Quote from: TrevorXavier on June 01, 2016, 06:54:40 PM

Quote from: casinobitco on June 01, 2016, 06:28:06 PM

I think that would be extremely valuable... also, how would a 'rigged casino' account for games that have unexpected customer behaviors? Like hitting or staying in Blackjack, or going randomly red / black in roulette?

Not discounting what you're saying technically, but I just don't see how a rigged casino could account for these variables.

Yes, so that's part of the heuristic I mentioned earlier. There are games, such as roulette, which require play history. However, there are others, such as blackjack, that are exclusive. The exploit works regardless. In addition, you don't really need to account for 'strange' plays, as the goal is to reduce favorable cards for the player, or encourage favorable cards for the dealer. Since the dealer doesn't play strangely, the exploit works. Here's a brief overview:

Roulette

Optimizations: favor one color over another; favor thirds; favor number; reduce instance of number, color, or third.
Heuristic: Brute-force. The arrangement space is computationally feasible.
Deployment: Requires at least one game played to stack decks.

Blackjack

Optimizations: player receives bust hand (13-16); deny player ace; house starts with 10, Ace, or non-bust card; reduce splitting; reduce doubling; reduce dealer busts, and more
Heuristic: Create translation decks using the seed space. Since most blackjack games average 6-7 cards total dealt, attempt to optimize by best-fit.
Deployment: Mutually-exclusive. Exploit works regardless of prior play.

For blackjack, you're not necessarily attempting to combat random play (random hits, random doubles), but rather, encourage favorable cards to the dealer and encourage bad cards for the player. So, you're looking for arrangements that give the dealer an Ace more often than not, give the player a 6, reduce the likelihood of splitting, doubling, and so on. Beyond that, you'd want to allow for the house to make their hand (try to keep a slug of low cards beyond the 7th position of the final deck, etc.). You can also optimize to combat basic strategy and 'upgrade' the cold decks when prior play history suggests the player is playing this way.

Blackjack works due to the extremely large arrangement space. You're talking 416! / 128! / (32!)⁹ possible arrangements in an 8-deck game. Since your target is only 2³², that means you need to find an arrangement that works well against the 2³² / (416! / 128! / (32!)⁹) shuffles in the final space. The number is so small that most calculators can't even represent it. It's possible there exists an arrangement that beats all possible seeds.

Video Poker

Optimizations: encourage dead hands for the first 10 cards; reduce royal flush, straight flush, and so on; allow for good primary hands (like four to a straight flush), but deny matching card, and more
Heuristic: Create translation decks using the seed space. Reduce translations to first 10 cards and attempt a best-fit optimization.
Deployment: Mutually-exclusive. Exploit works regardless of prior play.

This is just a partial list. I'll elaborate more when I publish the optimized decks. This is pretty much where I started when I attacked the problem.

Addendum: Also, remember, the goal of shufflepuff is to not discover the uber-optimized deck, just ones that perform better than others. So, a casino operator performing a random search would probably do well in the short term with shufflepuff vs. hiring a mathematician to construct a heuristic.

after reading this it is clear that Black Jack is best game to cheat ( for a provably fair casino )

it is like some casinos took out some 10 value cards to the decks to get an advantage or players added some cards to the decks to get an advantage without counting

thx for this detailed explanation