Players will set out a board made of hex shaped spaces. Players will also receive a personal scoring board, with 6 different scoring categories, one for each color on the board. Lastly players will receive 6 tiles. Each tile has two adjoined hexes, with a color on each hex.
On a player's turn, they will play one of their pieces to the board. They will then score the piece. I'd go into how, but frankly a picture does the job much better.
If players max out their score in a category, they are supposed to shout "INGENIOUS!" which is a rule I love enforcing, and then they get to place another tile. At the end of their turn players draw back up to 6 tiles. Alternatively, if the player has no tiles of the color of their lowest scoring category, they can discard their tiles and draw 6 new tiles. At the end of the game, players take the score from their lowest category as their final score. The player with the highest score from their lowest category is the winner.
How accessible is the game to new players?
There are numerous places for a new player to stumble. The scoring is relatively simple, with a single hang up. Tiles that have the same color in both hexes present unique edge cases. I often see players either try to have one side of the tile score a point off the other side. I also see players forget to score the single external hex that both sides of the tile point to. This is caused by a counter-intuitive aspect of the scoring rules.
Players tend to fall into two camps for what seems to be the obvious way to score. Some players intuitively want to trace rays out of all six sides of a hex for scoring. Since most pieces have a different color on each side, this stops the ray they would be tracing through the other side of the tile, and they play normally. That is until they get to a tile with the same color on both sides. It's a simple correction, you just tell them they only ever trace the 5 rays that point away from the tile, and ignore the 1 ray that points through the tile. But still, almost universally I hear "That's weird" when I explain this. Because, well, it is weird. The other camp of players intuitively want to count each space they score from only once. So when they have a double tile, they don't properly count twice the space that both sides point to. And once again, this is easily explained, but I usually hear "That's weird". Because as I already said, it is weird when you think about it.
What could have been done better?
When I think about it, I'm not sure the game would suffer greatly from dropping those two counter intuitive rules. I think in terms of scoring, there would be little difference.
For example, assume you are only counting each hex once, but tracing rays through double tiles, and that you just placed tile A. The point you lose by only counting the red hex on tile C once is offset by having one side of the tile A score a point off the other side of the tile.
A situation where the scoring is different however is the rare circumstance where you manage to sandwich a double tile in the middle of like colors on all sides. In the above picture, using the written scoring rules tile A scores 5 points. Using the intuitive rules I outlined it only scores 4. The other exception would be placing a double tile adjacent to nothing, in which case one side would score off the other, netting you a single point instead of zero.
So I have to wonder, which scoring method is better?
One argument I can see for using the written scoring method is that it is faster. You don't have to keep track of which spaces you already added into your score when you switch from one side of a double tile to the other. There are only 2 possible spaces around the tile where this can occur, but still.
Also, it prevents you from placing a tile adjacent to nothing and still scoring a single point, which would greatly alter end game strategy, and the ability of players to effectively block one another. This could be seen as a negative or a positive quality depending on your disposition. Personally I think it weakens what the game tries to accomplish.
How does the new player versus old player match up go?
The first game of this will certainly go to the more experienced player. Adjusting to only counting your lowest category as your final score takes time. New players will almost always completely neglect at least one of their categories, chasing after the mental high that accompanies a free extra turn when you complete a category. Experienced players are also more aware of blocking their opponents lowest categories in order to prevent them from catching up. A player's score is public information, and experienced players are more aware of using that information to their benefit than less experienced players.
That being said, new players will still greatly enjoy the game. There is something primally enjoyable about adding up your scores and earning extra turns. Even if you lose, you can look down at your board and see that you did well in some areas.
What could have been done better?
One thing that consistently nails new players is their lack of awareness about the mulligan rule. If you have zero tiles with the color of your lowest category, at the end of your turn you can draw a completely new set of six tiles. Every other facet of the game, a new player can observe what the old player does and learn from it in a timely manner. This is the single instance where a new player will get completely hosed.
What are the feelings the game evokes and why?
The game arcs through several feelings as it progressing. In the beginning it's pretty free and open. You'll be aiming to score as many points as possible in a single turn, with little regard for a balanced approach. You may even rush straight for one or two extra turns. Towards the middle of the game, you begin to get a bit more concerned about a decreasing number of scoring opportunities in both your lowest categories, but also your highest if you haven't earned your extra turns on them yet. You will also shift towards watching your opponents more closely, and beginning to block their lowest categories. The end of the game can either be a forgone conclusion where you know it's impossible to catch up, or a nail biting race to desperately drag your weakest category up just one more point, while simultaneously blocking your opponent.
Why is the game so enjoyable?
The game more or less nailed it's feel, and it accomplished this in a few ways. The first is that the board is properly balanced for the differing numbers of players. The board is color coded, and as you add players, it allows play in another band of hexes. This does a fantastic job of keeping the game tight, and encourages competition for placement right from the get go.
The mulligan rule also does a great job of preventing you from getting stuck in the game. In around 50 plays of this game, I have seen a player mulligan, only to draw a new hand of tiles that still don't have their lowest category exactly once. Definitely a statistical outlier.
Long term strategy, short term tactics, both or neither?
This game, like most games that can make it to 50 plays in my collection, does a good job of forcing players to balance short term goals against long term goals. This game accomplishes that extremely well through it's final scoring mechanic and it's extra turn mechanic. It forces players to balance attempting to bring up their weakest score against the benefits of an extra turn.
At a high level, players will get right up against the extra turn mark, and only use them when it can benefit bringing up their lowest category the most. Although many times these efforts at perfect timing are foiled by the competition for space closing off what the player needs to earn that extra turn.
In addition to the aforementioned pull between earning extra turns and giving attention to your lowest categories, players will have to do careful hand management and block their opponents. The last thing you want to do is place a tile such that it presents an even better opportunity to your opponent. That is unless you can count on them giving you an even better chance, which you can then proceed to use and close off.
Almost every action you take that benefits yourself could also benefit your opponents. Almost every large score is followed by an even bigger score unless you are careful or luck out into getting the final possible space.
Why are the dilemmas so fascinating?
What is most impressive is that the game accomplishes this with a minimum or complexity. It is almost an emergent quality of very simple constraints. Given that it is not Knizia's first game which uses a "Lowest score of multiple categories is your final score" rule, he likely had a lot of practice getting it just right. Knizia has stated numerous times that his ideal games are as stripped down as possible, while retaining the essence of what he was trying to achieve. I think in Ingenious he nailed that quality better than any of his other games.
Once again, I must applaud the simplicity of the rules, and the depth of the consequences with respect to scoring. Having every tile score off of every tile around it causes enormous chain reactions. Everything a player does will effect every other player. But the manner in which this happens isn't forced. The game isn't over burdened with extensive rules governing the numerous ways in which players can score off one another. You aren't required to remember a half dozen different ways to score points. There is a single unified way to score points, which is pulled in numerous directions by various mutually exclusive rewards. I believe it is a textbook example of emergence in gameplay, where simple system give rise to complex strategies.
Physical component design and limitations?
The only problem I've had with this game has already been corrected in more recent printings. I have an older edition where the score is tracked using cubes on a board. This were easily knocked around if someone's knee hit a table leg, or sneezed, or anything else disturbed the table. New editions use pegs and a pegboard to track the score.
Carcassonne, Rattus and others.