Four Ways to Screw Up a Calculation

Quick thoughts and I don’t have an example, but something I’ve been musing on. How and why do people mess up their calculations? I mean when the calculation can lead to clear material gains or checkmate, a tactic or combination rather than when the calculation leads to complex positional comparisons. I’m not thinking about evaluating, I’m thinking about how we screw up calculating forcing tactical lines, so I’m not really considering missing a quiet move in the middle or at the end either, that’s a different topic. So how do we screw up calculating tactical forcing lines?

1. We miss the idea entirely. People often say if they knew there was a tactic they’d find it, but without knowing they weren’t looking for it. What’s the weakness there? It’s either not automatically checking forcing continuations or not having cues that’d make you think ah there’s probably something here. This is not the one I’m interested in today. It can also apply when solving tactical puzzles, sometimes we miss the possible move entirely. For instance I got focused on Qg6 threatening Qh7# in a combinative puzzle I was working on recently. I did not see Qxg7+ sacrificing the queen at all. If I’d considered I’d have seen it was mate shortly, but the move was invisible to me. A few puzzles earlier I’d solved a Qxh7+ sacrifice where all the pieces were lined up in a way that there were cues for me, it was a move to consider, and considering it led to the result. In the Qxg7+ example I didn’t have those cues and I glazed over it. So this is the first type of error; you didn’t consider the move at all.
2. You didn’t learn from what you calculated. I find this one very interesting. In many positions the first move you check isn’t correct. Does that make it time wasted? No! Often it tells us hey this would work if not for one thing and maybe a new candidate move emerges that augments that one thing. There was a problem recently (I really should go find the problems) where Rf4-g4 would be mate if not for exf4, but then gxf4 in response would open the g file for Rg1… if not for a Bc5 ready to take it. So we’ve learned from what we calculated. If we could distract the e pawn (we could not) or the c5 bishop (we could) then we could set up the Rf4 …exf4 gxf4 followed by Rg1# sequence. We may not have considered the first move at all at first, but by calculating we came across a logical need, and can now find a move that fits that need, which was not obvious to us initially.
3. Bad sequencing. This is strongly connected to point (2) and I initially had them as the same broader category. A simple example is you consider Qh5 preparing to capture on h7, but do not consider capturing on h7 followed by Qh5. There are more complex ones though! The reason this goes with (2) is often you find an idea in one line, and now have to insert it in another variation. A problem recently I considered many a sacrifice on h3, usually with my f5 bishop, they didn’t work. I considered …Be4 pinning g2 so I could blast through on h3, it didn’t work. The answer was to sacrifice a rook on h3, then play …Be4 and suddenly it all worked. But I didn’t find this until I considered all the different configurations of ways I could play appealing moves. I’d seen all the ideas, but for a while I couldn’t get them to work, because I had only tried sequences which had obvious logic to me. How do you find sequences that are not obvious to you? You try different sequences! You learn from your calculations! Thus you can solve and learn patterns you don’t know yet, next time you’ll see it faster.
4. Not calculating far enough. This is the big one, and finding quiet moves at distance in the midst of a tactical sequence is very hard. I like to say that the right amount to calculate is always one move further than however far you did calculate. I think this is funny, but it’s not all that helpful. Instead I think there are two tips here I have found useful. One is when considering a tactic or combination we should be trying to figure out why it doesn’t work. Clearly evidenced in Think Like a Supergrandmaster is that strong players spend much greater portions of their time refuting ideas. Specifically at the end of the sequence is there anything the opponent could do that changes the eval. Just to give an example say you have 1.e4 e5 2.d4 exd4 3.c3 dxc3 4.Bc4 d5 5.Bxd5 Nf6, now this is still the right thing to play but you might spot 6.Bxf7+ Kxf7 7.Qxd8 and feel delighted. But if you thought a second more at the end you might realize 7…Bb4+ regains the queen. That kind of thing, do a scan of the final position just to make sure it doesn’t crumble, check that one last move, if you’ve got the time. The other is a thought from Yusupov I’m paraphrasing: don’t stop calculating if there are still forcing moves to make. Another problem I failed recently I found the first 5 moves of a sequence, 10 if you could opposing replies, but the king was starting to run away. We had further checks, clear ones to do, but we definitely weren’t checkmating so I gave up on the line. Wrong! It turned out within the next 3 moves we could pick off the opposing queen. But I was focused solely on the king and stopped calculating. I still had forcing moves to make and should’ve looked further. Just because the king was starting to wriggle free didn’t mean I should end the calculation.

When problem solving recently I’ve tried to categorize how I screw up. I’ve noticed:

1. If I miss the idea entirely it’s something like Qxg7+. It gives up large amounts of material and is thus somewhat invisible. There are many patterns where I’m used to sacrificing but this wasn’t one so I couldn’t see it. As a player gets better they stop spending time on unsafe moves unless they understand the tactical sequence involved. In conclusion I don’t feel bad about struggling on problems like this I feel good, I need to see more tactical sequences so these ones start popping out at me too! Much better to see the move now, in the solution, and spend a little time making sure I get it than to have it remain invisible to me forever more.
2. I’m working on making sure I learn from lines I’m calculating and am mostly not getting things wrong here. If I don’t get the move at all it’s like because it’s from (1) not because I didn’t properly learn ideas from the lines I’ve calculated. I’m really pleased with my work on this.
3. Bad sequencing goes with 2 and while I definitely make a lot of mistakes here the amount is dwindling. As I said, well spent work.
4. Not calculating far enough is tough. I really like the rule of not ending a calculation while you still have forcing moves and I think it’s good practice; it keeps the variations relatively narrow so doesn’t feel infinitely exhausting, and let’s you find ideas at the end. It also gives you a clear cutoff point to say yes, I’ve done enough, I can try a different line. I still make many mistakes here. But, progress.