The Best (and Worst) Ways to Shuffle Cards - Numberphile

[Blitzkrieg]

[I've given up trying to paste my previous reply I've typed up but haven't been able to post. Below is a paraphrase of the my comment that was meant to come after Blitzkriegs response to my first post in this thread]

When I talk about Snyder's article being about systems concerning itself with non-random shuffles, what I was referring to wasn't ST, NRT, AS/T but controversial systems that came about in the 80s/90s (I don't know the exact history). Such systems claimed that the regular approach to blackjack (whether BS or counting) was flawed since the strategies were generated assuming perfect randomness (or as close as pseudo-random RNGs computers use can get).

As has already been mentioned in this thread, it is true that an unshuffled deck will benefit the BS player because of how the high cards will clump together (due to the dealing procedure). However, there is a sharp fall off in the advantage. As you introduce even very weak shuffles (ie. ones that do a poor job of randomizing) the advantage disappears at an exponential rate (iirc, could be logarithmic, but exponential seems more intuitive to me).

Though sloppy shuffles may be the ST practitioner's holy grail, for systems utilizing weak advantage indicators such as wins/losses (streaks being even weaker, if they even correlate with anything at all) they might as well be playing against a perfectly random deck.

There is a lot to learn about how to crack a shuffle.

[Aslan]

If there is what I would call "a thorough shuffle," that is, several riffle shuffles that interlace the cards near perfectly, and the cards starting out had very few clumps, that is, high, low, high, low, high, low, etc,. would you say that the cards tend to stay in the same general configuration, "high, low, high, low," or tend to clump? Contrariwise, I believe when the cards are pretty much evenly distributed in the first place, I believe a terrible shuffle where the cards are shuffled in large clumps of cards rather than evenly interlaced tend to retain the same configuration, "high, low, high, low." When this happens I will either leave or request the dealer to carefully reshuffle.

[Aslan]

Here's one for you. If you are playing and the cards are coming out high, low, high, low, so that the count never goes anywhere, how far do you have to go in a deck or shoe before you conclude statistically that the cards will probably never change, that is, they are likely to continue to come out high, low, high, low? It's easy to say that the remaining cards can be in any configuration, but do the cards previously dealt have any predictive value over the card yet to be dealt, or is this just a case of random coincidence?

[Three]

Random includes all possible deck compositions so you can't call any composition nonrandom just by looking at it. As for clumps. Card counters need clumping to make money. Evenly distributed cards are not what is meant by random and they tend to make advantage situations have a small advantage and rare. The wash is very important to randomizing an ordered by rank, as they come in the pack, deck of cards. That is why they do it. If the cards were not random then players could exploit the nonrandom nature of the cards. It might not be from counting but if you know a skewed likelihood of the upcoming cards there is advantage to be had. Like if you knew their procedure produced a 30 card clump of low cards followed by a 30 card clump of high cards wouldn't that make knowing when to raise your bet easy? You wouldn't need to count the RC to use a lot of math to know when to raise your bet, you would just need to count how many cards of one clump came and raise your bet when the high card clump was about to come out. Even the biggest idiot in the world would be able to beat the game. The casinos don't want that. Unless you think they can shuffle to a cooler order (LOL) I wouldn't worry a lot about it.

As for washing some dealers are very good at washing cards to continually change the interlacing of the cards while other dealers are not. I have seen dealers tat do a good job of mixing cards in the wash in a very short period of time and others that could wash for 10 minutes and not change the cards much. A lot of the baccarat cheating involving dealers has them washing the cards poorly so a clump remains unmixed.

[Aslan]

Random includes all possible deck compositions so you can't call any composition nonrandom just by looking at it. As for clumps. Card counters need clumping to make money. Evenly distributed cards are not what is meant by random and they tend to make advantage situations have a small advantage and rare. The wash is very important to randomizing an ordered by rank, as they come in the pack, deck of cards. That is why they do it. If the cards were not random then players could exploit the nonrandom nature of the cards. It might not be from counting but if you know a skewed likelihood of the upcoming cards there is advantage to be had. Like if you knew their procedure produced a 30 card clump of low cards followed by a 30 card clump of high cards wouldn't that make knowing when to raise your bet easy? You wouldn't need to count the RC to use a lot of math to know when to raise your bet, you would just need to count how many cards of one clump came and raise your bet when the high card clump was about to come out. Even the biggest idiot in the world would be able to beat the game. The casinos don't want that. Unless you think they can shuffle to a cooler order (LOL) I wouldn't worry a lot about it.

As for washing some dealers are very good at washing cards to continually change the interlacing of the cards while other dealers are not. I have seen dealers tat do a good job of mixing cards in the wash in a very short period of time and others that could wash for 10 minutes and not change the cards much. A lot of the baccarat cheating involving dealers has them washing the cards poorly so a clump remains unmixed.

Somehow you managed not to answer any of my questions, but maybe you were not trying to.

As for what is random or not random, I understand what you are saying. Even the perfect order that comes with unshuffled cards right out of the wrapper is one of the possibilities for a random shuffle, but I don't think anyone would seriously call that a random shuffle. Remember those "unshuffled" cards used in Baccarat, which were supposed to be pre-shuffled-- by that measure you could claim they were actually shuffled but coincidentally resulted in a seemingly unshuffled configuration. Generally speaking we say that 'brand new order' and 'every other card alternately high and low' are to be considered non-random, even though they represent two of the random possibilities. That's the quid pro quo-- the alternative is prohibitively unlikely and to call either of them randomly shuffled is unacceptable, although technically speaking they might be, in the sense that a monkey with a typewriter writes all the works of Shakespeare given enough time.

[ohbehave]

"Random shuffle" shouldn't describe the card order. Certainly, every other card high or low could not be considered a random order. "Random shuffle" should mean out of all the possible shuffle orders, any one order is selected randomly. The "selection" is a result of the shuffle. Similar to a lottery drawing. One set of numbers is randomly selected out of all possible combinations, the selection process being prescribed for the particular lottery, e.g. pulling numbered ping pong balls.

[Aslan]

Another way to look at my question is this: Has anyone done a study to see whether cards that are heavily clumped tend to stay heavily clumped, or whether cards that are alternately high and low tend to stay alternately high and low using a normal casino shuffle (whatever that is)?

I already know (or think I know) that cards that are very poorly shuffled in a certain way tend to stay in the same configuration they were in the first place. For example, a dealer whose riffle shuffle does not interlace the cards alternately but shuffles in large clumps of cards, tends to keep the cards in their original configuration generally speaking. I would be astonished if such a shuffle put the cards into an even distribution of high and low cards. OTOH, If the cards are already evenly distributed, I would not be surprised to find that an excellent shuffle kept the cards evenly distributed, although that is the crux of my question and I am actually hoping the opposite is true. If not, it means that once the highs and lows are evenly distributed, they tend to stay that way with an ecellent shuffle where cards are near perfectly interlaced.

Should this be a separate thread?

[Three]

As Norm pointed out there are only 10 cards for Blackack A-9 and the T. That ordered by rank and suit looks very unusual but the truth is for BJ that is the same configuration as exchanging any equivalent card for another. You can exchange ranks of different suits and ant T's and it is the same BJ playing order. If you made it so no two of the same suit were adjacent and the T's were not in 10, J, Q, K order? The point is that order by rank and suit has a ridiculous number of equivalent orders. You only perceive that order as more unusual than any of the others but in BJ they are all the same. The odds of any order coming in concerning both rank and suit for each card is exactly the same so that exact order that you are seeing as truly random has the same chance of being the order as any other order. Once you see cards as BJ values there are only 10 cards to a deck instead of 52.

Sorry Aslan. The only question I see you asking recently I have to say coincidence unless I have more information to suggest otherwise. All deck configurations have the same likelihood. Because I see a pattern doesn't make it more likely that the rest of the cards will follow the pattern.

[Aslan]

Sorry Aslan. The only question I see you asking recently I have to say coincidence unless I have more information to suggest otherwise. All deck configurations have the same likelihood. Because I see a pattern doesn't make it more likely that the rest of the cards will follow the pattern.

Not exactly, Tthree. While it is true that the "out of the wrapper" new card order is just as likely as any random order, when you witness such an order in actual practice you know that it is non-random with near certainty, since you don't measure such an occurrence against the possibility of one other random possibility but against all other random possibilities. For this one particular configuration to appear is astronomical-- even, if you think about it, in your and my entire lifetimes.

I'm not a math guy, but what is it? 1/52! in the case of single deck?

Much, much less, I agree, for simply an even distribution which has many, many more possible ways of occurring.

Without someone simulating a perfect shuffle, I don't see how to mathematically decide whether an even distribution tends to stay evenly distributed. The way to do it might be to take two decks. Clump one 50/50 and the other perfectly evenly distributed, as to high and low cards. Then shuffle each perfectly, which can be done with a computer, and see the result of one shuffle (riffle), then two, then three, and so on, observing the configuration of cards after each individual shuffle (riffle).

[Aslan]

One might guess intuitively that the clumped deck becomes less and less clumped to some point, and the evenly distributed deck becomes clumped to some point. I'm sure there must be a "usual" degree of "clumpiness" (my word) for the average random shuffle. Whenever the cards are evenly distributed I scream when the dealer gives me a half-*ssed shuffle, believing that it takes several good shuffles to give clumpiness a chance to return.

[ohbehave]

Is there a practical point in regards to BJ in knowing the answer? You'll never see that shuffle.

[Aslan]

Is there a practical point in regards to BJ in knowing the answer? You'll never see that shuffle.

You will see dealers who shuffle near perfectly, interlacing most every card, and you will definitely see dealers who have great difficulty doing any better than pushing large clumps of cards together, that is, hardly shuffling the cards at all. The latter I know how to handle, the former, I'm not sure the effect of one, two, three, four, etc. shuffles on largely clumped cards, and evenly distributed cards. I am guessing that since seven shuffles represents a random shuffle in many circles, that one should hope for seven shuffles when the cards are evenly distributed between high and low cards in order to give large clumps a sufficient chance to occur, realizing that extremely large clumps are rarer than smaller clumps to begin with.

[Aslan]

With an evenly distributed deck you cannot possibly get large clumps with a single perfect riffle. Think about it. Nor with two. So with two good riffles (not perfect) you are not likely to go from an even distribution to one where there are large clumps of highs or lows.

I think it can be determinative whether you play the next shoe depending on the current configuration of the cards and the effectiveness of the dealer's shuffle.