The Magnus Challenge

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