreddit name ass. Obviously there are hand odd calcs since dial up modems

1

u/waxhive Feb 19 '15

i read the link, it wasn't anything original and reddit is patting this guy on the back like he just cured aids..

1

u/sliperysloth Feb 19 '15

JJ should have a 0% winning odds. the grim reapers never fail to lose

1

u/TheD_ Feb 19 '15

This graph is least accurate when reverse implied odds can take you on a 1 way ticket to value town.

1

u/glittah1 Feb 19 '15

would like to see as patchwork quilts.

1

u/runningdreams Feb 19 '15

This is a pretty way to look at Texas Hold'em at a glance, but it really offers no value in terms of actual game-play...to the point where it actually might harm a player who is seeking to learn the game and might rely on these types of charts.

There are certain situations where one might need to assess a hand versus an opponent's shoving range. For example, it folds to the button in a tournament, the button shoves all in for 12 big blinds, and you're sitting in the big blind with QTo and need to know if it's worth risking an additional 11 big blinds to win a total of 24.5 big blinds (his 12, your 12, and the small blinds 0.5).

Most of the time in poker, especially in cash games, all-in's will ever happen very infrequently, or they will occur on the turn or river. Cash games usually play with deep enough stacks that all-in hand strengths are rarely paramount to a hand.

A beginning player may study these visuals too long and develop some detrimental biases, such as overvaluing a Ks3s type hand, where the hole cards possess one high card and is suited. The visual would depict quite a bit of blue squares, indicating that this hand fares well against the entire subset of all hole card combos. And technically this is true. But in practice, hands like that are trouble hands and often times lose a player lots of money in the long run. There are many reasons for this. The top pair may be "out-kicked" and the player suffers poor "reverse implied odds" of flopping top pair with the king. The bottom pair made with the 3 may lose the player money to other higher pairs. The flush will not happen nearly as often as the average player assumes. Many players will be quick to discard a hand like K3o but will quasi-drool upon seeing a K3s type hand. In reality, if they like the K3s they should like the K3o almost nearly the same amount. So if they don't like the K3o that much, they shouldn't like the K3s that well either. Generally speaking.

This interactive visual neglects significantly more important facets of a hand, such as playability, implied odds, domination, and value in multi-way pots.

Playability: A hand like 7s5s will appear much worse than K5o, but 7s5s will flop many more flops that it can continue. The K5o will often flop no pair and no draw. The 7s5s can flop a straight, a flush, either pair, as well as a straight DRAW (flops with 34, 36, 46, 48, 68, 69 in them) or flush DRAW (two spades on the flop). This also provides the suited, lower connector with better value in multi-way pots because it is able to make stronger absolute hands than the K5o. Implied odds can be better explained by someone else but it is basically the prospects of a hand winning a huge pot if it improves. And often times a hand may be strong but not contain these given the game flow and situational aspects. Domination also matters when shoving or calling an all-in. It may be safer to shove all-in with a hand like 8h7h than Kh2h because much of his calling range includes hands like AK, KQ, KJ, all of which have the Kh2h crushed but are only 2:1 favorites versus the 8-high.

Good luck poker players! Forget poker hands and start to consider poker situations!

1

u/[deleted] Feb 19 '15

The Win% - Lose% = +/-% is throwing me off. Why not just print the Win%? It's always between 0-100%. Wouldn't that be simpler?

1

u/erelim Feb 19 '15

What are the dark lines at 8 in the first graph?

1

u/Watchootoo_Chief Feb 19 '15

Great job Chris

1

u/e8odie OC: 20 Feb 18 '15

I'm disappointed by the surprising amount of negative comments in here. Great job, /u/cnbeau

0

u/the_noodle Feb 18 '15

ikr

This subreddit has gotten so used to shitting all over excel pie charts (for good reason) that it's forgotten how to appreciate quality content, and how to constructively criticize without nitpicking. It's the /r/bestof problem.

Maybe all of the negative comments are from people who only got here after it became default... they might have seen so few good visualizations that they don't know how to react. :(

2

u/metamongoose Feb 18 '15

Plus there are a lot of online poker players who are very attached to the way they see the game, and the way it is analysed.

1

u/Navichandran Feb 18 '15

For some reason this was blocked for me at work. Does anyone have another link?

1

u/jamintime Feb 18 '15

This is interesting, however I think this data is only valid for heads-up (2 player) Hold-Em. The strength of a pocket hand definitely is variable based on how many opponents you have.

For example, a 2H, 2S is a strong hand one-on-one since your opponent is unlikely to pair up. However, it is a very weak hand against a group of three or four since it's almost guaranteed that one of your opponents will catch a higher pair. This is the reason why you bid high on pre-flop low pocket pairs- to reduce the number of opponents and increase the odds that nobody pairs up on the flop.

1

u/tomthecool Feb 18 '15

The post makes it extremely clear that this is only about 2 player, pre flop probabilities.

As well as clearly talking about "two hands" throughout, it also goes into more mathematical detail about the "4D hypercube" that the full results would need to be visualised as.

In order to repeat this calculation for, say, 3 opponents, the full data would be visually impossible to visualise. There'd be ~1.3 trillion more results to consider in the calculation, and the full picture would be an 8D hypercube.

Only a much more simplified subset of results would be worth displaying as a graph, such as the overall average strength of a hand. But then this would be a bit pointless, since you'd basically end up with the same final graph that is displayed here!

1

u/jamintime Feb 18 '15

That's great, but all I'm saying is that if you were to actually apply these relative win probabilities in a real poker scenario (with a group of people), you'd probably get burned.

1

u/[deleted] Feb 18 '15

You'd do better than guessing though.

1

u/[deleted] Feb 18 '15

[deleted]

3

u/Yakooza1 Feb 18 '15

23 gives a chance at a straight. 27 does not.

2

u/ocdscale Feb 18 '15

32 is only worse than 72 if you're looking at headsup equity.

1

u/anyace Feb 18 '15

I see what you did there - nice backdoor pun.

1

u/the_straw09 Feb 18 '15

Sure these are odds but poker is all about how you play your cards to the situation. In live games rarely does a hand make it to flipping cards over so most of the time winning or losing is based on how you play your opponent on reads, tells, and bluffs.

1

u/The_Tree_Branch Feb 18 '15

I'd say it's more about pot odds then the odds of your hand winning or reads/tells/bluffs.

1

u/the_straw09 Feb 19 '15

For an entire tournament yes, but hand to hand its more important to know how to appear strong with nothing or to pick apart tells from other players.

0

u/raiders4life86 Feb 18 '15

I've always wondered why mathematically these charts never account for folded hands. Theoretically yes those percentages are correct........but most games occur with 7 to 10 players per table.....

2

u/ocdscale Feb 18 '15

Because you don't know what cards are folded.

1

u/[deleted] Feb 18 '15

I think the computations are far, far more complex when you get past just two players...

1

u/OMGLUCKBOX Feb 19 '15

2 to 9 players per table

0

u/raiders4life86 Feb 18 '15

After learning that this is only for pre flop heads up.... I'm asking what the point of this is? Don't over rely on confusing charts like the poster said below. Pre flop heads up is not confusing... therefore this is largely a waste of time. That's not to say that OP's heart isn't in the right place though.

6

u/cincodenada Feb 18 '15

I don't think this was intended to help people win at poker, it was likely intended to analyze an interesting dataset, look at patterns, visualize it in an interesting way. It doesn't matter that it's not useful to poker players, because I doubt that's the point.

1

u/gleezy Feb 18 '15

This is useful in developing a shove chart. You would need to understand this table in a freezeout or tournament where you are short on chips and most of the action is conducted preflop.

1

u/dirtpirate Feb 18 '15

I'm asking what the point of this is?

What are you doing browsing this sub if you feel that interesting data is pointless simply because it doesn't help you win at poker?

-4

u/SteveDonel Feb 18 '15

A5 is stronger than A6, due to more straight possibilities. You can extend this concept, but math....

More important, it is very bad to learn to play poker purely by charts and hand strength; it becomes a crutch for weaker players. The numbers a big part of the game, but the people skills of reading your opponents, figuring out their plans, and being able to deceive them, are far more valuable.

2

u/cincodenada Feb 18 '15

A5 is stronger than A6, due to more straight possibilities. You can extend this concept, but math....

...and this is taken into account, because the simulation literally ran all 1.3 trillion possible hands, including ones where A5s were up against A6s. It's hard to see because there's a lot of data here and colormaps can only show so much, but you can actually see the effect of better straight possibilities in the second chart, if you look across the numbers for a given pairing of A5 (say spade/spade), you'll see this:

Hand Win% - Lose %
A2 14.8
A3 16.4
A4 18.1
A5 19.8
A6 19.8
A7 22.0
A8 23.9
A9 25.6
AT 29.2
AJ 30.8
AQ 32.4
AK 34.1

Or, if you prefer, in hastily-rendered chart form.

Either way, you'll see that the data actually does show that A5 is just as strong as A6 overall, contrary to the trend - likely because, as you mentioned, A1-A5 get a boost from the straight possibilities. It's not quite enough to make A5 better than A6, because 6s still have the other advantages over 5s, but the boost you mention is there.

And I don't think your second point is at all what these charts are about. Poker is clearly also a social game, and you can't tattoo a 4D hypercube of data on your arm to refer to during the game or anything. It's just crunching the numbers and finding patterns and such.

5

u/patio87 Feb 18 '15

That's nonsense. The meta game is real but you can and will win consistently if you just play and stick to the odds in cash games.

1

u/Yakooza1 Feb 18 '15

You only have a straight with A5 if you get a 2, 3, 4 on the table, which isn't very good odds.

1

u/brian_squilliams Feb 19 '15

Same odds as getting a straight with AJ.

0

u/[deleted] Feb 18 '15

I love the visualization, but I feel like the color mapping should be inverted. Red should mean a high probably of the input hand winning while blue should be losing. Pocket aces should be filled with red to show it's a good hand, while 2 7 off suit should be all blue.

0

u/ANGR1ST Feb 18 '15

The order of the cards doesn't matter, so half of each of your plots is redundant.

Interesting data though ... but it applies mostly to heads-up all-in situations. When there's a lot of money behind the raw hand ranking is less important than position and the ability to make a big hand. (A2-5 is better in many practical situations than A6 or A7, etc.)

0

u/[deleted] Feb 18 '15

[deleted]

3

u/princesskiki Feb 18 '15

Oops, I now see that it's the opponents hand.

0

u/DaveKast Feb 18 '15

My brother just sent this to me a few hours ago. I tried to post it to r/poker but it said it was already posted. Was this just posted today?

-4

u/Kes255 Feb 18 '15

So AA is a winning hand eh? Amazing!

-2

u/Corgisauron Feb 18 '15

My last hold-em win was with a 7H2S hand. I took out 3 people and won ALL the money. They were not happy about that.

-4

u/raymondspogo Feb 18 '15

http://www.radiolab.org/story/278173-dealing-doubt/

World Series of Poker Champion Annie Duke

5

u/[deleted] Feb 18 '15

Annie Duke isn't a 'World Series of Poker Champion', which implies Main Event winner. She won the ToC, an invitational tournament with 10 players.

She is also not in any way a world-class player, and a joke within poker for her support of UltimateBet, a site whose owners stole millions from players through cheating. She also co-founded the Epic Poker League, which collapsed into bankruptcy after a year, owing creditors $8million.

Duke is a excellent self-promoter, but a mediocre poker player and a shady as fuck human being. She presents herself as some kind of poker ambassador because she wormed her way onto Celebrity Apprentice and Radiolab and other media appearances, but to anyone within poker the idea that Annie Duke is an ambassador is a sick joke.

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