The problem with jump-in rules in card games

Short (better) version here

Jump-in rules are rules in card games that allow under specific conditions for players to jump-in and take their turn, then play continues from the player who jumped-in last, essentially skipping all the players from the player who just had their turn to the next player after the player who jumped in.

How Jump-in normally works

I'm going to use Uno as an example for this
A common house rule in Uno is the Jump-In rule, where if you have the exact same card (colour and number) you can jump-in and then play continues as if it was your turn In Uno, there are only two cards for each colour and number in the game (except in some versions there is only one 0 card) so only one other person can jump-in for each number, there are 112 card in uno so for every card played there is a 1/112 chance that a randomly chosen card will be a match to an arbitrary card. you get 7 cards at the start of uno, so there is a 7/112 chance that you wil have a card that matches an artbirtary uno card at the start of the game, it is uncommon for someone to jump-in in uno.

How not to apply this rule to other games

I was recently playing a game called mao (mao is a game played like Uno, but with a standard deck of cards) and this rule was applied very badly, instead of only jumping in when we had a card that matched the last one played, we could jump in when we had a card that had the same number as the last card played while this makes some sense (you are applying the rule to the game in a way that works) there are 4 cards of each number in a standard deck of cards, and there are only 52 cards in the deck this makes it a 4/52 or a 1/13 chance that a randomly chosen card will be a match to an arbitrary card. You are also given 7 cards at the start of a mao game this makes the chance 7/13 that you will have a matching card in your hand to an arbitrary card at the start of the game, this makes it more likely than not that you will be able to jump-in.

Why is this bad?

when it is common that you are able to jump-in it means that the game order is decided on reaction time, if you can jump-in before the next player takes their turn then you get rid of your card, otherwise you dont, the way a turn would go in a larger group is, someone would play a card, and then 3 other people would jump-in with a card and the next player would be randomly placed around the room. the problem is that your actual turn (where you get to draw cards if you have none or play a card of the same suit) is entirely dependent on the reaction-time and skill level of the person before you, if you only have 1 card left and all the cards of that type have been already played, you are waiting for your turn when you have a 1/4 chance of winning (4 suits and one of them matches yours) but if the person before you is never jumping in, it is never your turn and you get stuck waiting, doing nothing until the deck gets reshuffled (and someone else possible draws a card with the same number as you), and even then you cant draw cards because its never your turn and it has to be your turn to draw cards, so your just stuck their watching until someone plays the number you need. This is a problem as one of the things that keeps games fun is being able to do things, even if it it just drawing cards on your turn, but if its never your turn, you can never draw cards, and you can never play, and you just get stuck while someone else sitting next to a more compotent player wins because they actually had more turns than you.

TLDR

The reason its bad is that taking your actual turn (where you get to draw cards) is dependent on if the player before you jumps-in, and if they dont then you never get to take a turn

Conclusion

Jump-In rules are fun when there are an appropriate number of matching cards, and cards overall, however when there are more matching cards and less cards overall, instead of playing a card being based on your skill, it becomes based on the player who plays before you's skill, and that is unfair and doesnt make for a fun game for the person after the unskilled player because they dont end up playing.