Do lucky streaks actually exist?

Lucky streaks do exist as runs of results, because randomness naturally produces clusters of successes and failures. There is no force keeping them going, though: in a fair game, receiving good cards in one hand does not change what you will be dealt next.

Randomness is not as evenly distributed as we think

If you ask someone to invent twenty coin tosses, they will almost always alternate too much: heads, tails, heads, tails... Real randomness produces things like five heads in a row much more often than we think. That is why, when you play many hands, it is normal to string together several good ones or several bad ones.

Why it feels like a streak

Our brains look for patterns even in the clouds. We remember the afternoon we won six games in a row and forget the hundred normal afternoons. Furthermore, when we are winning, we play more calmly, and when we lose, we rush, so we create part of the "streak" ourselves.

And in cards?

With a well-shuffled deck, every deal is new. There is a nuance: within the same hand, what has already been played does matter. If in Brisca (a popular trick-taking game) three Ases [Aces] have already been played, the remaining one is worth more because it has no rival. That is not luck, it is card counting, and it is the best legal advantage there is.

The "I'm due a win" trap

Thinking that after many bad hands a good one "has to" come is the most famous error in randomness. It is called the gambler's fallacy, and it is exactly what fuels bad decisions in betting. Here we play for fun, without money, precisely to enjoy the game without that pressure. If you want to know more, read why we are not a casino.