Numbridge — Strategy

Playing against the bots

There is one bot program with five levels. The level is set per bot in that room's settings, not for the room as a whole: two bots at the same table can be on different levels, so look at your opponent, not at the room. A level is not "speed" or "hitting power": it says which sudoku techniques the bot uses and how many moves ahead it looks.

level    sudoku techniques              lookahead
first    single candidate in a cell     one move
second   + hidden singles               one move
third    + pairs and pointing pairs     one move
fourth   full deduction                 one move
fifth    full deduction                 two moves

The fourth and the fifth share the same sudoku techniques, and differ in two ways. First: the fifth nearly always takes the best move it found, while the fourth is sometimes distracted — and confuses the digit in a cell it deduced itself. In Bridge that is roughly one placement in ten; in Domains it is far rarer, because carelessness is low at every level there. The fifth never misses out of carelessness at all. Second: the fifth looks a move ahead. A move that only pays off one turn later works against the fourth and works worse against the fifth: it sees that the cell you take now will open the next one for you, and interferes in advance. That advantage is noticeable but not decisive.

The rungs of the ladder are low

We measured the ladder under the current rules. In Bridge neighbouring rungs give 0.575 to 0.645 in favour of the higher one — one step up costs you a few games out of ten, not all of them. The extreme pair, the fifth against the first, is 0.895.

In Domains the ladder is calibrated and looks much like the Bridge one: neighbouring rungs of 0.645, 0.635, 0.610 and 0.605, with 0.908 for the extreme pair.

For Blitz we quote no numbers: they were measured at a claim price of one tile, while blitz rooms play at two, so the ladder has to be measured again.

Both sets come from bots playing each other, not from games against people: they say how far apart the levels are, and nothing about how a level will fare against you.

Hence a simple rule for choosing an opponent: play one rung above your own level. An opponent who beats you six games out of ten is the best teacher; one who beats you nine teaches nothing, because in nine losses you never find out where you went wrong.

What a bot does worse than you

A bot does not know the solution. Like you, it deduces digits from what is visible, and when no deduced cell exists for any tile in its hand, it guesses — all five levels do. The difference is how they behave when a deduction is available: the first level may still go at random, while the other four move only on a sure thing — a deduced cell, a claim, or the pie.

The second weakness is carelessness: in some of the cells the bot deduced itself it takes the wrong digit among that cell's candidates and misses. The lower the level, the more often.

In Bridge that is what the game against the lower levels is built on. Misses are frequent there. The share of digits placed correctly was measured over a run of 240 games per pair of levels — six pairs, 1440 games. Each level played different opponents, so a level has several readings, and a band is the honest way to quote them: the first about six digits in ten (0.58–0.62), the second a little higher (0.62–0.65), the third about three quarters (0.72–0.76), the fourth nine in ten (0.90), the fifth 1.000 in all three pairs where it was measured.

These numbers are not an even ladder: by share of correct digits the first and the second are barely apart — their bands nearly touch. The visible jumps start above the second level. Play safe: take only cells you have deduced, and their misses will hand you the tempo.

In Domains that calculation fails. Carelessness is low at every level there: even the first places nearly every digit correctly, and there are no presents to wait for. A lower level's weakness in Domains has no single address — it is not that it "cannot count blocks", it simply picks a reasonable but not the best cell every move, losing a little at a time. You answer that not by catching mistakes but by counting: contested blocks, the pair of moves, the early finish (see Domains: tempo and blocks).

In Blitz a bot takes the same table of levels as in Bridge: there is no separate tuning for the small field, and the goal there is the same — connect your sides. The numbers above, though, do not carry over to Blitz: they were measured on the 9×9 Bridge board with thirty givens, while the Blitz board is 6×6, where a cell has fewer candidates, so the same carelessness yields a different share of correct digits.

A third thing the two lowest levels lack is technique. A cell that yields to pairs or pointing pairs is simply invisible to the first and the second and they walk past it; you will see it. From the third level up those techniques are available.

A bot thinks in positions, not in traps. It does not save a given for the endgame and does not prepare a free claim with an empty hand. The endgame is your chance: count the bag and your opponent's hand (see Managing your hand) and plan two or three moves further than the bot counts.

What a bot does better than you

It never tires: on the hundredth move it counts as evenly as on the first. Against the two higher levels there is no point hoping they will "overlook" a contested block or a short road to a side: they will not. You beat them by deduction — by closing cells with certainty more often than they do.

The study room

Numbridge Study gives you two minutes a move and does not count rating. It is the best place to work through deductions unhurried: make yourself a rule not to move until the cell is deduced, and play a few games that way. Speed comes later; the habit of looking before placing never comes at all unless you force it on yourself somewhere calm.