As of a little while ago, I discovered some new strats to decrease the time needed to beat any of the tournaments in Mario Hoops 3-on-3, and I wanted to explain exactly what I've been doing to make these times.

Step 1 ~ Time starts at the selection of "Tourney" on the main menu. Step 2 ~ Select Tourney (This step is skipped with a brand new file going for a Mushroom Tourney Normal run). Step 3 ~ Select Characters. Hit the Select button to get a randomly assorted team in the least amount of time. Ideally, you want a technical player such as Peach or Daisy, but it's possible to do this run with any assortment of characters. Step 4 ~ The tourney opening screen will appear with the bracket. Press and hold the B button to increase the speed of the menu there, and consistently tap the screen (I also press the A button repeatedly while still holding the B button here too) to make the "Vs." text box appear on the screen. Step 5 ~ Going into the match, continue to tap the screen, hold the B button, and tap the A button to make the court-opening cutscene skip to the jump ball sequence. Step 6 ~ First Half. Do not score or allow the other team to score at all. Step 7 ~ When the "Time's Up" text appears, perform the same actions as steps 4 and 5 to make it get to the second half slightly faster. Step 8 ~ Second Half. THIS IS THE HARD PART OF THE RUN. You don't want the other team to score at all, and you don't want to score until the very last second. Ideally, you want a technical player to have the ball right to the side of the hoop charging their shot for a couple seconds, and then complete your stroke up on the touch screen with about 0.82 seconds on the clock. This will ensure that the shot goes in with no time on the clock, barring a steal or block from the other team. Step 9 ~ Game! Immediately following your shot going in, begin tapping the screen to skip the shot replay cutscenes, and because you performed Last Second Shot in the second half, you skip the "Time's Up" text and go straight to the "Game!" text, saving a couple of seconds per match. Step 10 ~ Finally, as the team celebrates, begin tapping the screen in the area where the text box "Go to Next Round" will appear, and repeat steps 4-10 until "Game!" appears on the screen after the third match (or fourth in the Rainbow Cup).

I believe the lowest time possible for the Mushroom Cup Any% (Normal) run using this strategy is a 16:49, but I haven't quite confirmed that yet. Anyway, I hope this helps you guys out! Happy speedrunning! LiteBrite516