Random shuffler?

Is the card shuffler at Pai Gow Poker random? If so, does the hand shuffle, before putting the deck into the machine, accomplish anything?
When a new deck is introduced into the game is it necessary to wash and shuffle the deck? What would the hands look like if a new deck (with the cards in order a-k) were put into the shuffler?

Quote: docsjs

Is the card shuffler at Pai Gow Poker random? If so, does the hand shuffle, before putting the deck into the machine, accomplish anything?
When a new deck is introduced into the game is it necessary to wash and shuffle the deck? What would the hands look like if a new deck (with the cards in order a-k) were put into the shuffler?

This is a good question that I do not know the answer to. Obviously the camera needs to see the deck to make sure that all of the cards, including one joker, are present in the deck. Beyond that I do not know why they have to wash the cards. At my casino the dealers also do one shuffle before putting the cards in the machine after every hand.

The new shufflers are capable of counting every card and ensuring that all the cards are present and accounted for, thus the camera in the sky would not have a reason to see the cards before being put into the shuffler. I think spreading the cards is more for the players' benefit than anything else.

Personally, I don't believe that the shuffler is random enough. I think the shuffler has 8 "pockets", one for each of the 7 hands, and one for the four discards. As such, I think the algorithm probably works along the lines of this:

1. Take the next card off the pile.
2. Select a random number which indicates a pocket between 1 and 8.
3a. If that pocket is full (ie, 7 cards for pockets 1-7 or 4 cards for pocket8), then go back to number 2.
3b. If that pocket is not full, put the card in there.

Repeat as you go through the deck.

Since this is the case, the first card has a 7/8 chance of being in one of the hands, and only 1/8 chance of being in the discard. It's easy to see that subsequent cards will have different chances of being in one of the hands or in the discard, however, earlier cards will have more of a chance of being in a hand as opposed to in the discard.

For this reason, I think the hand shuffle prior to putting the cards into the machine is necessary. The hand shuffle will actually randomize the order that the cards are taken by the shuffler.

Quote: konceptum

The new shufflers are capable of counting every card and ensuring that all the cards are present and accounted for, thus the camera in the sky would not have a reason to see the cards before being put into the shuffler. I think spreading the cards is more for the players' benefit than anything else.

Personally, I don't believe that the shuffler is random enough. I think the shuffler has 8 "pockets", one for each of the 7 hands, and one for the four discards. As such, I think the algorithm probably works along the lines of this:

1. Take the next card off the pile.
2. Select a random number which indicates a pocket between 1 and 8.
3a. If that pocket is full (ie, 7 cards for pockets 1-7 or 4 cards for pocket8), then go back to number 2.
3b. If that pocket is not full, put the card in there.

Repeat as you go through the deck.

Since this is the case, the first card has a 7/8 chance of being in one of the hands, and only 1/8 chance of being in the discard. It's easy to see that subsequent cards will have different chances of being in one of the hands or in the discard, however, earlier cards will have more of a chance of being in a hand as opposed to in the discard.

For this reason, I think the hand shuffle prior to putting the cards into the machine is necessary. The hand shuffle will actually randomize the order that the cards are taken by the shuffler.

This is precisely how I imagine it works as well. But when you talk about the probability of cards going to certain spots decreases as the machine goes through the deck, this really shouldn't matter. Think about a hand shuffle, it's IMPOSSIBLE for the top card to get to the bottom after just one riffle.

Also the machine could actually create hands, because it actually recognizes cards, the machines have a 'Sort' feature. I was thinking once a brilliant hacker could cheat. Certainly, these machines aren't connected to the internet, but are there other ways to access it? Because a guy was telling me about this kid he knew, who was completely socially inept, but he could do ANYTHING with a computer. He told me they drove to and parked outside of a bank at night, then he pulled out his laptop and was able to turn off the lights. How the hell could he do this??

At ElCo this trip the shuffler at the PGP table quit workign after the second hand. the pitboss todl the dealer to replace the cards, and handed her new ones.

As I recall, she checked each deck to see whether all the 53 cards were there, then mixed up the cards ont he table, then shuffled them by hand.

Alas, this did not fix the shuffler.

Quote: ewjones080

This is precisely how I imagine it works as well. But when you talk about the probability of cards going to certain spots decreases as the machine goes through the deck, this really shouldn't matter. Think about a hand shuffle, it's IMPOSSIBLE for the top card to get to the bottom after just one riffle.

Which is why, if all you are doing is a hand shuffle, you would riffle more than once and intersperse some cutting of the deck. The shuffling machine, by itself, isn't random enough, but throwing in a riffle and a cut prior to placing the cards in the machine helps the randomization process.

Or, consider this. A full table of players. Thus, all cards will be exposed, meaning you can know for certainty what the 4 unseen discards are. Most of the places I've seen, the four discards are placed into the discard pile first, at the bottom. As the other hands are resolved, they are placed on top of those cards. In other words, the 4 unseen cards are at the bottom of the deck. With no riffle and cut, that stack of cards is placed into the machine, a machine that draws cards from the bottom first. Following the algorithm, you know that the chance of those 4 cards being in hands the next deal are pretty high. On the other hand, if a riffle and cut is done first, and then the deck is placed into the machine, those 4 cards are no longer at the bottom of the deck. They are now, most likely, somewhere in the middle of the deck, thus reducing the chances that the cards are going to be in the hands.

The fact that a card ends up in a random location is not nearly as important as the card having an equal probability of ending up in any of the locations.

I'm not sure exactly how much the following will make sense.

Take a hypothetical example, in which there are 3 cards, marked "1", "2", and "3". Hand "A" is composed of 2 cards, and hand "B" is composed of 1 card.

If the 3 cards are shuffled perfectly, then the are 3! = 6 permutations of the cards in the order they can appear:
123
132
213
231
312
321

If the first two cards were dealt into hand A and the final card dealt into hand B, you can see that there are essentially 3 different possible hands:
12(3)
21(3)

13(2)
31(2)

23(1)
32(1)

And each of those possibilities, based on a perfect shuffle, have a 1/3 chance of happening, in other words:
1/3 chance of 12(3)
1/3 chance of 13(2)
1/3 chance of 23(1)

Now let's look at our shuffling machine's algorithm, when only the shuffling machine is used, and no other riffles or cuts.

The first card, card 1, goes into the machine first. There's a 50% chance it goes to pocket A and a 50% chance of going to pocket B.
If card 1 goes to Pocket A, then card 2 is next. 50% chance to Pocket A and 50% to pocket B, since no pockets are filled. Card 3 then goes to the unfilled pocket.
On the other hand, if card 1 goes to pocket B, then pocket B is now full, so cards 2 and 3 automatically go to pocket A.

In other words, you end up with
1/4 chance of 12(3)
1/4 chance of 13(2)
1/2 chance of 23(1)

Clearly, if this is the algorithm used, then the shuffling machine is not sufficient.

If the algorithm is based upon the number of slots within the machine to begin with, then this also doesn't work.
In that situation, card 1 has a 2/3 chance of going to pocket A and 1/3 chance of going to pocket B. If card 1 goes to pocket A, then both pockets are still available,
so card 2 has 2/3 chance of going to pocket A and 1/3 chance of going to pocket B. Following the math on this, you come up with

4/9 chance of 12(3)
2/9 chance of 13(2)
1/3 chance of 23(1)

Again, not optimal.

Instead, the machine would have to take into account which slots are already partially filled, and reduce the number of possibilities as spots within pockets are taken.
In other words, card 1 has a 2/3 chance of going to pocket A. If it does go to pocket A, then card 2 has 1/2 chance of going to pocket A and 1/2 chance of going to pocket B. In this situation, you should come up with

1/3 chance of 12(3)
1/3 chance of 13(2)
1/3 chance of 23(1)

which is optimal.

Quote: ewjones080

Also the machine could actually create hands, because it actually recognizes cards, the machines have a 'Sort' feature. I was thinking once a brilliant hacker could cheat.

The people at Shufflemaster would have to be insane to build in a way for the shuffler to "make" certain hands. There would need to be a mode to make it do that (like the sort mode) and the logic would have to be programmed onto the internal logic chip(s). A hacker would have to be more than brilliant, they'd need to be a Shufflemaster engineer with access to a live shuffler. And they'd need someone on the other side of the table to put it into that mode. Then they'd better collect their winnings quick and run because after the third or fourth Royal Flush with aces in the low hand I'm guessing someone would be looking at the surveillance tape.

Quote: ewjones080

Certainly, these machines aren't connected to the internet, but are there other ways to access it?

FWIW, I'll take a closer look next time I'm on PGP, but I can't recall seeing a data port of any kind on any shuffler.

Quote: ewjones080

Because a guy was telling me about this kid he knew, who was completely socially inept, but he could do ANYTHING with a computer. He told me they drove to and parked outside of a bank at night, then he pulled out his laptop and was able to turn off the lights. How the hell could he do this??

Story sounds like BS to me. There are so many unlikely things that would have to be so that the odds against this being truth are astronomically against.

- The lights for some reason would have to be set up to be controlled by a computer. Unlikely, most automation of this sort doesn't require the expense or sophistication of a full blown computer to operate.

- Said computer would need to be on the bank's local network. Unlikely, as there's little to no need to do so.

- The network would have to be wireless and unsecured. Unlikely, that a financial institution runs an unsecured wireless network. Also unlikely that even a genius hacker is going to guess their way past the kind of encryption most secured networks use.

- The computer controlling the automation would need to be located on the network. Not that this step is impossible if you could get access, but it would be very likely time consuming, as getting access to find out if you had the right one would require figuring out a username (with proper access rights) and password for each machine you wished to examine.

- Once past these hurdles, said program running the building automation would likely have a password. Unlikely to brute force guess such a password.

So, yeah, if everything was just right and the kid had (a lot of) inside info, I guess it could be true. But, it sounds very unlikely, especially for a parlor trick like playing with the lights.