I've been away from my PC this winter break, so my partner and I have been playing an incredible amount of Board Game Island lately.
This run isn't the world record (because it had multiple human players, and I wasn't recording) but it very well could have been! I think I could play Wii Party for a lifetime and never tie this.
Board Game Island is a little like Chutes and Ladders, and a little more like Mario Party. A "round" consists of a 4-player minigame to get you dice, followed by rolling those dice to move forward on the board. (2d6 for first place, d6+d3 for second, d6+d2 for third, d6 for last. if you roll doubles, you get another d6, giving these probability distributions)
After maybe 50-100 games, we've seen it all - a few immediate UFOs on round 1, someone through the first wall a few times on round 1, the spikeball rolling down the slope 4 times without exploding, everyone at the top by the end of a game, and even a 7-round game, which is already rare enough!
This time, I got first place in every minigame. I got the first blue statue (the largest ladder by far, moving you 18 spaces out of 73) in round 2, 7 more spaces from a quick 1v1 minigame in round 3, and rolled a perfect 8 spaces to get me to the finish in round 4 - the only round where I didn't roll doubles!
I also didn't fall prey to any of the rubberbanding mechanics - I won the 1/2 for the wall, the 2/3 for not stumbling into the volcano, the 1/3 for the spikeball, and an immediate 1/6 at the very end. Nobody moved me back with a tornado, ufo, or 1v1 minigame. They didn't even get past the initial wall, which really speaks to the average length of one of these games!
So, it seems that the speedrunning strategy for this game is just get a really lucky run. The current world record is a 5-round game, but it didn't have a 1v1 minigame. I think my ineligible run was faster because of the minigame selections (a small part) and the whole cutting out a whole round of cutscenes (worth at least a minute).
This run could be beaten, but how? There are plenty more ways to get a 4-round run, and you could probably even dodge the 1v1 minigame with enough luck - call it one in a million or so? I'm sure somebody has done it with 3 CPUs, given that this game sold over 9 million copies, but "it likely happened in someone's house in 2011" doesn't really count as a speedrun.
More shockingly, the minimum number of rounds that a game could last is 3, and you can't win it if you get first place in every minigame. There's a handful of ways to do it, and I think the odds wind up being something like one in tens of millions. I really do wonder if it's ever happened! This one would probably be feasible to calculate the probability for, too... but I started and found out it's a lot of effort. You've got to have someone with a gold die get the first UFO on turn 1 or the second one on turn 2, and have the silver die player get exactly on a blue statue or +5 to even get far enough.
In the days since this run, I've reimplemented the board game island in Python on my phone, but after around 50000 games (some with fixed minigame results, some with random), the lowest I've seen is a handful of 5-round games. That's definitely a lifetime worth. I don't expect to live for 50000 days, nor will I sit through a half hour Wii game every day, even if I can reset after 4 rounds ≈ 8 minutes!
On the bright side, in games that I play more competitively, I strive for a PB I'll never beat. This time, I just got it handed to me!