King of Tokyo Endgame: Racing to 20 and Kill Math

King of Tokyo has two finish lines, and the endgame is about choosing which one to run for. You win by reaching 20 points or by being the last Monster standing. The game ends at the end of a turn when either happens. Every turn near the end, you should know which finish is closer, for you and for everyone else.

Two ways to win, one rule that overrides both

You must survive your turn to win. If a Power card takes you to 20 points and 0 Life in the same turn, you are eliminated. And if every Monster is eliminated at once, everyone loses.

That second rule is rare, but it matters when a Monster in Tokyo with low Life rolls a big Smash turn against a table of low-Life Monsters outside.

The points race

Points come from three places: number sets, Tokyo, and Power cards. Near the end, Tokyo is the most reliable.

• Starting your turn in Tokyo is a guaranteed 2 points, before you roll.
• Entering Tokyo is 1 point, during your enter Tokyo step.
• A set of three numbers is 1 to 3 points, plus 1 for each extra matching die.

So a Monster at 17 in Tokyo starts its turn at 19 and needs one more point. Almost any set wins. A Monster at 18 in Tokyo wins just by surviving to its next turn. That is why the teach sheet warns about the leader at 17 or more.

Never Yield to a Monster at 19

Here is the endgame trap that catches even experienced players. When a Monster outside wounds you in Tokyo and you Yield, that Monster must enter and scores 1 point. If it was at 19, it now has 20, and the game ends at the end of its turn with that Monster crowned.

The same logic, one step back: a Monster at 18 that moves in gets to 19, then starts its next turn in Tokyo with 2 more. Unless the table can knock it out in one round, letting it in decides the game.

When the Monster hitting you is close to 20, stay in Tokyo if you can survive. Staying is often the only thing standing between it and the win.

Kill math

Life is open information, so the knockout can be counted. Here are the odds when you keep every Smash result and reroll everything else, with the base 6 black dice and three rolls:

Read it this way. A Monster in Tokyo with 2 Life is in serious danger from any single player outside. One with 3 Life is a coin flip for each Monster that goes all in. One with 5 is fairly safe from any one player, but not from a whole table. Cards that add dice or rerolls push every number up.

Counting the table

To know whether the Monster in Tokyo survives the round, add up the swings that come before its next turn. Two Monsters outside that both go all in average about 5 damage between them, and they reach 4 or more about four times in five. Four Monsters going all in can deal far more.

Run the same count on yourself before you decide to stay. If you are in Tokyo with 4 Life and three Monsters outside, the table probably has the damage to finish you. If one of them is the leader, though, staying may still be right, because Yielding hands them points.

When the knockout beats the race

Sometimes last Monster standing is closer than 20. Look for it when:

• You are in Tokyo and several Monsters outside are low. Your Smash results hit all of them at once. If the only Monsters left are three at 3 Life, three Smash results end the game.
• Only two Monsters remain. As long as one of you holds Tokyo, every Smash result lands on the one opponent.
• The leader is ahead on points but low on Life. You may not catch their score, but you can still end their game.

And look for the reverse: if the only way to stop the leader is to knock them out, chase Smash results even if it costs you points.

A pre-roll check for the endgame

Before each roll once anyone passes 15 points:

1. How many points do I need, and where can they come from this turn?
2. Can I knock anyone out, and how many Smash results does it take?
3. If I hit Tokyo and they Yield, does entering help me or doom me?
4. What does the leader need on their turn, and can I stop it?

Four questions, ten seconds, and most endgame blunders disappear.