πŸ€‘ Analysis of casino shelf shuffling machines () | Hacker News

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In order to write a computer simulation program that would mimic the shuffle of a human blackjack dealer, it was first necessary to analyze the types of shuffles.


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It may not seem like much, but with perfect play the house edge is only about ​% in Blackjack[1] (depending on exact rules), so every little bit.


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Overview - possible shuffles in the game of blackjack of a shoe there is exactly one shoe composition so in that case combinatorial analysis is % accurate.


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Limiting their analysis to the riffle shuffle makes their findings more applicable to games like bridge and poker, where players continuously and deliberately put.


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It may not seem like much, but with perfect play the house edge is only about ​% in Blackjack[1] (depending on exact rules), so every little bit.


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Some of the first devices for casino gaming analysis enabled casinos to Shuffling at‐will is permitted in every state with blackjack, sometimes.


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It may not seem like much, but with perfect play the house edge is only about ​% in Blackjack[1] (depending on exact rules), so every little bit.


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This ensures the player edge obtained from card counting is literally as high as it can be. Shuffle Analysis: Smarter casinos use card shuffling machines that β€œ.


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Casinos are making the switch to Continuous Shuffling Machines (CSM) for Playing cards on Blackjack table in casino, close-up Odds--did a mathematical analysis of Continuous Shuffling Machines and found that there.


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blackjack shuffle analysis

One should make a mental note of how close the newly recorded counts are to the estimates, and also to compare this to the prediction of the true count i. One possibility is to go to a higher bet when either the shuffle-track OR the true count indicate that this is a good idea. If the unplayed cards all get shuffled into the top half of the shuffled pile, where should you cut the cards? Casinos do not use more thorough shuffles, because more thorough shuffles take more time and reduce profits and fortunately shuffling machines have not yet caught on. The count record chips are the counts of various regions in the current shoe. You might also want to pat yourself on the back and raise your betting during the first half of the shoe, even though the count will probably start to go negative. This can be counter-intuitive no pun intended. An important thing to remember during shuffle-tracking is that high count regions are bad and low count regions are good. In constrast, a simulated regular card counter did little better than break even in this game, if not permitted to abandon negative counts. Alas bjmath. I can't imagine that he would mind as it has been posted publicly for nearly 20 years. I am trying to locate Mike through mutual friends for permission to post it permanently. Also, while shuffle-tracking, I cut out more low cards than high cards, statistically significant to the The complete results of the hand-done trials are given in an appendix. For the next deck C you take the count difference and stack a chip representing this on the count record pile while also updating the record of the current running count. The profile shows how the tracking units are combined. Also, if you choose too small tracking units, you will not be able to "eyeball" the discard tray to determine which tracking unit you're in, but if you choose too large tracking units, you may have insufficient information to give you much of an edge. The chip notation is used to record the numbers, such as counts in various regions of the shoe. If you are really sharp, you can split this count unevenly according to previous tracking information. A shuffle-tracker who is playing through the second shoe at a table will have four groups of chips: betting chips, count record chips, running count chips, and shuffle-track prediction chips. A profile was listed in a previous section that look like this:. A glossary of blackjack, card counting, and shuffle-tracking terms can be found in the appendix. Counting is necessary to have some idea of the favorability of different regions of the played cards, so that these regions may be tracked through the shuffle. Generally, the tracking units relate to the dealer's pick sizes, otherwise the tracking predictions may be unnecessarily inaccurate. You record the running count for the first deck and call it A, the second B, and the third C. Using brute force is simpler, but also less disguised. Unfortunately, shuffle-tracking is still in its infancy, so there is not a large body of scientific literature on this subject. Then the pile looks like this:. If the shuffle-track predictions do not seem correlated to the observed counts, then you may be making mistakes or the shuffle may not be very trackable. The reason is that on average the first half of the shoe should now on average have a count of , which means there are ten more high cards than low cards. The running count chips denote the running count when the last count record chip was placed. A common shuffle used by casinos is the "zone shuffle". After the first deck A , you place a chip to denote the running count. A great deal of randomness was put into the shuffle, making it difficult to track, and the tracking and card counting was not done perfectly. You can still bet according to true count. You would bet more aggressively in the -3 region and more conservatively elsewhere. You can use different colors to represent positive versus negative or versus You can use patterns in how the chips are stacked, perhaps offset to the left or right. The plus sign indicates that the estimated count in each two deck region is simply the sum of two tracking units. It is a fact that high cards favor a player and low cards favor the dealer; hence, removing a high card from the shoe reduces the running count and removing a low card from the shoe increases the running count. Suppose that shuffle starts by putting the unplayed cards on top of the played cards. You not only have to know how to shuffle-track well, but you also have to know how to avoid detection by casino personnel. Tracking more regions can give you more detailed information about the next shoe. In place of paper and pencil or computers, shuffle-trackers use their chips to provide "memory". At the end of the played portion of the shoe, you take the opposite of the running count and assign this to D. This is just a precomputed diagram showing how to combine different portions of the shoe. However, tracking gives you additional information that will either allow you to raise your bets more often or more safely or perhaps both.

This paper was posted by Michael Hall on rec. The premise of shuffle-tracking is that shuffles are nonrandom - by this I mean that the location of cards after the shuffle is to some degree predictable. Empirical Results in Support of Shuffle-Tracking I ran my shuffle-tracking simulator on a casino shuffle, using a realistic "clumpiness" of the riff and realistic inaccuracies in pick sizes and randomness in plugging.

For casinos that use blackjack kindle in blackbelt same exact shuffle each time with no randomness in the order of picks or pluggingyou can analyze the shuffle away from the tables and come up with blackjack shuffle analysis "profile".

Thus, even with the uncertainty in pick sizes and riffs, a particular card has a zero percent probability of being in certain portions most of the shuffled pile, and a high probability of being in one or two particular portions of the shuffled pile. Here, you would cut as close to the bottom, trying to keep the -3 in front blackjack shuffle analysis the end-of-play card.

And the shuffle-track prediction chips are the predictions of the counts in the current shoe. As the shoe is played through, the shuffle-track prediction pile s shrink and the count record chip pile s grow. With a spread, never abandoning the table, it achieved a 1. The recorded running count is for each deck individually, so you must either take differences in the new and previous running counts.

The technique involves keeping track of the count in different portions of the discarded cards, as they are observed during play. The other possibility is to go to a higher bet only when both the shuffle-track AND the true count agree that this is a good idea.

The betting chips are an unorganized mess from which all bets are placed and into which all winnings are placed. Suppose it is a four deck game, with three decks actually dealt.

By abandoning hopeless shoes, the shuffle-tracker's blackjack shuffle analysis could be increased - a regular card counter blackjack shuffle analysis about 0.

Therefore, my limited empirical studies of shuffle-tracking may be the only such studies.

After all, a casinos won't allow you whip out paper and pencil or your shuffle-tracking computer at the blackjack tables!

And if the top blackjack shuffle analysis are shuffled together and then the bottom halves are shuffled together and placed on top, you wind up with this "profile":. Here, you actually "shuffle" your chips the same way in which the dealer shuffles the cards.

The complete results of these blackjack shuffle analysis trials are given in an appendix. For example, suppose that a four deck shoe is being tracked with four regions, A, B, C, and D the latter being the unplayed cards.

I am assuming that the reader has some knowledge of blackjack and card learn more here. You stack this chip on top of the previous and then record the current running count separately.

Here, the cards are broken into piles, and then the shuffling is only performed between the piles. This profile can be memorized and a small cheat sheet of it perhaps on the back of a business card brought to the casino in case you freeze under pressure. Shuffle-tracking requires a lot of "table smarts", just like card counting.

The shuffle-tracker was blackjack shuffle analysis the cut card every time, however. Shuffle-tracking teams can be effective.

In fact, shuffle-tracking is based on card counting. If there were more than one tracking unit that was unplayed, then this final count would be split among the unplayed tracking units as an estimate. The answer is right in the middle. Deciding what tracking units to use is important. All this is well and good, but how can it work in practice? You can use clock notation to represent 0 12 o'clock through 11 11 o'clock. Shuffle-tracking is based on a simple, sound theory, and there are computer simulations and hand trials to back up the theory. Penetration was set at Shuffle-tracking also had an overall accuracy in all regions of the shoe greater than the accuracy of true count half way through the shoe. Shuffle-tracking is a mathematically-based approach, just like card counting. True count is running count divided by the number of unplayed decks, and for the high-low system each unit of true count is worth. Always remember that shuffle-tracking is not mutually exclusive to card counting. Actually, you should listen to shuffle-track predictions more towards the beginning of the shoe, and true count more towards the end of the shoe, because true count is of no help at the beginning of the shoe but is very accurate at the end of the shoe. Unfortunately, he also disappeared from the scene in As I look, I'll keep the paper here. The unplayed deck is D, and it is assigned the opposite of the final running count. After the second deck B , you subtract the current running count from the previous running count. For shuffles where the dealer has some randomization effect, like mixing up the order of picks, the tracking requires more of a brute force approach. Thus, it could identify favorable situations even at the start of the shoe, allowing the shuffle-tracker to bet big off the top of the shoe intelligently, not just as counter-camouflage. Obviously, you must be discrete, but many gamblers play with their chips. A Simple Shuffle-Tracking Strategy The previous section gave a trivial example of shuffle-tracking, where you just use the running count at the end of the shoe. The higher the running count, the more favorable or less unfavorable the game is for the player. Shuffle-trackers actively exploit the inherent nonrandomness in casino shuffles.