Let's say one of the automatic shufflers in your local poker room went on the fritz and instead of shuffling was only able to cut the deck once. This cut would randomly be anywhere from 1 to 51 cards deep. Would anyone ever notice? I have my doubts anyone ever would.

I highly doubt anyone would notice, even if there was no cut, and the dumbass that says "gee queens and eights keep coming up on the board together" would still like a dumbass when he says it.

dealers usually give it a quick riffle before sticking it in the machine but even if they didnt, it would be very difficult for anyone to use the information effectively.

assume there is no riffle... when cards are mucked, they're put together all sloppy so there's an element of randomness for all the cards that were exposed.


there are some small things you could conclude though. if you mucked As,9s the previous hand, saw the cards were stuck together, and saw the 9 of spades as the first card on the flop followed by two cards that arent the ace of spades, it's much more likely that the button or cutoff has the bare ace of spades than would otherwise be the case.

Obviously you could get some information if you knew there was no shuffle, but I'm asking if anyone would notice this in the first place?

Why don't u try it and see lol.

Take the case of no cut because with a cut done at a random point things are already very random to kill any such discussion although more elaborate tests can still be developed for it.

Well clearly Abbaddabba would notice as soon as the player that he claimed to have the ace of spades proved to have it by the way he played the hand . How likely it is to have this be revealed and the test hypothesis be confirmed would depend on the chance for the hand to be seen so something like 10-20% maybe each time he has it? . But thats not all. You also need for the conditions to be right for such possibility to even become potential . I mean you have to ask what is the chance the guy with the As got it paired with another decent card to play it and that nobody had raised big preflop for all those other weak X cases etc to be played too. So it gets very difficult to be observed that first time. If it worked of course you would only need a few more tests like that to know what is going on . In fact right after the very first test confirmation a lot more would follow because you would have started observing all hands you get and see on board . I say by the time you notice the concept in your brain it will be about 10 hands dealt on you or less to have full proof in a table of 10 by starting to observe all sequences if you have a good memory or a way to register them in some notebook (good luck with that ) . The problem is when do you start the test to notice such things? Starting it is the key. Because unless you are after some expected pattern you will almost never spot it until that very remarkable rare board thing happens twice within a few hands to alert your curiosity. And that is very hard to happen . But clearly something that involves several same cards like 777 or all 5 of the same suit could have significant chance to be replicated partially. Still it wouldnt trigger anyone to think what is going on unless it was a very clean similarity and this in itself is quite difficult to occur due to how people play hands depending on position etc. I mean you may fold A7o on early position or raise with it as small blind with no other activity before you so the same 2 cards get a different entry in the deck a kind of partial shuffling takes place due to the way people behave with them and of course depending on how many players you have at the table. Sometimes the game ends with 3 board cards or 4 or 5 so 2 cards that were together have significant chance to be separated and the pattern to never be noticed for the systematic observational experimentation to begin. A board of 777AA for example will not come as board again 777AA and it may not even come as XY777 or X777A etc. You may have it come as 77,7A,AX dealt to 3 players who never get the chance to see what the others had . The intrinsic randomness of decision making of the game would introduce such a significant complexity that the chance a significant repetition (by the criteria we notice patterns to begin with, like seeing the board look as funny as 777AA or come as 23456 or whatever that looks spectacularly rare) emerged in a game of many players would be probably astronomically low.

In fact the more i think that the more i am convinced that the lack of shuffling will take a huge time to be noticed by the way we tend to notice things. If however you started the game with the test already being expected all you would need to do is spot a great sequence of cards that you saw and then start anticipating reasonably acceptable combinations of them 52 cards later. In fact since you have absolute freedom to do such tests every hand you get you would soon enough get confirmation by something that failed to be naturally shuffled by the nature of the game. But to have this suspicion triggered in my opinion would take forever in a big table. Practically i am prepared to claim it would not happen. A natural coincidence of the type that is evident (ie a board coincidence) is so unlikely to occur due to the natural mixing and the significant difference in playing style between opponents as well as positions they have.

So yes once you are after confirming it you will spot it within a few rounds if you have a notebook and keep data or excellent memory (personally i cant recall more than few cards and play well at the same time). But to get the natural suspicion triggered to start observing you would need a huge number of hands dealt since you are after a remarkably obvious and rare event to occur twice within reasonable time and the natural mixing of the game works against it. Of course patterns like As4s8c9cKd are as rare as 7s7d7cAcAd but nobody says hey look A was followed by 4,8,9,k again how incredible yet most will recall and spot 777 followed by 2 aces if it comes again as board . So you need 2 things; A rare combination that is easily admired to occur and then to form again in some entirety hopefully or partially if the observer is alert and smart. The chance of those 2 occuring together is astronomically low so the natural curiosity would never be triggered in a big table especially while players are more focused on their own game and how much are they down or up, bad beats etc lol .


It will now be very good to develop a fast algorithm to test for such within a few rounds once you start a game anyway. There will have to be some statistical test that fails easily. For example how often do you expect to see As on a baord or in your hands. Well if reshuffling doesnt take palce clearly not for a couple or 3 rounds even more depending on game action. Lets say that you see on every round 3 cards plus 2 of yours. So you have at least 5 visible cards sometimes more. Lets focus on a game of 6 people where things will be a bit easier and we can go to 10 eventually if it makes sense. A round at most requires 2*6+5=17 cards . So you have at least 2 (maybe 3 depending on position) clean rounds that none of those 5 or more cards you noticed appear again in your hand or the board. Now you can ask the question; What is the probability if you select 5 random cards that none of them appear in the next 2 rounds in the board or your hand if you say see 10 new cards total? If on each round that we had a flop seen we have at least visible 5 cards we have a total of 10 cards seen after the tests starts in only 2 rounds typically . So lets give an example that the first 5 cards you observe are;

2s 6d 7c Ah Ks

Now if there was reshuffling you can answer the question what is the probability none of those 5 cards appear in the next 10 you see (before we deplete the 52 deck and start over among 6 players) . Clearly they would not appear if there is no reshuffling going on so the probability is 0. Under natural reshuffling however the chance of no occurence is ;
(52-5=47 other cards that are allowed )
(47*46*45*44*43*42*41*40*39*38)/(52*51*50*49*48*47*46*45*44*43)=
(47!/10!/37!)/(52!/10!/42!)=32.7%

So you have 100-32.7=67.3% chance of reccurance of at least one of those 5 in the next 10 you see . Notice that even when you get no flop they all use just 12 so you have some flexibility to see again a total of 10 in most cases unless someone goes all in or makes huge raises back to back in which case you will see only 8 min (4*2) until the deck gets to be used. The point is that its easy to see at leats 10 while the deck is supposed to not be shuffled in most games.

You then only need to perform a few of those tests for the next 10 hands dealt and you will have your answer . Clearly 32.7% per trial is small enough that for it to happen say 4 times in a row that there is no occurence there is only 2% each time you do such combination packet test. So i guess after 20-25 hands played you would have had plenty of such tests to net 4 total and you are already very low in the 1-2% range if nothing reappeared . This means 98% of the time you will have a failure of the claim and a card will reappear before its "due" so you know this is ok (or at least some partially sensible reshuffling takes place)

Am i about to start every game looking for this ? LOL. Noway. But i mean here is one answer that takes only 20-25 hands to get you to 98% curiosity. Some other test may be even more efficient. In a real game due to 32.7% being an underdog to begin with its veyr likely that you would spot a reappearing card in the next 4-6 rounds and end your suspicion . Typically the test would fail very fast to offer some assurance.

Now wouldnt you rather have the test for reshuffling fail and suddenly emerge a killer player for a while? LOL . I wonder what is the EV boost one gets if this was a standard hint given for you but nobody else. Certainly it helps to know 3 maybe 4 aces are not coming any time soon, lol. Now i am not so sure you would be able to spot the sequence well enough to anticipate particular cards creatively since it would require some tremendous effort but i guess some card counting methods used in BJ would be offering substantial edge in how you play certain hands you get in the absence or elevated probability of some critical cards in the current round. Savant anyone?

The cut will mess things up big time though. Especially if its at random point each time. One can even claim that a random cut every round is enough to produce a failry random game that will have little difference from a full reshuffling. If the cut was done at a fixed point always you might be able to eventually use it to your advantage but it would require such serious effort to spot where it takes place that its practically worthless (unless i fail to see someting elementary here) since it would require so much observation from you that would mess up your game.


To be honest with you a serious problem regarding reshuffling appears here nomatter how well it happens. I mean take the case for example that a sequence like 2222 appears in a deck. Now ask yourself how much effective the reshuffling on the very next round has to be for the chance to appear again to be the mathematically expected. How complicated a reshuffling and cut has to be to start from
...X2222YZ... and get potential new ..Z2222W... I would be tempted to think that any partial deep enough reshuffling that takes place makes exactly 0 the chance this will occur on the very next round . Does this mess up the game? Not really but it clearly fails to make it pure enough in the absolute math sense. See my point is if the reshuffling is primitive simple it makes the probability of reappearance significantly large and if its deep enough it makes it precisely 0 or a number vastly smaller than the real thing.

wut???

The easiest way to "notice" this happening is when the flop comes identical to the previous hand once every 52 hands. When the turn card on the second hand is the same as the river card of the first hand, there is a good chance there is no shuffling taking place.

If I was trying to figure out if the deck was being shuffled or not, I could use the above to figure it out (with a high % of confidence) within an average of 52 hands.

This assumes that when the dealer mucks the stub, he does not wash the cards, and carefully places the board into the deck in the same order it reads.
It also assumes every hand sees a river.

Even if you do see this happen there is still the chance that the flop was random, and it hit the "1 outer" to make you think it wasn't shuffled.

It's a cool idea, but the way the dealers wash the deck together at the end of every hand is already 90% of a random shuffle. The rest of the shuffle is just to prevent deliberate cheating and appease the players.

Is max probability on speed or something?

Nice post!

Typed the whole thing with one hand. Took him 2.6 seconds.

cliffnotes please

Cliffnotes: I copy paste stuff I find on the internet to look smart

You're saying he copied and pasted that? WTF? Of course not. MaxProb is awesome.

i once tried to see what the minimum riffles needed to make the deck somewhat random was. i split the deck into 13 piles based on value, washed, riffled twice, and cut. i found 7 pairs in the deck when i searched it. that's a lot.

\\end scientific method.

Which is exactly my point regarding sequences not being either totally broken up or even allowed to reappear by luck ( failure to break them enough times to render reconstruction by luck possible) on the very next deal. Either one shuffles just a bit and the sequences are maintained to a degree or shuffles enough to definitely break them down but not enough to allow them to reappear right away with the kind of natural probability they deserve for it. Its an interesting project to define the problem mathematically as this;

Start with a collection of 52 sorted (by whatever initial method) objects and introduce n operations where you pick a straight subset of the 52 that is say up to length 10 (and reintroduce it in some other place of the initial sequence. Repeat k times starting from random points say 10 to 40. Then study correlations between 2 randomly selected cards . How do those correlations behave as function of n,k ? If you start from a given relation between 2 initially consequetive objects how long until it has practically broken down to the random one (ie no correlation) ?

Its natural to expect that brief washing of say 12 at the table just used cards and then say 2, 3 or 4 deck cuts and repositioning operations are nowhere near enough to destroy the starting patterns enough to offer properties of true randomness in the resulting game if one is able to carefully observe the flow of cards revealed round after round. By that i mean an observer with substantial data collecting and processing power can easily produce for the resulting rounds probability distributions about what card comes next based on prior observations. The correlations persit round after round so all you need is to observe a sequence of cards that are revealed and anticipate some of the properties of the sequence are maintained. It is not going to be something anywhere near a crystal clear prediction of what the next card is given one you see but it will definitely be of the form ;(observe initially a board like
As2sKdQhAd ) and then deduce on the very next hand once you see on the flop next card after Qc3dAs ie turn is 35% 2s ,25% Kd, 15% Qh, 8% Ad, plus the natural probability for all other cards etc (thats quite a bias and then if it proves turn is indeed a 2s even more correlations again etc...) way different than statistically expected.

That can definitely alter a game in a big way especially when it comes to draws and trapping people. I mean you may have second pair at flop and expect you are at a typical 20-25% chance by river to improve against the opponent in the other side of the table that was dealt way before the flop cards came -in a natural random deck- if you think he has say top pair leading now and in reality -in this not random situation based on what you saw on last round exposed-that 25% may easily be a 50% (things like that will happen occasionally and the more data you have plus processing power the easier the estimation). Same for potential flushes if on the prior round many all suited cards appeared eg As10sJsKs2s and then on the next flop the same suit appears with one of the prior round grouped suited cards appearing in it say flop is Qs9dAs (very big chance the others 10s,Js,Ks,2s are nearby too improving the chance for a flush on this hand played significantly over the natural chance).


So how many elementary deck shuffling operations are needed to destroy all information gained by observing the round before? I wont be suprised if the decent answer is a huge number that is nowhere near the practical real life experience of just a few mechanical moves counted in one hand's fingers.

Can you practically beat the game this way? Damn right you can as long as you observe careful video tape of a table and allow for observational experiments to be performed in order to establish correlations and how they decay to 0 . I suspect some elementary counting tricks will emerge that can allow you to alter estimating the true outs by a factor of 2 or more very often. It will not be a huge gain since humans are not like computers able to collect all data and decide later what to use but it might be possible to enhance your EV by at least a factor of 2 . Typically a huge probability boost of what will happen by river in specific situations will be as good as holding preflop AA. Obviously i am offering here fictitious numbers that could be the result of a well studied correlation effort looking at a particalur table for hours . I mean imagine if you know a Q or 8 will come by river with chance that is 2 times bigger than the natural one making your open ended draw a massively different equity position equivalent to that of a set maybe! at flop not 35% but say 75%. Can you see a big reraise or even an all in against an opponent that raised you just now? What if you had once in 10 hands a 55-65% gift situation at flop where you otherwise would have only 35% that is massively well hidden and unexpected by anyone (ie a bad beat that is 5 times given to happen more often than naturally) . Nobody can really give any credit to such examples until a correlation study is performed but i suspect much like in the quoted simple test useful relationships will emerge that may alter specific situation dynamics enormously. Get yourself a deck and simulate a game at a table . Organize the deck to have all 13 suits placed in order and then shuffle it 3-4 times , deal it and try to predict what card comes next at say turn and what cards the other players have likely.


If the natural chance of Ah to follow say As is 3/49 = 6% and you can observe an experimental one of 35% instead ,every time you start with an ordered deck that includes AsAh at some point before trivially shuffled ,you can imagine what this means. It could be 8sJd that we started as initial 2 consequetive cards which nobody would care for observationally but the conclusion would be equally impressive in terms of predictive power every time say you saw an 8s on flop. Human brain bombared by such correlations simly abandons the task and renders the non truly random deck irrelavant for playing the game until someone sits down observes the correlations and then designs counting tricks every time the board looks a bit interesting (which can be decided what is in advance based on its future utility ie all suited board or board with 3 of a kind etc ). Absolutely nontrivial to gain any edge from this until first experiments are performed to gain insight but i am thoroughly convinced powerful patterns exist when the shuffling is stupidly simple. The integrity of the game is protected only from our limited human capacity to recall short term information like that until someone emerges with a powerful economical system that can slightly change one's EV enough to alter everything.

This is certainly a fun topic to consider. Do many tests at home and verify indeed how pathetic elementary shuffling is in destroying originally observed sequences to a degree correlations are practically worthless. I wonder what shuffling method automatic machines use. Maybe anyone with experience on the specifics can say something. If the automated shuffling is extremelly rapid then it may have enough time to kill correlations in a brief 2-3 seconds it may be in action. I doubt a human dealer say at home does an efficient job at it, especially when you consider that it happens almost mechanically and fast enough to allow the game to not take forever lol. The information is still there , we are just too lazy, too human to exploit it until someone makes it a project...

I don't imagine this would be all that big a deal as far as poker games go. Obv it's exploitable in theory but I imagine it would be somewhat difficult in practice, especially with the various randomizers like if cards are being burned, and folds are placed in the muck (as opposed to just on top of it). Cutting the deck and so on.

If you're not doing any of that at all, then it would be a pretty big edge, especially in shorthanded and HU flop games, draw games would be much more complex.

But, eh. The games aren't this bad yet.

You would probably notice that certain cards were coming up together. Flops over time would tend to have many of the same cards together. Hole cards would tend to be the exact same two cards more often, etc. I think over time, it would start to look fishy. Note that a cut actually doesn't change ANYTHING. All of the cards that were next to each other are still next to each other, except for one pair of cards, and one pair of cards that weren't next to each other now are. However, the quick washing of the deck the dealer does before they put it in the machine would change the deck a bit. How much? I'm not sure, and it's probably hard to model/simulate that very accurately.

However, as for the person who asked how many riffle shuffles you need in order to get a "random" deck, it takes about 7. This is a fairly well established guideline. It turns out that one can model/simulate riffle shuffles fairly easily, and in fact in an R probability modelling class, I actually have done that. About 15 years ago roughly a magician/probabilist named Persi Diaconis wrote a fairly groundbreaking paper on the subject, using what are called "rising sequences" - it turns out you can count these to determine how "random" the deck sequence is. If you google the term rising sequences, you can find some more information about it which I won't really go into here.

In short to answer your question, it's hard to say how many shuffles would be needed for a particular person to not notice, but I think it would be pretty apparent if there was zero shuffling going on to most of the players.

The only reason I included a cut was in the rare instance all four aces (or something else) where in the bottom half of the deck. It would DEFINITELY be noticed if an ace/king, etc. hadn't been flopped/dealt during a session.