Sequence (PC) (2011)*
*Now known as Before the Echo (PC) (2011)
: Jax Ltd. (manufacturer and distributor of the board game Sequence) filed a claim against Iridium Studios (developer of this video game) over the name Sequence. To avoid any complications and fees, Iridium Studios renamed Sequence to Before the Echo.

Sequence (PC) (MetaCritic.com)
Before the Echo (Steam Store Page)

20121029: [20130104]
This game was pretty fun. It employs several interesting gameplay mechanics. One such mechanic is using experience (XP) points to pay for crafting recipes (synthesis). One can increase the amount of XP points to improve the probability that such a recipe will succeed.

Note: If the attempt to synthesize a recipe fails, the ingredients do not get used, only the XP points are consumed.

Of course the main mechanic of interest is switching between three possible music fields: spell, defense, and mana. When battling, attack arrows will occasionally fill the defense field and every arrow that is missed damages the player. Colored arrows damage the player more than regular arrows. In order to attack the enemy, heal, or defend, the player casts a spell and must successfully execute the sequence under the spell field. Casting a spell consumes mana and mana must be recovered under the mana field.

 Difficulty options.
Tip: There exists an optimal amount of experience points to use to craft a recipe. Let's say the cost X gives a probability of Y. At probability Y, one can compute the expected number of tries it would take for there to be a success. Math below. Multiply that amount by X to get the average cost. As you increase X, you increase Y. At first this lowers the average cost, but eventually the average cost begins increasing again.

Optimal Use of XP Chart:
Difficulty 01: 010XP for 79.5% is an expected 012.578XP
Difficulty 03: 039XP for 67.3% is an expected 057.949XP
Difficulty 04: 056XP for 63.7% is an expected 087.912XP
Difficulty 0X: 074XP for 60.5% is an expected 122.314XP
Difficulty 0X: 117XP for 57.4% is an expected 203.832XP
Difficulty 08: 145XP for 57.8% is an expected 250.865XP
Difficulty 09: 168XP for 55.7% is an expected 301.615XP
Difficulty 13: 287XP for 52.7% is an expected 544.592XP
Difficulty 15: 347XP for 50.4% is an expected 688.492XP
Difficulty 17: 425XP for 50.1% is an expected 848.303XP

 Battle. Red = Defense, Blue = Mana, Green = Spell
Caution: There was a situation where I loaded an enormous amount of experience for something, in order to record X and Y above, and then accidentally went ahead with the crafting. This situation is equivalent to playing a game for several hours and then losing the save file. It's equivalent because some of the time spent used to earn the experience has been lost. This was upsetting. I hope you can avoid the same error I made.

I should also note that I liked the voice acting.

Steam Achievements:
20121029 2:09pm Defeat your first enemy
20121029 2:34pm Obtain all three droppable items from any single enemy.
20121029 2:36pm Defeat the Holiday Whompa.
20121029 2:42pm Complete a battle without failing a spell.

Math:
Let $X=1$ be a success and $X=0$ be a failure, with the probability of success being $p$. Now we want to compute the expected number of trials until $X=1$. If there were $k$ trials until success, that means we had to have had $k-1$ failures and one success. Thus the probability of requiring $k$ trials is $p \cdot (1-p)^k$. Thus the expected number of trials until $X=1$ is $$\sum_{k=1}^\infty k \cdot p \cdot (1-p)^{k-1}.$$ This can be rearranged as $$-p \cdot \frac{d}{dp} \sum_{k=1}^\infty (1-p)^k$$ which in turn equals $$-p \cdot \frac{d}{dp} \left( \frac {1-p}{1-(1-p)} \right)=\frac{1}{p}$$
 You synth (create) items using XP and can desynth (sell) items for XP.
20130104:
Upon booting up the game again in two months, I went back to replay all the enemies from Floor 1, Floor 2, and Floor 3. Then I did some grinding on Floor 3 until I had the ingredients to synthesize Inhibitor the Third, and more ingredients to synthesize Key the Third. On floors after the first, there is a corresponding floor guardian who uses his/her power to try to screw you over. Synthesizing the Inhibitor for the corresponding floor prevents the power from being used on the floor, with the exception of when you battle the guardian in person. To advance from one floor to the next, you have to synthesize the corresponding Key.

In any case, I was also reminded of how great the music is. I believe in the long run, the actual number of soundtracks used for gameplay gets repetitive, but the spells and difficulty of the monster changes. As such, repetition is actually good, since then you get used to parts of it enough to get a flow, but other parts of the game change.

As a side note, I had skimmed one review and the reviewer oversimplified the game as being a rhythm game with RPG elements slapped on, making the game needlessly complex and requires excessive grinding. In defense of the game, I would first say that grinding often goes hand-in-hand with RPGs. I would also point out that the rhythm game is being used as the battle mechanism. That is, one could have theoretically stripped this game of the rhythm game, replace it with a standard RPG battle mechanism, keep the story, and turn it into a standard RPG. The combination of the rhythm mechanic is what makes the game exciting and novel.

 After you successfully synth a scroll, you have to complete a goal to unlock it.

Of course, the fact of the matter is that Sequence has a lower metascore than Puzzle Quest: Challenge of the Warlords (2007), an RPG with Bejeweled as the battle mechanic. Thus I did some more reading and it seems other complaints consisted of a lack of songs and childish dialogue. I already mentioned how I saw the limited number of songs in a positive light, but its a fair point to put forth. However, on the point of the dialogue being childish, I would disagree. I believe the dialogue matches the subtle humor found throughout the game. After all, there's a weapon named Doublerain Bow and the description of a Goblet is "A little goblin. His name is Billy."

Overall, the game seems to have several qualities worth loving or hating, and the combination of where you stand on each quality will determine if you like the game or not. I like the game, and would be willing to grind if I had the time, but alas, I have to move on to other games for the moment.

 Some of the dialogue can be pretty funny.