Bananagrams is not my type of game. It is, however, a game I played a few times this holiday and I thought it would be fun to talk about how it works and in what ways it pleases or displeases me. Here is the basic idea:
1. Every player gets a bunch of letters like in Scrabble but more of them.
2. Everyone tries to make their letters into word combinations in rows and columns, just like Scrabble. However, each player is playing on their own 'board' that has no special boxes or anything.
3. When you run out of letters you say 'Peel' and everyone takes 1 more letter at random from the pile. If you want you can toss a letter back in the pile and take 3 new ones out at random.
4. When the pile gets smaller than the number of players the first person to use all their letters wins.
The bizarre part about this system is that you can be 'winning' throughout the entire game, constantly running out of letters and calling Peel and then on the last turn you draw a Z as your random tile, can't place it and lose to someone who drew A as their random and makes SMASH to finish up. As long as you keep your stack of letters fairly modest it hardly matters at all whether you are running out regularly or not so figuring out who is winning at any given point is nearly impossible. You can say safely that someone who has a huge stack of letters in front of them and no words placed is losing but we regularly had games where the last letters came out and it was completely clear that those letters determined who would win.
Of course, that doesn't mean the game isn't fun. You can have fun tossing away all the challenging letters like Q and Z back into the pile, taking 3 more letters for each and try to build tons of easy words. You could try to collect both Zs and both Vs and build DAZZLE and DIVVY (I did!). There are all kinds of random things you can do and it doesn't seem to impact your chances of winning very much either way as long as you try to lay down that last word quickly when the pile runs out.
There probably is an optimal strategy that involves laying down or trading in unfavourable letters to hit the endgame with a specific set of very easy letters including an optimal vowel mix to maximize your chances of being able to cash out very quickly. You are actually allowed to unbuild and rebuild your matrix of words so it would be possible to develop a set of letters you want, attach them to your matrix to call Peel and push towards endgame and then take those letters off to use up your last draw. I assume that such a strategy exists, though I certainly do not have sufficient experience to show that it does.
This game definitely fits into the 'almost solitaire' category of games. What your opponents do hardly matters except that eventually you will have to have done something or you lose. You can't change your opponent's options, you can't force them to do anything, and you can't tailor your strategy to what they are doing. It can certainly be amusing to play but the lack of strategy and the inability of the player to influence the course of the game meaningfully means I won't be playing this one over and over. I also find it very bizarre that 3/4 of the way through the game there is usually no way to determine who is closest to victory at all - you can perhaps count someone out if they are obviously terrible but figuring who will win is generally not feasible. That is not to say that there is no skill, because there is, but that what you do up until the very last turn doesn't affect your chances of winning very much. The best player will win a lot more often, but they will win mostly on their ability to play the last 10 seconds better.
The final question I will address is "Why is the game called Bananagrams?" The answer is that there is no reason whatsoever, except that the case the pieces come in looks like a banana. It looks like that because the game is called Bananagrams I presume. Useful, my answer is not, but it is all we have.