King + Rook + Bishop vs King + Rook is often a draw, but in practice it can be tricky to defend. On the other hand, if you would like to play this endgame vs Tablebase, good luck. You will need lots of it.
Consider this position, white to move.
At first glance, it looks like White has achieved a lot. The defending King is on the edge of the board without too many options. Honestly, when I looked it over, I figured this is mate in 15 or so. It isn't. With best play, it's mate in 52! Now, this isn't one of those endgames that transcends the 50 move rule, because near the end, Black has to sacrifice the Exchange to prolong things. Still, the game goes through a ridiculous number of nodes. In fact, this position goes through seven consecutive nodes at this point. That's right. For seven consecutive moves, White has one and only one move that preserves a win.
That leads to my challenge. Can you make the first seven moves without letting the game slip into a draw? Try it. Here's some advice if you do try it. Pretend you are playing this position in a game situation, and that you have lots of time on your clock. Don't blitz it. Think about what you are doing.
Naturally, I came nowhere near running that seven move gantlet when I tried this the first time. I did get it on the third time, mostly thanks to just remembering the line.
The reasons behind these moves are sometimes just way beyond subtle, and a lot more than I want to get into in this post. I mean, really. Who is going to find 7.Kc6 with so many other reasonable looking alternatives?
For completeness, I will now show a line of best play in this position, up to the point where Black has to sacrifice the Exchange. Besides those seven opening nodes, there are ten other points where White has one and only one move to preserve the win. Seventeen in all.
Besides the seventeen points where White has only one move to continue to a win, there's a stalemate trap to avoid at move 27. Just another example of how simple endgame positions often require Byzantine processes to convert them.