The Magnus Challenge — Taylor G. Lunt

Let’s say you’re a club chess player with an Elo of 1500 (early intermediate). If you can beat Magnus Carlsen, rated 2800, at a game of one minute bullet chess, you win a billion dollars. Magnus only gets one minute on his clock, but you get one year on your clock.

Even given that advantage, you don’t have a chance. However, there’s a twist: During your year of time, you can challenge any other player to a chess game. They get one minute on their clock, you get as much time as you like. If you beat them, they can play Magnus for you instead, using the rest of your remaining time. Or, they can challenge another player, who can challenge another player… who can play Magnus in your stead. If at any point you or one of your proxies lose a game, you lose the challenge and go home empty-handed. We’ll just pretend draws never happen.

The question: What is the optimal strategy for beating Magnus, and do you have enough time to have at least even odds of beating him?

Some assumptions:

Based on how Elo works, being 100 points stronger than someone means you win about 64% of games against them. Being 400 points stronger means you win about 91% of games against them. To win 99%, you’d need to be 800 Elo higher than them.
Extra thinking time makes you play above your Elo, but with diminishing returns. 10x your opponent’s time is worth +250 Elo (approximately). 1000x your opponent’s time is worth +500 Elo. 100 million times your opponent’s time is worth +750. To have an even chance of beating Magnus by yourself, you would require a +1300 Elo advantage. There’s no time advantage that will give you a +1300 Elo boost.

You don’t want to play Magnus directly, or you’ll lose. Instead, you want to beat someone slightly better than you, who beats someone slightly better than them, and so on, until finally you beat Magnus. You rely on having a time advantage at each step.

How many steps should you take? Too few, and you’ll get smoked in the first round. Too many, and you have to win too many games in a row. Each game is a chance to lose, and the more steps you take, the less of a time advantage your proxies have in each match.

You can choose the players you want to play and ensure they have an even distribution of Elos from your Elo of 1500 to Magnus’ Elo of 2800. That means it’s best to split your time advantage evenly across steps.

Let’s say you chose to play 20 games, so you would play the first game, your first proxy would play the second game, … and your 19th proxy would play Magnus. Each opponent would be 65 Elo higher than the last. Each game would get about 18 days, or 26,000x their opponent’s one-minute clock. This time advantage puts your proxies effectively around 535 Elo ahead (net), winning around 96% of the time. That sounds high, but winning 20 games with probability 96% is only a 41% chance of winning every single one.

Not quite the 50/50 we wanted as a minimum. Plus, sitting through 20 stressful chess matches with a billion dollars on the line sounds like a drag. At the other extreme, you could play two games, with only a single proxy. Each player would be 650 Elo higher than the previous. Each game would be 6 months vs. one minute, giving a total advantage of 10 Elo in your favor in each game. Each game is basically a coin flip, and you end around a 27% chance of winning.

The sweet spot is somewhere in the middle. Seven games with six proxies. Each opponent is 185 Elo higher than the last. Each game is about 52 days vs. one minute, or 75,000x time advantage, which is worth +630 Elo. This means your players are net 445 Elo stronger, winning 93% of the time. To win seven games at 93% each is 59%. So you can have greater than even odds against Magnus after all!

If we don’t already, we will soon have the first superhuman intelligences (these will probably be human-AI teams for now, and later pure AI). In order to ensure the godlike ASI we eventually build will be aligned to our values, we need to ensure each previous intelligence is also aligned. One failure anywhere on the ladder kills us.

Right now we are that lowly club player, hoping we can beat Magnus. Whether or not we can depends on whether the AI story lines up with the chess story or it doesn’t. The chess story was chosen because I could actually estimate the relevant variables based on how chess is played, and it neatly communicates the idea. But, here are some ways the AI story might be different:

In the Magnus Challenge, we got to allocate our time as we saw fit, among a number of opponents we decided was optimal. With AI, we don’t get to choose the intelligence jumps of our opponents. One big leap could doom us. And we don’t necessarily get to allocate our time as we see fit. New AI models will come out at an unpredictable pace, and we have to ensure the model is aligned before it is released. An AI pause is our one tool to adjust timing, but it’s a limited resource. Remember that to allocate our time optimally in the Magnus Challenge, we give more time to larger leaps in Elo. (Since the leaps in Elo were all equal, we gave them equal time.) If we waste our extra time by initiating an AI pause before a model that probably would have been easy to align anyway, that’s sub-optimal compared to using our pause before the largest jump. But wait too long and we could lose our chance to use it! (Note that “aligning” a model in this case doesn’t mean making it perfectly aligned, only aligned enough that we survive until the next model. “Handoff alignment.” This may not be much easier, but I’d say current models are probably roughly handoff-aligned, but not perfectly aligned.)
Each chess game is independent, but it’s possible alignment techniques that can align one model will meaningfully carry through to help align successive models. There’s a limit to how much this matters. If you can come up with an alignment method with your human pea-brain, a superhuman intelligence much smarter than you would come up with that same idea instantly when trying to align its successor. It doesn’t need your help.
You are a human being with a brain, and so is Magnus. There’s a limit to how much better at chess than you he can be. The gap between humans and machines can be (is) much greater. If the gap between peak human intelligence and godlike ASI is larger than the gap between a club chess player and a super-grandmaster, then aligning AI will be harder than the Magnus Challenge. (Note that the gap will not be arbitrarily high: Once ASI is smart enough to do everything we want, if it is aligned but can’t guarantee alignment of its smarter successor model, we can instruct it not to create one, as any extra intelligence is pointless to us and pure risk from an alignment perspective. Put another way, if you’re comfortable merely defeating Levy Rozman and stopping there, instead of Magnus Carlsen, you face much less danger in total!)
The curve of diminishing returns chess players see against other chess players when they have more time may not reflect the curve of diminishing returns AI safety researchers see against the difficulty of aligning the next model. In the Magnus Challenge, each opponent having a fixed Elo and getting one minute of clock time is supposed to represent the increasing challenge of aligning sufficiently more intelligent models (who have a fixed time during training to resist alignment), but playing chess against an opponent and figuring out how to align an AI model are not actually the same activity.
Alignment is not all-or-nothing. A model can have some probability of being misaligned, or be misaligned in some circumstances but not others. This model is a simplification.
We might not have a first-mover advantage as significant as 1 year:1 minute. It might be more like 1 hour:1 minute (in which case your chances of beating Magnus are ~8%). How much of an advantage you think we have determines how likely we are to succeed.
Successive AI models might think faster, skewing the diminishing returns curve. AI definitely thinks faster than humans, so it’s a problem at least for the first step.
On the other hand, AI model releases might get faster and faster due to recursive self-improvement, and if that happens in a way that’s too fast compared to thinking speed increases, that lowers the time advantage for previous models to align the next.
59% is pretty good odds for winning a billion dollars. It’s not fantastic odds for preventing apocalypse. The reliability requirements of alignment are higher. Over 7 steps, if you want a 99% chance of success, you need ~99.86% chance of success at each step.

On the one hand, the Magnus Challenge is an inspiring story. You, a lowly 1500 Elo club player, have absolutely no chance of beating Magnus by yourself, even if he spends the first 6 moves swapping his king and queen just to troll you. But by defeating a successive chain of opponents and gaining their strength for yourself, you can beat him more likely than not.

A lot of people suggest the same plan for aligning AI. Will it work? Well, AI is already not perfectly aligned, so in a sense we’ve failed. But we don’t need perfect alignment at each step in the chain. We need enough alignment that we survive until the next model, and the current model makes a sincere attempt to help us align the next model (or will get caught if it tries otherwise). Still, it’s a high bar, and for the reasons mentioned above, the AI alignment chain might not be as easy as the chess victory chain.

The one timing lever we have, the AI pause, is something we have to carefully balance between blowing it at a point where it’s not needed, vs. holding onto it so long we die before we can use it, when it could have helped. Ideally we pause before the biggest capabilities jump so we have more time when we are at the greatest risk of losing. Since capabilities jumps are currently not very high, I would personally lean toward “not yet”. But get the infrastructure in place so we can do it quickly once it’s time.

Whatever we do, we have to make sure we’re not just aiming for reasonable certainty that the very next step in the chain won’t cause disaster. We need much more certainty than that to ensure the entire chain is safe.