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A target board consists of four parts, and each part has different numbers on it. You will make at most $10$ shots, and every shot's point will be added to your score. If you get a score of $20$ points at any point while you are shooting, you win the game.

The most interesting part of this game is that you decide what numbers are on each part of the target board, and you know that your probabilities of hitting each of these parts and missing the board are equal.

So

What numbers you should put on each part of the board to maximize your chance to win?

and

What is your chance to win the game?

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  • $\begingroup$ Is it the same board for all contenders? How many contenders are there? Do they have to take all 10 shots if they don't end up on a score of 20? $\endgroup$ – Ontamu Sep 5 '18 at 8:24
  • $\begingroup$ @Kruga each part has different numbers $\endgroup$ – Ontamu Sep 5 '18 at 8:24
  • $\begingroup$ @Ontamu it is invidivual race, the order does not matter, you just want to increase your chance to win. imagine that you are the only contender. $\endgroup$ – Oray Sep 5 '18 at 8:25
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    $\begingroup$ @Oray I really like your puzzles! They're all slightly more math/logic oriented than just wordplay! Here's a +1. Please don't stop making these puzzles :) $\endgroup$ – nikki Sep 6 '18 at 0:28
  • $\begingroup$ Can the player put negative numbers? $\endgroup$ – Royi Feb 9 at 9:11
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Very rough guestimate as I don't have the option to do the math right now but

20, 0, 10, -10. Chances are 1 in 5 to win on the first throw, 2/5 to miss the board or hit a zero (giving you 1/5 for the following throw), 1/5 to hit a 10 which kinda leaves you in the same 1/5 situation to win on next throw or hit a 0 or 20 (which still gives you 1/5 to win on the 3rd throw). The only bad outcome is hitting the -10 on the first throw.

Thanks to @EightAndAHalfTails for making a script to calculate the odds.

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  • $\begingroup$ This looks like it going to be impossible to beat. It might be interesting to explore what the best answer would be without negative numbers on the board. $\endgroup$ – Jaap Scherphuis Sep 5 '18 at 9:40
  • $\begingroup$ I made a Python script to calculate the success rate of this strategy. I make it 73%: Try it online! $\endgroup$ – EightAndAHalfTails Sep 5 '18 at 11:26
  • $\begingroup$ For non-negative only, my guess would be to replace the -10 with 5 which gives 57% $\endgroup$ – EightAndAHalfTails Sep 5 '18 at 11:36
  • $\begingroup$ According to the question, it's also possible to miss the board, with probability equal to that of hitting each given segment - I assume that this uses up a shot and gives 0 points. $\endgroup$ – EightAndAHalfTails Sep 5 '18 at 14:45
  • $\begingroup$ @EightAndAHalfTails: You are right. I missed that. I've deleted my previous incorrect comments. $\endgroup$ – Jaap Scherphuis Sep 5 '18 at 15:15

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