The Long Journey Home

Jassikan's Teeth is a game played with the alien race Ilitza. When you first meet the alien race and open up the dialogue options, you can gossip with them. If you choose the gossip option under the "Ask" category with an Ilitza Privateer or Slaver, they will talk about the game and add it as a dialogue option to the "Ask" category. Now you can select the "Jassikan's Teeth" option from the dialogue tree which will start a game.

Starting the game will give you an item, Jassikan's Teeth, you are asked to use with team members. The problem is, the game's mechanics and rules are never explained in game. You need to guess what happens and even then, it is quite obscure. The game is based on luck and chance. What you need to do to win the game is to get more points than your opponent. Your opponent will always score 11 points. A tie will cause you to loose and, as all losses, cost you money.

For each of the four rounds, crew members are assigned a score they can contribute. Depending on your choices, it will either be possible to get 12+ points or simply impossible. Fortunately, the people over on Fandom [1] have figured the points out. You can look at the table if you happen to have a crew configuration that differs from those I'll suggest to see if a win is possible. Here are crew combinations that will work. I will note them in the order you need to pick them to use the Jassikan's Teeth. In parenthesis I will note the score they might contribute. If there are multiple numbers, that is where the random chance comes in:

Zoe (4) -> Miri, Simon, or Alessandra (0,4) -> Malcolm or Lebedev (3) -> Siobhan, Alessandra, Kirsten, Miri, or Simon (1,2)
With this combination and optimal odds, you can get 4 + 4 + 3 + 2 = 13 points. Your last roll doesn't matter so it boils down to just one random roll of 0 or 4 points. Hence, possibly a 50/50 chance depending on how the game treats these internally (which we can only guess). As I noted, there are alternatives but those include more randomness. In round 1, you could also use Siobhan (1,3) or Kirsten (1,4). In round 3, Siobhan and Kirsten offer both (1,3) as scores.

The good thing is that you can abuse the save system to your advantage. Play the game and if you happen to loose, quit to the main menu. It will say that the game won't be saves. That is a good thing. Quit and choose continue. It will put you right back at the beginning of the encounter with the Ilitza and you can ask them again to play.

[1] https://thelongjourneyhome.fandom.com/wiki/Jassikan%27s_Teet...