But what if that last turn is the first turn? Once played a game of Rude Mood where the game terminated at the end of Turn 1 because the French were unable to attain their VC simply because the Germans stayed alive in a CC. I certainly felt cheated even though I won, just because of the preparation and analysis time spent on setting up the scenario. Ever since that playing I have avoided scenarios with VCs of that ilk like the plague!
If decks were truly well-shuffled between pulls, you would get the same result as dice. The original poster wanted something different from what dice give you. So while such a machine helps a casino achieve its goal, it would not help the original poster in the least.
Depending on what length of sequence you consider and the parameters of your dice deck, a dice deck may not help you noticeably. For instance if all it takes is three "good" rolls (say in the range 2-4), then a reasonably-sized dice deck is not going to help you that much. With dice, that will be (1/6)³ = .4630%, and with a fresh deck of size 144 (four sets of thirty-six) it will be 24/144*23/143*22*142 = .4153%. That's different, but is it different enough to enhance your enjoyment?
Well, with dice decks, you don't need a dice tower. IIRC in casinos, they do have vast stacks of decks in card shuffling machines. Install those on the ASL gaming table instead of the dice towers. Surely an eye-catcher. Complaints might shift from "loud" dice towers to "loud" card-shuffling procedure, but that's really details.
Ah, sampling without replacement. Draws would most certainly not be IID, and would significantly reduce or eliminate the "lucky runs."
"signficantly" is a key question here. Above I calculated a simple sequence of three DRs within the range of values 2-4. The likelihood was less using a dice-deck (no replacement) than with dice, but that was expected (I hope). In a statistical sense (something like 95% significance; and here I am throwing out terms without fully understanding them nor having calculated them, so I may be wrong but I think not), they are significantly different. In a gaming sense? Am I likely to notice the difference? I don't think so. Might it make me feel better? I think I would be too busy counting cards to feel one way or the other about it, but it might sooth other players.
Indeed - an important insight of behavioural science is just how poorly the human brain acts when asked to calculate probabilities (which has obvious implications for decision making). Actual Random sequences look very different to how we often assume - streaks should be expected in the course of many random draws, but your typical human mind doesn't see things that way. So, the human mind mistakenly declares 'aberration' when, actually, the absence of such streaks would be highly unlikely.
Very true. At some point when I was teaching a course using probabilities, I would ask students to either flip a coin 100 times and record the sequence, or make up by themselves a "random" sequence - and I could tell which they had done, without using any computing equipment. I don't think I ever got it wrong. The trick was typically to look for the longest sequence of consecutive "heads"; in a made-up sequence, it would almost always be no longer than 5, which is quite unlikely in a random sequence.
Virtually anything is.I just watched "The Big Bang Theory". But this is better...
von Marwitz
Indeed. I go especially nuts when people say "that's dicebot for you" if it happens on VASL when real dice can and should do the same sort of thing, and, while people while, almost never does someone actually feel the dice are unfair.
Just one more amplifying comment for those who are unfamiliar with basic probability theory: Don't bet the family nest egg on any particular low probability sequence of rolls occurring, but you can be pretty certain that some will.
Look at the mess you made.
If we remember that mess, we are a non shuffled deck.
