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How many shuffles? (2 Viewers)

Chipandchair said:
I think they only wash a brand new deck
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It's been a year since I've played live poker, but my recollection is that in the rooms I played in, they would switch decks every level (so, every 20 or 30 minutes) and when they switched decks, they'd wash.
 
we have two decks (of different color so we don't mix them up) so that the dealer can shuffle his deck as much as he can while players are thinking.
 
If I the only Dealer => riffle, riffle, box, riffle, cut or riffle, riffle, box, cut

If 2 Decks in play => riffle, riffle, box, riffle and the next dealer will Cut
 
So the magic number is 7, but you should also wash them. I've been dealing underground games since I was 17, I was into card magic as well and I remeber reading early on that to proper shuffle you'd need 7 riffle shuffles. Though after randomized most do 2 shuffles a box and a shuffle and get the cards in the air.

Someone posted here on this forum a break down of the randomization of the deck mate shuffler, and found that it actually needed like 9 to 10 shuffles to properly randomize the cards. so I typically hit 7 and then 3 while I mess with the second deck. It was really great info, with bell curves of each shuffle, wish I remebered the thread.

What would this forum be without a link to a youtube with a goofy looking guy and funny accent talking about math and randomization?

 
dtxkgb said:
Was curious to see how many timeyou guys shuffle the deck before a hand for your cash games/tournaments?

Came across youtube video that says the perfect amount was 7 bridge shuffles. Any pro dealers on the forum? lol
Click to expand...

I wrote a paper in grad school that aimed to solve this problem using Monte Carlo simulations and rising sequences. If you're interested in it, I can send it to you. It's in PDF format. But here's a screen shot of the most relevant plots from the project. The blue line represents the distribution of rising sequences from a completely randomized deck, and the tan histograms are the distributions for the number of rising sequences found in decks that were shuffled n times.


Screenshot_20220131-163511.png
 
RainmanTrail said:
I wrote a paper in grad school that aimed to solve this problem using Monte Carlo simulations and rising sequences. If you're interested in it, I can send it to you. It's in PDF format. But here's a screen shot of the most relevant plots from the project. The blue line represents the distribution of rising sequences from a completely randomized deck, and the tan histograms are the distributions for the number of rising sequences found in decks that were shuffled n times.


View attachment 856423
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I'm actually very interested in this. (email removed)
 
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I'll just post screen shots of the paper here. It's a fairly short read. It also has some R code in it for anyone wanting to duplicate the experiment and run it themselves.

Note: A "rising sequence" just means a run of ordered cards in the deck of any length. It can be sequential or can have cards in between, but it must be ordered from top to bottom (e.g., :2s::3s::8h::4s:, or :9d::td::jd::qd::kd:, or :6c::7c::3d::th::8c:, etc.). If you start with an ordered deck and shuffle it n times, you can count the number of rising sequences that occur in the deck after shuffling to determine if it is sufficiently random. A deck of cards that has been shuffled a zillion times will have 26.5 rising sequences on average with a standard deviation of 2.1.

Cliff notes: Yes, 7 riffle shuffles should be sufficient for preventing someone from being able to take advantage of the order of the cards in the deck. Anything less is exploitable. 3 shuffles is very exploitable. And while I don't address this in the paper, it's worth pointing out that box shuffles are effectively useless. Washing the cards is best.

Wash > riffle shuffle >>>>>>>>>>>>> box shuffle


Shuffling-1.pngShuffling-2.pngShuffling-3.pngShufflling-4.pngShuffling-5.pngShuffling-6.pngShuffling-7.png
 
I thought you did something specific for the deckmate shuffler, but you're saying 7 is adequate, but at 10 shuffles it the highest randomization you can achieve? anything more is just wasted.
 
Machine said:
I thought you did something specific for the deckmate shuffler, but you're saying 7 is adequate, but at 10 shuffles it the highest randomization you can achieve? anything more is just wasted.
Click to expand...

Not quite. Basically, 7 shuffles is needed to be able to prevent someone from being able to exploit the ordering of the cards in the deck. But the distribution of decks that have been shuffled 7 times is definitely still not quite as randomized as decks that have been shuffled infinitely many times. You'd need about 12 shuffles before the distribution of the ordering of the decks is indistinguishable from a distribution of truly randomized decks.

But practically speaking, I'd say any game where the deck is either shuffled 7 times or washed and shuffled a few times is sufficient for preventing anyone from being able to exploit the deck. However, if you just grab a deck and use the shuffle, shuffle, box, shuffle, cut approach, then anyone could easily exploit that deck if they were paying close attention.

As an example. Let's say the previous hand had a board with 4 spades on it, and 3 players saw the river, one who had 2 spades in his hand, the other with the Ace, and the other with the King. So 8 spades total. The dealer pushes all the hands up along with the board, then gathers the stub of the deck and the cut cards, then groups the live hands and the board all together and placed them all on top of the deck and squares it up. Then he does a standard shuffle, shuffle, box, shuffle, cut. You look down and see two spades. Then, on the flop, there are two more spades, both of which were in play from that previous hand. In this situation, the likelihood that you will hit your flush draw is much higher than the standard 35% odds you would have from a truly randomized deck because the dealer only shuffled 3 times. The ordering of the cards is not completely random. It is still somewhat correlated to the ordering from the hand before. And since spades smashed the previous hand and this flop contains 2 of those cards, it is highly likely that another one will fall because only shuffling 3 times leaves the deck "chunked". Note, this is not the same as saying "last hand was all hearts" or "all paint" and saying that the next hand will likely be the same before it gets dealt since the deck was only shuffled 3 times. You'd need to see those same cards show up on the flop in order to exploit it in holdem. It's easier to exploit a poorly shuffled deck in 7 card stud games.
 
You'd need about 12 shuffles before the distribution of the ordering of the decks is indistinguishable from a distribution of truly randomized decks.
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awesome.

And since spades smashed the previous hand and this flop contains 2 of those cards, it is highly likely that another one will fall because only shuffling 3 times leaves the deck "chunked".
Click to expand...
While only one deck, it would be like shuffle trucking.

I typically wash (swoosh, the dude says that in the vid I linked, I find it funny) and then shuffle 7 to 10 times, after which I have a shuffler and hit the 7. if I have to hand shuffle I typically s, s, b, s, then after 3 or 4 hands wash.

Thanks!
 

RainmanTrail said:
I'll just post screen shots of the paper here. It's a fairly short read. It also has some R code in it for anyone wanting to duplicate the experiment and run it themselves.

Note: A "rising sequence" just means a run of ordered cards in the deck of any length. It can be sequential or can have cards in between, but it must be ordered from top to bottom (e.g., :2s::3s::8h::4s:, or :9d::td::jd::qd::kd:, or :6c::7c::3d::th::8c:, etc.). If you start with an ordered deck and shuffle it n times, you can count the number of rising sequences that occur in the deck after shuffling to determine if it is sufficiently random. A deck of cards that has been shuffled a zillion times will have 26.5 rising sequences on average with a standard deviation of 2.1.

Cliff notes: Yes, 7 riffle shuffles should be sufficient for preventing someone from being able to take advantage of the order of the cards in the deck. Anything less is exploitable. 3 shuffles is very exploitable. And while I don't address this in the paper, it's worth pointing out that box shuffles are effectively useless. Washing the cards is best.

Wash > riffle shuffle >>>>>>>>>>>>> box shuffle


View attachment 856448View attachment 856449View attachment 856450View attachment 856451View attachment 856452View attachment 856453View attachment 856454
Click to expand...
I dig this so much...

In fact, I dug it so much I spent most of my Sunday rewriting it in PHP (I'm not much for R) to try a few things out. I'll admit I was initially skeptical, but I'm happy to report I ended up confirming your results :cool

I think I did some things a little differently (because not R, and because I was trying to work out what you were doing along the way).
- I'm looking for rising sequences (that is the next card higher than my card) and starting with my ordered deck that's the case for every card apart from the last one so my shuffling reduces the sequences, rather than increase them. I initially had a suited deck with 48 sequences in it, but decided the important thing was fore-knowledge of the total order, not the way the suits fell, so I switched to a single 52 card order.
- I don't use a binomial when splitting the deck, instead I assume a 10% +/- accuracy on the dealer's part in making two "equal" stacks. I then randomly picked from either half stack when riffling together.
- I modelled a strip because I wanted to compare with the riffle. It takes 1/6 (+/- 10%) of the cards from the top to make the bottom of the new stack, then takes the bottom 1/5 of what's left and puts them on top of the new stack, then top 1/4, bottom 1/3...

My results iterated over 10,000 instances of each shuffle type are below.
- My fully randomized model tends towards 25.5 sequences. I think this is an artefact of me counting down vs. you getting 26.5 counting up.
- 12 riffles is 25.7 - almost the same as fully random.
- 7 riffles is 28.9 - Within an SD or 2 of fully random.
- The strip isn't useless, but it's not great. 7 Strips will get you down to 38 sequences.
- 7 Strips is about the same as 4 riffles, 12 strips about the same as 5 riffles, or a 4 riffle, 3 strip combo :LOL: :laugh:
- The standard riffle, riffle, strip, riffle, cut has 40.3 sequences leaving the deck on the dirty side. I'm definitely not going to let folks do less than this from now on and will wash the deck periodically.
- I don't have any pretty pictures. Sorry.

Thanks for the inspiration!

1650242024744.png
 
Kentucky said:
I dig this so much...

In fact, I dug it so much I spent most of my Sunday rewriting it in PHP (I'm not much for R) to try a few things out. I'll admit I was initially skeptical, but I'm happy to report I ended up confirming your results :cool

I think I did some things a little differently (because not R, and because I was trying to work out what you were doing along the way).
- I'm looking for rising sequences (that is the next card higher than my card) and starting with my ordered deck that's the case for every card apart from the last one so my shuffling reduces the sequences, rather than increase them. I initially had a suited deck with 48 sequences in it, but decided the important thing was fore-knowledge of the total order, not the way the suits fell, so I switched to a single 52 card order.
- I don't use a binomial when splitting the deck, instead I assume a 10% +/- accuracy on the dealer's part in making two "equal" stacks. I then randomly picked from either half stack when riffling together.
- I modelled a strip because I wanted to compare with the riffle. It takes 1/6 (+/- 10%) of the cards from the top to make the bottom of the new stack, then takes the bottom 1/5 of what's left and puts them on top of the new stack, then top 1/4, bottom 1/3...

My results iterated over 10,000 instances of each shuffle type are below.
- My fully randomized model tends towards 25.5 sequences. I think this is an artefact of me counting down vs. you getting 26.5 counting up.
- 12 riffles is 25.7 - almost the same as fully random.
- 7 riffles is 28.9 - Within an SD or 2 of fully random.
- The strip isn't useless, but it's not great. 7 Strips will get you down to 38 sequences.
- 7 Strips is about the same as 4 riffles, 12 strips about the same as 5 riffles, or a 4 riffle, 3 strip combo :LOL: :laugh:
- The standard riffle, riffle, strip, riffle, cut has 40.3 sequences leaving the deck on the dirty side. I'm definitely not going to let folks do less than this from now on and will wash the deck periodically.
- I don't have any pretty pictures. Sorry.

Thanks for the inspiration!

View attachment 897667
Click to expand...
... and the Oscar goes to....
 
Kentucky said:
I dig this so much...

In fact, I dug it so much I spent most of my Sunday rewriting it in PHP (I'm not much for R) to try a few things out. I'll admit I was initially skeptical, but I'm happy to report I ended up confirming your results :cool

I think I did some things a little differently (because not R, and because I was trying to work out what you were doing along the way).
- I'm looking for rising sequences (that is the next card higher than my card) and starting with my ordered deck that's the case for every card apart from the last one so my shuffling reduces the sequences, rather than increase them. I initially had a suited deck with 48 sequences in it, but decided the important thing was fore-knowledge of the total order, not the way the suits fell, so I switched to a single 52 card order.
- I don't use a binomial when splitting the deck, instead I assume a 10% +/- accuracy on the dealer's part in making two "equal" stacks. I then randomly picked from either half stack when riffling together.
- I modelled a strip because I wanted to compare with the riffle. It takes 1/6 (+/- 10%) of the cards from the top to make the bottom of the new stack, then takes the bottom 1/5 of what's left and puts them on top of the new stack, then top 1/4, bottom 1/3...

My results iterated over 10,000 instances of each shuffle type are below.
- My fully randomized model tends towards 25.5 sequences. I think this is an artefact of me counting down vs. you getting 26.5 counting up.
- 12 riffles is 25.7 - almost the same as fully random.
- 7 riffles is 28.9 - Within an SD or 2 of fully random.
- The strip isn't useless, but it's not great. 7 Strips will get you down to 38 sequences.
- 7 Strips is about the same as 4 riffles, 12 strips about the same as 5 riffles, or a 4 riffle, 3 strip combo :LOL: :laugh:
- The standard riffle, riffle, strip, riffle, cut has 40.3 sequences leaving the deck on the dirty side. I'm definitely not going to let folks do less than this from now on and will wash the deck periodically.
- I don't have any pretty pictures. Sorry.

Thanks for the inspiration!

View attachment 897667
Click to expand...

Awesome! Glad to see someone else had fun nerding out over this problem! :ROFL: :ROFLMAO:
 
I used to always do riffle, strip, riffle, riffle as was done at casinos before shufflers became common. But they also always “washed” the cards first. Now I add another strip section. The recent posts make me feel that was a good idea :oops:

That said most of my poker friends cant shuffle at all. I wish more people would practice as it would speed up the game without needing a second deck
 
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Nothing beats a good washing of the cards. It's far better than any shuffle can do, by many multiples over too.
 
7-10 for me, with a box or 2 in the middle. Never taking the cards off the table or exposing a card. I’m a pretty quick shuffler too
 
scramble
shuffle
shuffle
riffle
shuffle
cut and go

isn't that the procedure for pretty much every casino? A good dealer can start the scramble and get every card out to a full table inside 30 seconds.
 
I don’t know if this has come up in this thread yet, but I’ve definitely heard more than once that most washes are way too quick to be effective - that a good wash is like 30 seconds long.
 
upNdown said:
Yes it is. But casinos don’t care about randomized decks. They care about quick shuffles, leading to more hands, leading to more rake.
Click to expand...
Yeah. casino procedure is built for speed and game protection. It's tough to control cards while doing a proper shuffle sequence. Anything more than that is pretty over the top. Its funny how particular you guys are about your poker.

I was just accused of stealing from a home game because I made more than their "best dealer" who was drunk and high the entire night we were working. I tried talking to the hosts of the game and they didn't even understand what was so important about hands per hour. smh
 
Are you factoring in “stripping” the deck while shuffling? Taking little groups of cards off while doing a traditional shuffle. Casino dealers always do this during their 4 shuffles
 
57chevy said:
Are you factoring in “stripping” the deck while shuffling? Taking little groups of cards off while doing a traditional shuffle. Casino dealers always do this during their 4 shuffles
Click to expand...
That’s also known as boxing, and was mentioned previously as being not very effective.
Yet all the dealers do it between riffles.
 

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