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Texas Hold'em Experiment (benjoffe.com)
148 points by slig on Sept 11, 2010 | hide | past | web | favorite | 34 comments

Previous discussion on HN: http://news.ycombinator.com/item?id=1132991

At that time, he only had solutions for up to 5 players. I submitted the first 6-player solution [0], which is also the only constructed solution I have seen (the others were found using brute force algorithms.)

[0] http://news.ycombinator.com/item?id=1134906

Thanks again for passing on that idea for the 6 player deck. The concept that a repeating deck can be easily found was what helped find most of the higher order decks.

edit: I'm not sure if brute force is the correct term (though I may be wrong), it's kind of simulated annealing. The difference being I'm not checking all possible decks, only the ones that appear promising.

I remember going back to the site a while after submitting my solution. I'd been so happy that I'd given you the solution for the largest number of players yet, feeling like I had made a real contribution, and was somewhat disappointed to see that you'd surpassed it many times over. I am again restored to happiness, knowing that my contribution played a part in those solutions. Thanks for letting me know!


Also, you are right; "brute force" appears to specifically refer to exhaustive search methods. It was a poor word choice on my part.

Hi I'm the author of that page. I also recently put up similar decks for Omaha: http://www.benjoffe.com/omaha Feel free to ask questions.

Henceforth, these decks are called Joffe decks.

And it needs a wikipedia article.

No original research. We need to find a professor at Harvard or a NYT reporter to bless it on dead tree first.

No Original Research means that Ben Joffe can't write the wikipedia article about it.

The more general rule of Verifiability will be greatly aided by dead tree, yes.

But even once that's accomplished, establishing Notability will be difficult, I think. I guess if the Harvard professor writes it up, and then the NYT reporter writes that up, that might do it.

Interesting, but the practical use of such a deck is negligible. Winning hands don't have an absolute value in poker, but are only worth the amount your opponent values his own second-best hand.

I suppose the greatest benefit from this type of a rig would be the ability to call off big bluffs, meaning that representing a weak hand in any circumstance is optimal.

I wouldn't call this negligible. Sitting in an 8-player game where you know for sure you're going to win is a huge advantage. You can act meekly all the way, which will almost surely drag at least one player in, and only bet strongly at the end. In the hands of an experienced player, such a deck can give a huge payoff.

It would be interesting to rerun the algorithm, looking for decks that give everyone a big hand, but a certain player the win. In other words, not just look for any deck that matches the goals, but look for one which will cause a lot more money to be bet.

It is negligible. I am an experienced player, and I can't see how the limited value of this in a real game compensates for the incredible downside of being caught cheating.

Making money at (cash game, not tournament) poker doesn't have much to do with your cards. To make money you have to convince another player with a second-best hand to put money in the pot. In that sense it's all about the other players' cards.

And in order to get a "huge payoff" your opponents must hold cards that justify calling a huge bet. But almost none of the second-best hands in these decks are anywhere near strong enough to justify committing any significant amount of money to the pot.

Things get more interesting if in fact a deck can be found that gives multiple players "big" hands. But that is a lot harder, and kind of subjective. For instance, would you call a pot-sized raise on the river holding the 10 of spades with four lower spades on the board? I know I wouldn't, even though a flush is a "big" hand.

I guess ultimately it comes down to the fact that poker is a mostly situational game. And one that is played out over the course of many hands. Knowing that you will definitely win one hand during a session where you may see 200 hands doesn't really do you much good.

That said, it is a cool party trick.

P.S. In a game with experienced players, acting meekly all the way and then betting strongly at the end is a sure-fire way to get all but the top 5 or so possible hands to fold.

It is definitely not negligible. Slow playing is a valid strategy even against great players. If all but the top 5 hands or so fold every time you slow play, you're not playing against good players (experienced != good when it comes to poker) and you should just start slow playing and stealing every pot. Then when they figure it out, don't do it again until you get a monster. Most of abusing amateurs is simply doing this, exploiting a weakness until they realize it, then doing the opposite. By the time it stops working you're ready to go.

Regardless, presumably you'd have to memorize this order of the deck in order to stack it that way, thus you could look at your hand and determine the opponent's hand and what the board would be. You could play accordingly. It's easy to make a lot of money at poker when you know what all the cards are.

On the other hand, I've never seen a game for significant stakes where the players were dealt, and I've sure never known anyone good enough to take a deck and sort it into a specific 52 card pattern without being noticed.

We can debate this all day probably, but slow-playing is not a valid strategy if you actually want to make money. By not betting in early rounds you are giving up a lot of value in the hand. And more importantly you are not setting the appropriate price for other players to continue in the hand. Very few hands that are best on the flop are unbeatable on the river. Unless you can put your opponent on a very tight range of hands, it's not a good idea to slow-play, and I rarely do it. I've had much better success just betting for value.

You're simply wrong. It's a valid strategy in the right context. Almost all strategies are.

Don't get me wrong, you're generally correct, it's generally better not to slowplay, but it's still a valuable tool in your arsenal.

Yes you are correct that strategy depends on context. My contention is that even when you think the context is appropriate for slow-playing, you are probably wrong.

If anyone wants to know more about actual poker theory they should read "The Mathematics of Poker" (a warning - it's not a light read).

It would be much easier for them to have a stacked deck at the ready, and just swap it out for the deck in play.

Doing this every 200 hands would add a minimum of 0.75 big blinds per 100 hands to your winrate - more realistically it would be well over 1 big blind. That is very significant in a tough game.

Actually, the 2 player deck is pretty much what you're looking for.

Just for kicks, I went through the first 20 hands, putting myself in the position of the small blind and thinking how many rounds of betting I would go through on that hand.

Leaving out the minimum bet the SB is required to make at the start, there are 3 rounds of betting per hand x 20 hands makes 60 possible rounds. Based on the cards I could see at the time, I would have bet in 37 of them. I'm a novice player and not very good, so probably a better player would have dropped out more often, but I was trying hard to bet with the percentages. In any case, I think there's definitely enough advantage in this deck to win you some money at the table.

EDIT: I see that I got ninja'd by an experienced poker player who is saying the opposite. You're probably right that experienced players would not bet on most of these second-best hands. But there are a lot more inexperienced players like me than experienced ones like you. And, if you can act a bit, you might be able to bluff that your hand is weak on a hand where you know you'll win.

I agree that the two- (or possibly three-) player deck is the only way this has any practical value. And that's because in heads-up poker you're only playing against a single opponent so the starting value of each of your hands goes way up.

I disagree though that a better player would drop out more often. I think better players stay in more often. How can you win if you're not in?

I am not an expert, but you cannot lose more once you are out, either. 'cut your losses' and 'pick your battles' also are arts good players must master.

or give the others players a good pocket/early hand, whilst saving the winner's triumph for the later cards.

Are you kidding? A guaranteed win is hardly negligible. Sure, it's not optimal, in the sense that winning hand dominance is varied, but it provides an entire hand to play with absolutely no risk. You're guaranteed to win, on average, the average pot size. That is a massive advantage.

More importantly, I think the sort of "deck hacking" mindset the author has created can open up a world of research into this topic. Producing decks with some sort of "mean winning hand dominance" that is low would be the step you are describing.

As for practicality, that's another world of research. Would it be possible to create a deck such that when shuffled a specific and non-conspicuous way produces a high likelihood of a Joffe deck? Off the top of my head, one could take the decks provided and produce decks that when riffle shuffled twice, produce a Joffe deck. So, for example, you could take out a "fresh deck" (which is rigged) from a box, and riffle shuffle it twice, pass it to be cut, and still be guaranteed a win.

And don't forget that there are professionals that, with enough practice, could take an actually fresh deck and come up with a way to shuffle it so that it ends up a Joffe deck. In fact, one could come up with a sorting algorithm that takes the different types of sorts available (riffle, cut, hindu, faro, etc) and figure out the optimal path to get a Joffe deck. (maybe).

Actually if you "hover your mouse over the cards to see the hands that would be dealt" you'll see that the opponent gets quite a good 'second best' hand as well. Lot's of things like '4 of a kind' beats 'full house' action. For some reason the author doesn't state this is one of the requirements but it must have been.

> For some reason the author doesn't state this is one of the requirements but it must have been.

Not necessarily. I think this is just a consequence of the way the cards get reused. Cut one card later, and SB now has many of the same cards as dealer had. Many of the same cards as a good hand isn't necessarily a good hand, but it's certainly more likely to be good than from a random deal.

The two and three player decks have indeed been optimised to increase the opponents' hand values. The decks for higher number of players are too sparse for me to bother yet. -Ben Joffe

This experiment is not meant for practical poker. It is neat though.

kinda scary knowing this...

I guess people should start implementing dual cuts or something. Or maybe another way to alter the deck by a 2nd player that makes it incredibly hard to cheat.

There are various ways to cut (in the "Scarne cut" you pull cards out of the middle and put them on top, then repeat several time) but the short answer is that if you're playing cards against a professional cheat or magician in anything less than laboratory conditions, you're going to lose. Period, end of story.

I started picking up a bit of card magic a year or so ago, and I was amazed at how easy it is to fiddle a deck, and how many ways there are to do it. I was also amazed at just how inattentive and easily distracted people are, especially when they think they are watching you like a hawk. I've done incredibly blatant top changes and card reverses right in front of people and gotten away with it...and I'm a novice.

It's been a while since I played poker, but surely to do this you'd have to shuffle an out-of-order deck into the correct order while in public view? That sounds like enough to make it "incredibly hard to cheat".

I think that it's called "cold deck" because the trick is to replace the playing deck with another one, that was perviously "prepared" into some specific permutation.

Exactly. The term comes from the way you spot the switch -- cards that have been being handled a lot warm up in the players' hands. If you touch the deck and it feels cool (i.e., it is room temperature), that means it just got introduced to play.

Or it's warm because somebody just took it out of his pocket ;)

Interesting. We use the terms cooler and cold deck for an unlucky situation all the time without thinking of where they came from.

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