# Scamming Horse Race

Used as Main Match of Season 1, Round 5, and inspires Main Match of Season 1, Round 10, for a later issue.

**Rules**

There is a horse race involving eight horses, traveling across 20 spaces. There are 12 rounds; in each round, each horse advances by a predetermined amount between 0 and 3 spaces, inclusive. (The result of the race is already determined.) Players should bet on which horses will finish first or second; there are no distinction on whether they bet on the horse placing first or the horse placing second.

Players have 20 chips at the beginning, and they may bet at most three chips after each round. They may not bet on horses in no-bet zone, the last four spaces of the race. Unused chips are discarded, and correct bets receive payoffs depending on their odds; the less chips bet on a horse, the larger the payoff per chip will be.

Each player has received a hint at the beginning of the game, and they may also look at any of three additional hints by paying three garnets for each hint.

Chips not wagered on any horse are lost at the end. The player with the biggest payout wins, and the smallest payout loses.

**Strategy**

Here are the complete list of hints that are revealed in the game. By the way, I’m too lazy to write the Korean names now.

- Eunji: Horse 4 finishes before horse 2, which finishes before horse 5.
- Gura: Horse 3 finishes before or ties with horse 5.
- Jinho: Horse 6 finishes right after horse 4.
- Jungmoon: Horse 3 finishes before horse 8.
- Kyungran: The horses that finish first and second have higher numbers than the horse that finish third.
- Poong: The horse that finishes first in round 9 finishes first.
- Sangmin: The sum of the numbers of the top three horses is 12.
- Sunggyu: Horse 1 finishes before horse 7.
- Yuram: Horse 1 finishes in the top three.
- Additional hint 3: Horse 6 finishes sixth.

Before starting, there is a relatively good way to avoid last place: bet two chips on each horse, and let the remaining four be decided while collecting information. Assuming someone lies, which is very likely, most chips will be oriented at a non-winning horse, and thus there are not much contest on whichever horse that wins.

Next, there’s something interesting (and unfair) with those clues. Note that how Jinho, Kyungran, Sangmin, and Yuram alone can decide the top two. (From Yuram’s hint, 1 finishes in top three, and from Kyungran’s, 1 must be third. From Sangmin’s, the sum of the top two is 11, and from Jinho, neither 4-7 nor 5-6 fits, so the top two are 3 and 8.) Jinho can also be replaced by Eunji and Sunggyu together (Eunji’s says that 5 cannot be in top three, while Sunggyu’s along with the deduction above says 7 cannot be in top three).

On the other hand, without any one of Kyungran’s, Sangmin’s, or Yuram’s hints, the top two cannot be determined. (Without Kyungran’s, the top two can be 3 and 1 (third is 8); without Sangmin’s, the top two can be 4 and 6 (third is 1); without Yuram’s the top two can be 4 and 6 (third is 2).) The good thing is that Eunji’s, Jinho’s, and the additional hint suffice to lock down 4-6-2-5 as the bottom four, leaving 1,3,7,8 for the top four. Along with Kyungran’s and Sunggyu’s, this suffices to lock 1-7 for the third and fourth positions, so we can ignore either Sangmin’s or Yuram’s. But Kyungran’s hint is still the most crucial, which still can’t be ignored even with the remaining hints collected together. Lying about these important hints is very easy: simply utter any other random hint (such as “horse 1 finishes before horse 2”).

Thus, I can definitely claim that Kyungran has a massive advantage here (hence the win). (Of course, with the remaining two clues unaired, I can’t be sure that the remaining two clues suffice to replace Kyungran’s hint, but still.) Sangmin and Yuram also have large advantages, as both are indispensable without the additional hint. I’m not sure why Yuram loses; she simply doesn’t find the correct people. Jinho has a decent advantage, requiring both Eunji and Sunggyu to replace him.

Of course, the easiest method is to make all the hints of the same pattern, or at least to make sure that any combination of six or seven hints is enough while five isn’t. Or something like that.