Wednesday, 14 August 2019

Yoshi's crafted world: not for 100% run players


A late review on the Yoshi's crafted world as one of the iconic Nintendo game made for switch. I am so obsessed with Yoshi's island 1 and 2 so is no way that I would miss that.

First, why Yoshi and what's my expectation?

Yoshi became popular due to the great success of the Super Mario World so it gets a spinoff game that is also a 2D platformer but with some twist.

Yoshi's island encourages exploration by introducing non-linear stages and collectibles - flowers and red coins. Exploration can be done by either Yoshi itself or the eggs. Yoshi has a slightly more Jiggling physics comparing with Mario who is designed to run. This is the core mechanics of the Yoshi series.

Yoshi's Island is heavily praised for its vast variety of enemy (and enemy physics). The enemy showroom in Yoshi's island is such a fantastic idea especially when you can interact with them.

As for someone who loved Yoshi's islands, I am expecting a sequel that preserves the standing-out designs from the past while entertaining modern players at the same time. So, am I satisfied of the game?

Well, yes and no.

From the artistic point of view this is another success -- from wool to cardboard based Yoshi you can clearly feel the Nintendo style behind. Every single stage is unique in its enemy and even game mechanism. By advancing in the stage you gradually understand how things work and solve the incoming puzzles.

This is however, not a strictly positive comment. Just as IGN said, "but it's a bummer that even the best ideas are rarely ever revisited later". Since every stage is unique on its own, that means we are not going to see integrated stages featuring multiple mechanics. I can understand the situation in a sense that the themes of even neighboring stages differ too much to be integrated, but this should not be a hard thing to amend.

The integration of multiple mechanism is one of my favourite in Yoshi's island -- we have 3 ordinary stages, then 1 castle (x-4 and x-8) stage where we have mechanics from the last 3 stages but also something new. The castle itself is already fun with the maze design, and even more interesting with these integration. And that brings us to the next point.

Game stages are largely linear. This is of course not a rare thing  among 2D platformers, but Yoshi's crated world is particularly linear  due to the flippable design. By such we have an obvious direction to clear the stage, and also a clear hint to collect hidden items -- just look for the opposite direction.

While individual stages are too linear, the stage sequence is non-linear. One may somehow divide the game into 5 worlds, where you have access to world 2, 3 and 4 simultaneously. But that also means world 2, 3 and 4 are of similar difficulty -- which are all far too easy. Even world 5 is unbelievably easy. But then you suddenly get 3 unforgiving extra stages -- the big difficulty gap is kind of annoying. Why would you introduce instant death rules in the extra stages while the players are not well-equipped for them by clearing the game? If you look at extra stages in Yoshi's island the first 5 extra stages are a bit harder than their respective main boss stage (x-8), while 6-E is pure hell. With proper difficulty progression from x-1 to x-8 in each world, the corresponding extra stage gives a reasonable challenge for those who mastered the previous contents. But in Yoshi's crafted world we only get thse after clearing the whole game, and they are notoriously hard comparing to the rest.

Finishing the 3 extra stages is just the easiest part for those who aim to collect all flowers...I say the easiest not because it's technically the easiest, but this is kind of a new content that you are happy to clear it.

And there are contents that you are not happy to clear.

Flip-side. Oh yes, flip side. Great artistic concept but has a down side on gameplay, Finding puppies is a nice idea (and the pups are fun to play with), but this is technically easy throughout (especially with the sound turned on) hence less attractive for experienced players.

Then you have the find items quest...which is the worse thing in the game. Extremely boring and forces you to play the stage multiple times and wasting so much time looking at every corner. I appreciate the game art, but it is not necessary for me to check every detail. Right? You cannot even access to those quest before clearing the stage, and you can only do one quest at a time, meaning that you have to play stages multiple times even if you managed to find all quest items on the first run. Staged are played like at least 4-5 times in order for one to find all items, and this is pure redundant.

Boss stages...very fun bosses, but I would rather have a complete boss stage, or just a themed castle before the boss. Boss fight is of moderate difficulty but the boss challenges are really hard. That brings us back to the point where the difficulty gap is huge. Of course this is less of a problm because players shoud have already cleared the game for at least once. The time limit gives zero-tolerance to any error that delays the cycle, but it makes the battles a lot more interesting. To meet the time requirement you need to push back even further, so that you have rooms for minor mistakes when you misses some other parts of the challenge.

Costumes. I take it as a quality of life improvement from the 30 seconds count where you do not need to restart the whole stage after making mistakes. Most super rare costumes are very cool -- that's a plus for the game. My favourite is the raven one, probably because raven appeared Yoshi's island too. (Yoshi's island 5-8 is one of the best stages ever made...)

One last thing that I must say -- most score-based stages is uniquely fun, EXCEPT for one, the go-go Yoshi. While being cute and fun, that thing is surprisingly hard to control precisely (I found using the left d-pad gives more accurate control), and the score requirement is damn high -- and that is in the middle of world 1! It also comes back to haunt you in the Kamek boss -- pretty sure many of you failed to clear the stage within time limit just because you missed a single punch in the final Kamek form...

To conclude, Yoshi's crafted world is an amazing game who gives great art and good first-time experience. But it lacks the design to serve experienced players properly. Even worse it frustrates completionists in many way.

Verdict: 7.1/10
Game time: 20 hours for any%, 40-60 hours for 100%

Thursday, 25 July 2019

MSN minesweeper revisited (in 2019)

I have expressed numerous time my love on the MSN minesweeper...and now it is back online. It is a pity the mienfield was down without any support...but hopefully this is going to last longer.

So here this is a question related to the grid efficiency in MSN minesweeper.

\square & \square & B_1 & B_2 & B_3 & \square & \square\\
\cdots & 1 & 1 & 1 & 1 & 1 & \cdots \\
\cdots & 0 & 0 & 0 & 0 & 0 & \cdots

Suppose that you have a line of 1s along a long enough edge (basically you do not get any information from the two endpoints of the edge), then at any of the 1s, the chance of a mine appearing on a random grid should be 1/3...or is it?

Assume that the universal distribution is uniform. I.e. that is an equal chance of getting any of the $C^n_r$ many combinations (ignoring the corner rule since it is less relevant). Similarly without further hints, if we have n remaining unrevealed grids and r remaining mines, then the number of possible combinations is again $C^n_r$.

Out of the formula there is one single variable that varies with actual config - the number of remaining mines depends on the length of the edge modulo 3. Let $r_i$ be the remaining mines count after revealing the row given the configuration $B_i$. Then

$P(B_i) = \frac{C^n_{r_i}}{\sum C^n _{r_k}}$

If the number of mines to be revealed is independent of the configuration then we can conclude that the chance are equal. Otherwise we can compare the binomial terms:

$C^n_{r+1} = C^n_r \frac{n-r-1}{r+1}$

The usual ratio between grids and mines is 5:1 -- but that varies greatly depending on the given situation. In particular there are loads of 1s and 0s in our example, which boosts the ratio greatly. At the ratio of 2:1 the increase of mines would not increase the likelihood of the evisceration, but of course such ratio is unrealistic in a minesweeper setup, so we can say that the configuration that the configuration that leads to less mines on the row, is more likely.

One may raise the question: shouldn't the equilibrium happens at 3:1 instead of 2:1, from a likelihood perspective? We can visualize the likelihood approach by the following problem.

In a box there are $n$ balls, in which $r\approx n/x$ are white, and the rest are black. (i.e., the ratio between balls and white balls is $x:1$). Suppose we draw $\alpha$ balls out of it and we want to compare the chance of having $\beta \approx \alpha /3$ or $\beta +1$ white balls in the draw. If we want the chance between the two events to be comparable:

$\frac{C^{n-\alpha}_{r-\beta}C^{\alpha}_{\beta}}{C^{n-\alpha}_{r-\beta-1}C^{\alpha}_{\beta +1}} = \frac{(n-\alpha-(r-\beta))(\beta +1)}{(r-\beta)(\alpha -\beta-1)} \approx \frac{1}{2} \frac{n-\alpha - (r-\beta)}{r-\beta} = 1$

That gives $n-\alpha \approx 3(r-\beta)$, or $n \approx 3r$.

In our problem however, the term $C^{\alpha}_{\beta}$ does not exist, because we do not take the full combination within the balls drawn. In other words, we do not allow orders like


The three only allowed scenarios are


Once we fixed that in our formula, similar calculations yield $n\approx 2r$, instead of $3r$.


Of course there is no such 'infinite edge' in minesweeper. The endpoints is definitely giving extra information unless it looks like the following:

\square & \square & \square & \square & \square & \square & \square & \square & \square\\
\square & 1 & 1 & 1 & \cdots & 1 & 1 & 1 & \square\\
\square & 1 & 0 & 0 & \cdots & 0 & 0 & 1 & \square\\
\square & 1 & 0 & 0 & \cdots & 0 & 0 & 1 & \square\\
\square & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \square

Any extra information would impose extra difficulty on these kind of analyses, but I am here to give some primary idea on what's happening.

To give an application, consider the following example. I said on my twitter that red made a bad move:

The reason behind is simple. There is only [something between 1/4 and 1/2] chance that the grid contains a mine. On the other hand if it does not the opponent gets a free flag immediately with everything else remains the same. it possible to calculate the exact chance? Yes, and this is not hard at all: this is a 16x16 board with 51 mines. The shown area is the only revealed portion. To calculate the probability we list the few only scenarios then the chance follows by the binomial coefficients.

Tuesday, 23 July 2019

Fire Emblem: Three Houses and Rokkr Sieges

Back to something casual...Fire Emblem. Surely quite a lot happened since last time I wrote about FE and now it is a good time to talk about that again, since Three Houses is coming soon.

Well what should I expect? Unfortunately it's very hard for me to make a fair comment because I have not played the main franchise since the GBA era, a time where skills did not exist and information was sacrce because you didn't know Japanese back in the days...But FEH players should beware of the vast difference between playing FEH and the main franchise.

In FEH the key word is competitiveness. We keep facing stronger and stronger metas and we need to use the same team to work around it (unless you spend heavily). When you use more or less the same team against the opponent, what brings you victories is either the tiny bit of stat difference, or a well-desgined tactic which after all tricks the AI.

In the main franchise it is a totally different story. You are not really fighting in the fair setup -- instead of a 4v4 battle you are doing a 15v50 battle in a well designed stage where you are expected to solve the puzzle bit by bit. Restrictions are kind of loosened but you often ended up putting soft restirctions on yourself: units can be "killed" without failing the stage, but you want to unlock all stories. Time limit is less of a problem but you want to get all secret items and recruit hidden characters...the flexibility is much higher but the difficulty can be no less than what we have met in FEH. The most important bit is, you need to know how to work with a complete army, instread of your precious 4 units.

But yeah I can't wait further for the game. And I am going for Edgelord. Based on the official tease and FEH unit intro she's gotta have an interesting story behind.


Back to FEH we now have two more game modes which I also want to talk about.

- Alligence battle -

Interesting concept, but competitiveness forces the highest difficulty and hence very tense and allows very limited unit choices. It's also very luck based when you are not using a DC/CC based team, then you will have to play multiple times to get a high enough score.

But the reward is kind of reasonable - taking 900 as the threshold, the effort required to climb above 900 is hard but not very rewarding, while scoring a 860 is of moderate difficulty. I believe a large portion of the players are settled to the casually playing state on this mode.

- Rokkr Siege -

The opposite of the alligence battle. Fun, promotes casual play and allows huge flexibility. The three difficulty means you can score quite a lot without getting into trouble, and the score cap means you do not need to strike for the optimal. For sure the reward is not the most attractive but 10k feather is still 10k feather and I will take it.

In the discord channel we have seen many different setups, but today I want to talk about my setup.

Three features about the dynamax (taking a lesson from the shitty pokemon sword&shield -- that's another story for another day) boss:
1) Swaps upon special proc
2) AOE damage upon special proc
3) Always counterattack creating non-zero damage

If you are taking lower difficulties, damage is not a problem and you can deploy simple means of recovery to overcome the damage like recover 3, or breath of life. In advanced however, you will either need to stop special from processing, or use a strong means of healing, like using a staff or heal based moves.

Swapping means your defense tiles will then be occupied by the boss, or that the boss will escape from your lineup. In lower difficulty, it is hard to hit the score cap just because the multiplier is too low, so stragety that adapts swapping is essential if we want to hit the score cap, especially if we are fighting cavalries.

With that being said, to tackle lower difficulties steadily you would like to:
- mobility to tackle swapping
- minimum healing power

And to tackle the advanced difficulty you would like to:
- much stronger healing
- ability to take down generic enemies
- not necessary to keep a full team to the end; in fact it would be easier to finish the battle within 5 or 6 turns with some units defeated

Some like to use tank units with guard and healing special to lock down the boss, but without enough merging it is hard to hit the score cap. Don't forget that special fighter and guard are both premium skills and quite costly to inherit (if you do not use to do that).

Another problem with guard is the 70% HP requirement which is hard to maintain during enemy phase. My brave sword guard DC Ayra strategy failed miserably -- not to mention that such build is so impractical in PVP battles.

So with my newly merged +10 Catria, I had an idea. A lesson taken from my Cherche.

The setup is basically dancer + flying healer (witchy hand) + 2 fliers

Dancer - Partial tank, need to tank attacks with triangle disadvantage

Olivia in my case
A - Atk/Def Bond 3
B - Wings of Mercy 3
C - Hone Atk 4 [flexible C-skill or depends on your flier performance]
S - Atk/Def Bond 3

L!Azura is of course a perfect choice for fliers, but she cannot tank physical attacks and you may not have enough Iote shields.

Flying healer - putting guard effect on enemy

HS!Sakura [with H!Mia inherited]
A - Iote shield [use something else if you have it on the S-slot]
B - Live to serve 3
C - Hone fliers [spur buffs are also preferred, since the units may move around]
S - Breath of life 3

Fliers - to block boss on one quadrant and DPS
Units depends on the color of enemy but they should be brave based with galeforce. Without galeforce we can steadily hit the cap in 5 turns. It is suggested to bring at least one galeforce flier. If you do not have galeforce, sol is a temporary solution.

Standard builds:
Weapon - Brave weapon [or amiti / whitewing weapons]
Special - Galeforce / Sol
A - Iote shield / Swift sparrow / Death blow / Life and death
B - Seal atk / seal def
C - Ward fliers
S - Iote shield / defensive based seals

We start by blocking the boss on one of the quadrant - attacking is of second priority because we have enough time. It is important to keep the right formation to keep things predictable.
(1): Cherche to destory the wall
(2): Sakura to attack so as to reset the special cooldown
(3): Catria attacks [quad attack due to whitewing effect] 3 times [galeforce + dancing]

If we are fighting close attack bosses then it's not going to move but otherwise the boss may move by a grid, then we have to reform. We first move the unit to facilitate Sakura - remember that when you are using Brave weapons, a second attack would trigger boss' special so we must use Sakura before the second attack.

Here Sonya moved up a grid.
(1): Cherche moved up and attack [galeforce activated so that she looks active again]
(2): Sakura goes up to attack
(3): Catria and Olivia go up accordingly

It is important to deal with other generic enemies. That's the advantage of using galeforce -- we wait until they approach the fliers and attack, within the attack range the two fliers can kill the enemy then going back to the original position without further dancing. The dancer is also expected to be capable to kill most non-armor enemy by floating around.

It is relatively easy to lock the boss using this strategy, unless it's cavalry distant boss -- then we will need to carefully corner her.

The theoretical limit is 6.5 mil points. I somehow used 2 crests in the first round, so this is a pretty good score. It's definitely not a very rewarding act, yet this is a fun mode to play.


Oh and the Three Houses banner is out. Bitybroken by Chrom I spent 400 orbs to get Edgelord and Byleth. Now I am not prepared for Ayra revival...