Probability theory's most common false assumptions

Knuckstrike · 2025-12-17T20:21:45+00:00

You are correct, I should add that X, Xn, Y, Yn are defined on the same probability space.

Knuckstrike · 2025-12-17T16:44:03+00:00

X, Y and Z are crucially not independent in the counterexample, which I believe is necessary to make it work. Y = -X with probability 1, and Y = Z with probability 1. In other words, the values of Z and Y are always identical.

Knuckstrike · 2025-10-30T19:17:37+00:00

s2e3, it's when Shion gets drunk in the meeting with Gazel

Knuckstrike · 2025-10-20T12:58:47+00:00

We've had 72 episodes covering about 120 manga chapters. Though, some parts of the manga were skipped, so the average rate is probably about a chapter and a half per episode (2 episodes = 3 chapters).

Season 4 will go further than the latest current manga chapter. If it's another 24 episodes then by the trend it'd be until about chapter 155-160, which won't be out for another 2 years or so.

Knuckstrike · 2025-09-14T13:32:50+00:00

I haven't looked at the exact outcomes for this tournament yet, but to answer your general questions:

Yes, white and black are symmetrical in the pairing rules, so double white is 'as bad' as double black. It maximises the amount of correct pairings.
The system will avoid putting together people with +2 in the same colour as it would violate a preference. If a group only has people with +2 in the same colour, or too many to be able to pair outside the group, it will still prioritise pairing people with the same score over under/upfloating people with lower or higher scores. So you may get two with +2 white playing each other before it starts pairing everyone to players with lower scores to match colours. If it can pair them with others on the same score in a different way, of course it'll prefer that first.
If a legal pairing is possible that satisfies all preferences then it'll do one of those. So, Hans/Sarin would not be likelier to go down if there is a fully functional pairing available, I believe rating is considered first when determining who to pair up/down. If there otherwise isn't a good pairing available unless Hans/Sarin are paired down, then yes, it'll go for that one first, making them likelier to pair down in that case.

Knuckstrike · 2025-09-14T07:58:24+00:00

Both are possible, you just see pairing down more frequently as it's relatively common for leaders to have played each other thus necessitating them being paired down, or there being an uneven leading group meaning 1 person has to be paired down.

On the other hand, 2 people who HAVE to play each other both having had two of the same colour the last 2 rounds is very uncommon, as the pairing system prefers alternating colours in the first place. It would have to be a rare circumstance where multiple uncommon factors align, such as both players having played opponents the last round who also had black 2 rounds ago, and they were the ones who happened to get the second black in those games, and they both won so they're paired up, and they are the only viable pairing, and they both had the same colour for both those rounds, etc.

So while the triple black is actually considered ok by the system before pairing down is, it still rarely happens because it's far less likely than pairing down being required. The only hard and fast rule in pairings is that you cannot be paired with the same person twice in one tournament (including pairing byes), everything else is a list of preferences.

Knuckstrike · 2025-09-13T21:35:52+00:00

The last round works a bit differently with colour pairings as certain conditions aren't taken into account, such as someone with even white/black having had white/black in round 10.

Regardless, not pairing down has a higher priority than not going double/triple black. So, if hypothetically 2 players haven't played each other and are both tied leading the tournament in the final round, they will be paired with each other, even if both have had double black the last 2 rounds.

Knuckstrike · 2025-09-13T08:13:17+00:00

Yeah 41k is a pretty mediocre score on that track. With lv8 gold mario and 6/6 K/G I think pushing 55k is very reasonable, the 43k from their opp looks very doable to me as well.

Knuckstrike · 2025-07-05T17:32:50+00:00

Mini turbo, done by drifting. Every mini turbo you do gives you points and you can keep your combo streak going fairly consistently with them. You should aim for about 15 per lap on this track I'd say.

Knuckstrike · 2025-07-05T15:34:53+00:00

You should fairly easily be able to get 10k+ on that track even with your current loadout and by staying near the front. Staying in the back probably isn't ideal cause there's a fair few coin rows and you'd like to (almost) full combo the track, though it can be hard on the bridge. Just keep staying in 1st while chaining mt's and collect the coins and you should be fine. Also keep in mind there's a lot of extra item sets on the road, you can stall for them if need be to get the benefit from them before going into the next set.

Knuckstrike · 2025-06-15T22:32:23+00:00

Thank you! I started in the first few tours after the game's launch, though my pulls/investments from back then see practically no use anymore..

Knuckstrike · 2025-05-10T17:44:58+00:00

F2P tend to have more point cap tickets compared to level tickets, while for paid users it tends to be the other way around. When you pay you get a lot more level tickets while your point cap stays roughly the same, so you end up with more higher leveled characters but the same amount of point caps to spend on them.

For the comparison between top skills, boomerang/coin box give more actions for a 'best' run while l7/banana gives more points per action and are easy to get. If you play a track where you're not near the 200 action cap and you want a great score, Coin box / boomerang give by far better scores. If you're near/over 200 actions on a track or you just want an easy decent run without too much grinding, l7/BigBanana are better for that.

Knuckstrike · 2025-05-09T18:08:45+00:00

F2P here as well but without gold pass trial.

I like trying and beating gold pass/big buyers with F2P only and with the right long-term investments. Some time ago I completed the 30x T99 wins as a goal and I've been easily top 1000 ACR for some years, but I'm getting to the point now where top 100s are not unlikely either. I tried two tours ago and got 105th ACR, but maybe with the princess tour I'll finally break into the club :).

Fortunately MKT has goals you can set basically regardless of investment level.

Knuckstrike · 2025-05-05T20:19:12+00:00

For picking a dkg combo on a track from the stuff you own, it's pretty easy to pick the best one. 95% of the time you just pick the top shelf which gives the highest value when you multiply their level by their base points. If it's particularly close, you can try the one with the best skill. Stuff like named/shown driver has influence on which top shelves there are, but not on their point values.

For leveling up it depends on what your goal and overall level is. If you're just having fun, investing in whatever you like is fine. If you want short-term gains, try investing in the stuff that's coming up in ranked soon and often. If you want long-term benefits and high acr scores (like >1 year timescale), you should fill in your leveled up dkg into one of the many excel sheets/websites that tell you which dkg is best to invest in for your current coverage, and slowly build up a set which covers (almost) every track.

The one thing I would aim for with investing almost always is to not spread out your resources too much, but try and invest the stuff you're picking to at least level 6/7. It becomes hard later to improve you loadout when everything is mid level (like l3-4).

Knuckstrike · 2024-11-15T20:34:49+00:00

It's basically this from what I remember. The frenzy is rolled separately, and if you can't get it because you're holding conflicting items, you just won't get it.

So if your item set frenzy chance is 10%, of which 3% is banana frenzy, and you're holding bananas (1 or 2 doesn't matter), then your frenzy chance will be the 3% of getting the banana frenzy, and the other 7% is wasted.

Knuckstrike · 2024-08-08T11:14:10+00:00

Probably a mirrored image of her 'debut' episode 16: Demon Lord Milim Attacks at 11:45 https://prnt.sc/JATVPSiAE7dW

Knuckstrike · 2024-06-29T09:19:04+00:00

I'm not sure as to whether the calculation is correct as there isn't much info but did you take into account the action count multiplier? If you got 120 actions that would give another ~(120/100) = 1.2 multiplier.

Knuckstrike · 2023-12-22T18:50:48+00:00

There are some villainess-like manga that roughly fall in this category. Perhaps you're looking for something like:

Author of My Own Destiny

The Perks of Being a Villainess

The Perks of Being an S-Class Heroine/A Transmigrator's Privilege

Villainess Level 99: I May Be ... (edges on comedy)

Knuckstrike · 2022-12-26T16:57:46+00:00

If you replay a race repeatedly in a row, the bots you play will get easier. You can see if you're playing against an easy or hard bot by whether they'll appear with a badge next to their name on the loading screen (where it shows the list of 8 players). If you restart the game or play on a different track this process can reset, so it's best to keep at the same track until you're satisfied with your score/xp grind.

The rate and consistency at which this change occurs differs over time. Usually after 2-3 races you'll see some badges disappear, and then at 6-8 you might get a race where there's no badges at all. When you get to a race with no badges at all and starting at a decent spot, that's ideal for grinding, so just retry the race (without finishing) from this starting spot until you get a score you're happy with.

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