I have a question for the more advanced player?

How helpful do you think it is for a beginner to learn how to mate with two bishops and a knight and bishop? I say this because so many mating patters on TT are based on those two pieces working together. Wouldnt learning and mastering it help in that regard?

Learning to mate with two bishops is easy.  You should almost be able to figure this out over-the-board.

Learning to mate with a bishop and a knight is NOT as easy, but it can be  fun to learn.  It does take some time and practice to be able to do it effortlessly.

Learning either skill won't be needed in 99.99% of all of the games you play. 

That all being said, you should spend SOME time on it, but there is no reason to go overboard.

For a beginner, every little bit helps.

IMHO, practicing basic endgames helps a lot to understand how the pieces work together.

Btw: BBK vs K is trivial, as you will see when you study it.

I learned it from this video. It's a clear, step-by-step process that is easy to learn.

I'd say learn the N+B mate method up to but not including any technical parts.  Don't bother memorizing the technical positions where only 1 move is best and so on.  Instead notice the useful configurations of the knight and bishop and their ability to work together to make "walls" to confine the king.

For example look at the position below.

And now look how effective it is.

And now you can go to wiki and see a very conceptual way to do it (emphasising how the knight and bishop can work together) without memorizing moves.  I think this is the most useful and easiest way to learn the mate.  http://en.wikipedia.org/wiki/Bishop_and_knight_checkmate#Deletang.27s_triangle_method

Maybe that is how we should be learning chess: backwards. From the endgames towards the opening. Mastering a few pieces at a time, instead of jumping into the deep end.

The problem I always had with the triangle method was when the king stays on the central diaganol, running back and forth. I think the w maneuver is much easier.

Capablanca has you beat by about 100 years on that bit of advice

Hmm, maybe I'm mixing them up.  The one that has you memorize lines I didn't find very useful.  When I realized there was a general method of just confining the king to a smaller box it made it much easier for me.

You only have to really memorize one position though, the one where the knight and bishop trap the queen. All of the other moves are just to reach that position.

Here is me using the w against a comp.

I could have mated about 5 move faster but we can't always be perfect.

The 2 Bishop ending is theoretical at best, when will you ever encounter it? Hardly ever. Show me a real game OTB where this technique has actually been used, maybe in sub-1000 play. I don't see how you can maintain both bishops and lose all your pawns. I am not in anyway a strong player but I think King-pawn endings will be more useful practically.

But yeah, as Estragon said I'd fear the player who had spent countless hours on practical rook endgames a lot.  The player who instead mastered many difficult Q vs R and B+R vs R positions (for example) wouldn't be intimidating in the least.

Usually these positions are a last ditch effort by the opponent.  e.g. they have minor pieces too, but they sacrifice them to win your last few pawns.  If there's any time trouble then these mates can be difficult even if you've studied them a bit.

There is only one thing to learn from this endgame: 2 bishops can create a diagonal barrier that a king can't cross. Trivial, but every player should know that, and it takes just a few minutes to see it.

So I am assuming it was a 2Bishop+pawn vs. a Bishop... probable yes I agree, he "sacrifices" his Bishop to force you into time trouble... maybe... still a rather hypothetical situation... if he has a bishop you just need to place your pawn in opposite color and force a piece exchange with one of your Bishops... show me a real game at least 1500 rated where this position occured OTB I would be glad to see it.

But Capa could only get into advantageous endgames because he played solid openings and middle games, and built a subtle positional advantage that the opponent only discovers too late - Karpov was a master of positional play as well... I think this quote from Capa was slightly overstated by journalists trying to get a catchy phrase... all aspects of the game are important

Well, the two bishop mate is easy enough I think anyone OTB would just resign.  I've never seen king vs two bishops OTB.  Maybe for the kid mildly interesting in scholastic tournaments it'd be useful to check off your list of things to know though.

B+B is easy.

N+B is not easy. And almost never happens that you will need it. In thousands of chess games, I've had this engame come up exactly once.

But studying the N+B is helpful nonetheless. It teaches the student how to make pieces complement each other. I am glad I learned it.

I am 1599 FIDE. I had a position against an 1680 for the tournament championship where he had a night and 2 pawns vs my B+N and 2 pawns I had a pin , but he managed to get rid of the pawns with some sacrifices. I had to win with B+N+K to get the medal.