Mathematically cards are massively different from dice because *they have memory*.
When you talk about your “luck running out” it’s an abstract, almost spiritual concept – Lady Luck has taken her eye off you.
With cards your luck literally runs out – if you’ve pulled all your tens and face cards out of the deck, you have no more “luck” left; you’ve only got “bad luck” to look forward to.
This can give opponents hope to hang on in there against a “lucky” opponent.

With dice, the chance of rolling a six after a run of four sixes in a row remains one-in-six. With cards, every card you draw affects the odds of your drawing a similar (or higher, or lower) value on subsequent draws.

In short, cards are nothing at all like dice!

I think it’s fair to say that a mechanic which requires you to draw a card, return it to the deck then shuffle it back in is pretty broken 😉
*Most* games require you to shuffle a discard pile once they’ve all been exhausted- but even if not, and your “luck repeats” it alters the mathematic probability of drawing a certain number after each draw – that’s still very different to a dice roll.

The main point was: card-based “random” mechanics work really well in tabletop games. Far better than dice – and this is precisely *because* mathematically, drawing cards differs greatly from dice and *are* significantly different to a simple D50 dice roll (assuming you’re not drawing and shuffling after every draw, which would just be madness!).

I feel like we’re dicussing two different things here.
A mechanic to replicate the rolling of dice by using cards feels like a “broken card mechanic” (after all, why use cards and all the extra effort of shuffling after every draw, in order to replicate what could be more easily acheived rolling a dice?). Yes, you can simulate dice rolling by drawing cards, but to do so would be a failure of a card-drawing mechanic.

The original claim “mathematically cards shouldn’t differ greatly from dice, depending on the types of dice” overlooks the way that drawing cards is used in gaming – i.e. they’re *not* shuffled after every draw, and therefore *mathemetically* cards *should* differ greatly from dice.

The idea of a “guaranteed” result (after drawing many cards) holds true if you’re an amazing card counter and have just one card left – even those of us capable of basic card counting (tracking how many “high” cards and “low” cards have passed) couldn’t give an exact percentage chance of success, but would have a general feel for “how things are going” (i.e. is the deck stacked with more high value cards, or mostly low value cards?). For me this isn’t a bad thing – and makes the game (note, the game, not the random number generator) better; if you know you’ve had a run of luck, don’t expect it to last!

I believe this is a better *game mechanic* as it mitigates (somewhat) against a “lucky player” hitting a load of high dice rolls early on in the game. Using dice, they’re just as likely to hit lucky results with every roll. As such, players can play a good game, but still be defeated by your opponent’s dice. With cards, the chance of getting lucky diminishes every time you draw a high value card.

Now, this isn’t how real life works.
But tabletop games aren’t real life simulators either – they are *games*.
And the original point (that elicited my response “cards are better than dice”) was about how cards can be used to represent “luck” and how it’s exhausted thoughout a game – something that can’t be simulated with just simple dice rolls, but comes naturally to drawing cards. And this is true because drawing cards (with the exception of always drawing a card and shuffling it back into the deck) is *mathematically* different to rolling dice.

You *can* simulate dice rolls with drawing cards.
But if you do, you’re ruining a perfectly good game mechanic, which is to draw cards to simulate the amount of “luck” each player has. Yes, in real life, some people might have good luck all the time (roll 6s) and some people always roll a one – but sometimes real life sucks and we’re playing a game here, where both players should be having fun and for a *game mechanic*, cards (for me) beat dice every time.

(for what it’s worth, in most electronic gambling devices – fruit machines, roulette tables at casinos etc. – to *prove* that every number has an equal chance of being drawn, a “card system” is used to demonstrate that every number *will be drawn at some point* – the machine chooses random times to “shuffle the deck” to create a random pattern. In the 90s I worked for a company and we had to disassemble the machine code for pub machines to prove that a pseudo-random-number generator wasn’t “weighted” to show the machine was “fair”.
Imagine rolling a dice a thousand times. You might never roll a two (unlikely but technically possible). But create a pseudo-random list of numbers 1-6 that doesn’t include a 2 and, while it may be “true to life”, it’s also unfair. For a machine to be fair, we had to demonstrate that every number *appeared equally in the sequence* – by changing the point at which you read from the list, you can create a random sequence of seemingly random results, where some numbers are drawn more than others, but the whole system remains fair.

On a side note, in doing so, we also discovered that about 80% of all fruit machines that used the hi-lo mechanic were actually unlawful in the UK, as they almost all included some form of “if successful after x turns, always choose the opposite to their hi/lo choice”).

Cards make games “more fair” because both players have to deal with drawing the same list of numbers – just in a different order and at different times during the game.