Computational bounds for the 2048 game

Alexey Slizkov

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Computational bounds for the 2048 game

Alexey Slizkov

Data Structures and Algorithms · Submitted 9 Mar 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove rigorously for the first time that there is an algorithm with winning probability at least 0.99969, and that there is a strategy for achieving the 256 tile guaranteed (with probability 1).

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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,290 input tokens.

What the abstract itself states, as probabilities: claims first 0.90 · states limitation 0.09 · human participants 0.03 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.17 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

2048 is a single player video game, played by millions mostly on mobile devices. We prove rigorously for the first time that there is an algorithm with winning probability at least 0.99969, and that there is a strategy for achieving the 256 tile guaranteed (with probability 1).

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	2048 is a single player video game, played by millions mostly on mobile devices.	background 1.00	0.05	0.02	asserted 1.00
s1	We prove rigorously for the first time that there is an algorithm with winning probability at least 0.99969, and that there is a strategy for achieving the 256 tile guaranteed (with probability 1).	result 0.88	0.95	0.93	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

2048 is a single player video game, played by millions mostly on mobile devices. We prove rigorously for the first time that there is an algorithm with winning probability at least 0.99969, and that there is a strategy for achieving the 256 tile guaranteed (with probability 1).

Human review

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How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites

Cites as background 1 paper

For example, [ref] and [ref] prove some hardness results (NP-hardness and PSPACE-hardness).

2048 is (PSPACE) Hard, but Sometimes Easy · Introduction · 0.95

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