I think you have an incorrect expectation of the results of random events.
Let me simplify by playing some games around the 4 suits in a deck of card, Clubs, hearts, diamonds and spades.
I tell you you will have a 1:4 chance of seeing each suit. In the game, you will draw a card from the pile I have prepared and record what suit it is.
Scenario 1: The pile has four cards, and every time you pick a card, I secretly put it back on the bottom of the deck. In this scenario, at times some suit counts will be 1 higher than others. but every 4 cards drawn the distribution will be evenly spread and the ratios will be 1:4 for all. And everyone else playing the same game under the same conditions will see the same behavior. Play slow or fast; spend money to play more, 1:4, regular, average, consistent. You could run a game like this. I don't think anyone does.
Scenario 1a: After every 4 cards, I shuffle the deck. Short term behavior, you won't know what order the 4 plays will come, but statistically similar results, counts differ by 1, perfect distributions every 4.
Scenario 2: The pile has 8 cards, 2 each, and every time you pick a card, I secretly put it on the bottom of the deck. In this scenario, you will occasionally see the counts separate by 2, but every 8 cards drawn the distribution will again be evenly spread and the ratios will be 1:4 for all. Again, everyone else will see the same behavior. You could run a game like this. I don't think anyone does.
Scenario 2a: After every 8 cards, I shuffle the deck. Similar to 1a.
Scenario 3: The pile has 52 cards, 13 of each, each draw returned to the bottom. More chaotic behavior, increasing local deviations up to 13 counts different over time, but again, there will be periodic evening of the odds back to exact 1:4 ratios.
Scenario 3a: Reshuffle every 52. Similar. (By the way, this is how most board games tend to operate, from Candy Land to Monopoly.)
Scenario 4: The pile has multiple decks. Scenario 4a: Reshuffle ever full run.
By my understanding, scenario 4a is close to what gets done in many physical casino card games. I don't think they let the pile of cards go to the end, so the long term odds for card frequencies won't periodic return to perfect odds.
All of the above 8 scenarios will provide short-term variations, but will guarantee long term exact ratios for everyone involved. Programmatically, you could implement them with a continuous list that you cycle through one at a time. Or a list you randomize then walk completely through, then randomize and repeat. Or a pool of choices with counters that you randomly pick from until the counters are zero, then reset all the counters. You could implement any of the above. I think it's safe to say, any of these are almost always never used.
Then we have Scenario 5. The pile has 4 cards, or 8 cards, or 52 cards, or multiple decks, whatever, but after every draw, the card is reinserted and the entire deck is reshuffled. Nobody sees the same sequence. Nobody is guaranteed to ever see perfect outcomes long term, not on a defined, continuous basis, not once in a blue moon. Some players will see highly unlikely sequences, like getting the same suit 20 times in a row or not seeing a particular suit in 28 consecutive plays. Long term, the trend will be near 1:4 ratios, but things will go in all kinds of directions. But each and every individual choice with the same, perfect 1:4 odds.
This is what we normally see implemented. Calls to Rand() indexed into a list with weighted probabilities.
PS Lastly, for completeness sake, let's consider Scenario 6, which is what my completely uninformed brain guesses is what would be similar to what gets down with most modern electronic gambling devices. Each individual play is randomly done to the above weighted probability, but the machine peeks at the card before showing it to you. Internally, the machine has been tracking the full history of plays, and has some additional rules it follows to nudge the short and long term behaviors. While straight statistics says that, while highly unlikely, it is possible for a 1 in a million play to occur four times in a row. Or three times in ten minutes. Or twice in a day. All possible outcomes, all highly unlikely and unusual, and all bad for the casino. So, the machine massages the outcomes. If a perfectly fine random event would produce an unlikely cluster, a "this is occuring more frequently than average", then rejectthe play and internally try again. And possibly the same thing in reverse, if the machine has been seeing an uncommonly long dry spell. There's probably sophisticated and proprietary stuff going on that is both random (no one knows what's going on play-to-play) but massaged so that the overall trends don't drift to far from the center of expected outcomes. You legally have to justify the stated odds of the game. Jackpots need to be given out eventually, and 1:1,000,000 odds need to be justified as 1:1,000,000, but you don't want to have that play out as 4,999,999 misses and 5 consecutive wins, even if that is a reasonable (but highly unlikely) outcome.
TL
R - When playing games that state the odds for a random occurrence, don't expect personal or large group perfect statistics.
