From blackjack to bridge: our ranking of game difficulty for computers

Working on CUBE Backgammon makes the comparison with other games hard to resist. Chess has no dice to account for, yet building a strong chess player demanded an enormous effort. Bridge has fewer cards to choose from than Go has empty intersections, but a bridge program cannot see all the cards that determine which choice is best.

Here is our ranking, from the most tractable to the most demanding task: blackjack → English checkers → backgammon → chess → Go → bridge. We are judging the challenge of building a strong computer player for the full game, using known techniques. This is an editorial assessment of search, evaluation and information, informed by published work; the six games have not been measured in one common experiment.

1. Blackjack: the dealer has no strategic freedom

Blackjack has chance and concealed cards, but its dealer follows fixed rules. Once those rules and the remaining-card assumptions are specified, the computer can calculate what taking a card or standing is expected to earn. It does not have to model a dealer who deliberately chooses the most difficult response.

The authors of the 1956 mathematical analysis identified that restriction as essential to making the problem manageable. It earns casino blackjack the lowest place in our ranking. A favourable return is a different issue: our worked example has a best available choice that still expects to lose.

2. English checkers: a game whose result has been proved

English checkers, also called American checkers, is the eight-by-eight version. It has neither random draws nor concealed pieces, and its forced captures constrain many positions. In 2007, researchers proved a draw from the starting position with perfect play, supplying a strategy that guarantees that result.

This was a weak solution from the start, not a lookup answer for every legal position, and it required years of work. It nevertheless gives checkers something the higher board games in this list lack: a proved starting-position result with a strategy to achieve it. That is a substantial reason to place it near the tractable end.

3. Backgammon: the dice make search expensive, and learning productive

Backgammon has chance without concealed information about the current board. Both players see the same position, and the roll is public before its player chooses a move. The engine must combine adversarial choices with probability-weighted future dice.

This creates a wide search tree. Gerald Tesauro’s 1995 paper contrasted roughly 30–40 choices per chess move with several hundred backgammon branches when future rolls were included. Yet TD-Gammon reached a very strong standard through learned position evaluation with comparatively shallow search. The dice also varied its self-play experience, a benefit we examine in the learning article.

That combination is why we put backgammon here: difficult to calculate exhaustively, but historically receptive to a useful learned evaluator.

4. Chess: a narrow forcing line can overturn a promising position

Chess removes the chance branches, but every reply belongs to an opponent trying to defeat the plan. A position can have attractive material and activity, yet contain a forcing sequence that loses. The engine needs to find enough of those lines and judge the positions reached when its search stops.

We put chess above backgammon because strong chess programs have depended so heavily on combining tactical search with position judgment. This is one of our closest calls. Ranking the games by raw branching alone would reverse the pair; ranking their practical engineering challenges includes how useful an evaluator can become before deep search is available.

The AlphaZero paper describes both the earlier search-intensive chess tradition and a learned alternative combining value and move probabilities with tree search. The methods changed, but the task still involved deciding where to search and what to believe about the positions encountered.

5. Go: too many plausible moves, and a difficult position to judge

Go has no random move generator and no concealed stones. Its difficulty comes from the breadth of choices and the way a local move can affect territory, influence and the survival of groups elsewhere on the board. Following every plausible continuation soon becomes impractical, while a simple count of stones does not tell you who is winning.

That combination puts Go above chess in our ranking. The original AlphaGo paper explicitly identified both the enormous search space and the difficulty of evaluating positions. AlphaGo learned a policy that helped it select promising moves and a value function that estimated outcomes, then used them in search.

This is why its success was so interesting: a computer could spend its effort on selected futures and make useful judgments before reaching the end of the game. A larger tree alone would not explain the breakthrough; learning which positions were good was central to making the search effective.

6. Bridge: the player cannot know which world they are in

For the full game of bridge, add the random deal, hidden hands, bidding, partnership communication and strategic opponents. The program has to infer what other players might hold while choosing a plan that can actually be followed with the information available.

A solver can play brilliantly when shown all four hands and still mislead a player whose opponents’ cards remain concealed. As Ginsberg’s work on GIB explains, exposed-card calculation and play under uncertainty are separate tasks. Our bridge example shows how combining individually winning continuations can produce a plan no uninformed player can execute.

Putting bridge above Go is the most debatable choice in the list. We give it this place because the complete player must combine reasoning about cards, a partner and the information revealed by play; solving exposed hands addresses only part of that job. Recent research makes the distinction concrete: a 2025 result solved all 28-card double-dummy hands, where the cards are visible, while LeadGenius in 2026 studied the opening lead using information from bidding. Neither result alone describes a complete bridge player.

Why more branches do not automatically mean a harder game

A tree with ten options at every step has a thousand paths after three individual moves. Real games also have repeated positions, obvious mistakes that can be discarded, and lines worth examining much further than others. Counting every branch measures what exhaustive search would face, not how much useful work a strong program must do.

Chance changes how the branches are combined. At backgammon there are 21 unordered dice pairs, weighted as 36 equally likely ordered outcomes. The engine averages over those future rolls, while accounting for an opponent who chooses a reply. At chess and Go it needs no dice average, but it still has to search the opponent’s choices.

The value function that makes search useful

When the engine cannot reach the end, it needs a value for the position where it stops. That estimate might be expected points at backgammon, a win/draw/loss assessment at chess, or an expected result from a Go position. A learned function supplies judgment that the search cannot obtain by finishing every possible game.

Counting branches does not choose the move

Imagine an invented game with exactly ten choices at every position, all examined. Searching three individual moves ahead gives 10 × 10 × 10 = 1,000 positions at the last level. The engine still has to evaluate them.

Invented values for two moves, in expected points

Move	Assumed exact value	Engine estimate
A	+0.10	+0.30
B	+0.08	+0.28

Does the engine choose correctly?

It chooses A, the better move in this example. Both estimates are too high by 0.20, but their difference of 0.02 is correct. Accurate values and accurate move rankings are separate things to test.

An original teaching example; these values are not position-analysis results.

Building that function means supplying examples and a learning target, then adjusting a model so it can estimate unfamiliar positions. The target can come from stronger analysis or from self-play outcomes. We explain the process through the equity estimates used in CUBE Backgammon, including why the number is not a guarantee and how search can improve it.

Why parameter count does not settle the ranking

AlphaZero used the same general algorithm and network architecture for chess, shogi and Go, with separate training for each. Model size also interacts with training and search: a quicker evaluator may leave time to examine more replies. Counting weights alone does not measure the challenge we have ranked.

Would the same ranking describe learning to play?

For a person, pattern recognition, memory, access to good feedback and the gap between beginner and expert all matter. Researchers studying strategic depth have considered ladders of increasingly strong strategies, an approach closer to sustained improvement than raw tree size.

Our computer ranking therefore places backgammon in the middle for a specific reason: the dice make deep calculation costly, while learned judgment has proved remarkably useful. Go and full bridge sit higher because their combination of search and evaluation, or search and concealed information, asks more of the complete player. How long you need to learn any of them remains a question about your practice and understanding as well as the game.