Board Thread:Fun and Games/@comment-34263638-20180427174424/@comment-34224387-20180624185807

Unlike what I thought at first, this game has much more than just luck to it.

I was going to keep this information for myself but I decided to share it. Listen up students!

Let’s assume three players: A, B and C. A and B pick the numbers 52 and 51, respectively.

MS Paint mode activated

It’s now C’s turn to choose. The average Joe would go for something random like 31, but in fact, there’s a much better choice in this case – assuming he’s the last to choose – which is 50. Since the winner is identified as the closest number to the random generated number, choosing 50 means each number from 50 all the way to 1 will return victory to player C. Player C in this case is dominating with a 96% chance of winning the round. I call this aggressively claiming an open end. Aggressively means choosing a number that is right next to another player’schoice, like 51 and 50.

So now you should just claim every open end you see aggressively, right? Wrong. Let’s look at another example:

A and B pick numbers 1 and 2 respectively. It seems common sense to choose 3, but you should be able to distinct winning a round from winning points. Even if you win the round, you won’t get that much points as your choice is a very small number. If I had to choose, I would go for something like 20, covering every possible number from 20 to 52 (open end) and having equal probability with player B from 20 to 2. This gives player A roughly 1.92% chance of winning, player B 19.3%, and player C 80.76%.

This is a “probability for points” sacrifice. In my view, I’d rather have a decent chance of getting a decent number rather than a high chance of getting a small number. After all, even if you don’t win the round, the other players won’t get that much points.

This is a much different approach when you’re not sure if you’re the last person to choose in that round, as it is much easier for another person to claim your open end and leave you with nothing. Here’s an example:

Player A and B choose numbers 10 and 11 respectively. It makes perfect sense to pick 12 and get a 78% chance of winning the round, in case you don’t want to sacrifice probability. Little did you know, Player D comes over and picks 13, wrecking your plans and claiming your open end. Now you, along with player B, are left with 1.92% chance of winning each, with player D getting almost 77% and player A – which seemed at a disadvantage at first – securing a 19.23% chance, literally 10 times more likely to win than you.

Forking
Forking is trapping a number between two other numbers. Here’s an example:

Player A chooses 26, which is not the best opening – it is almost guaranteed to be forked.

Player B has to claim an open end aggressively to get the best possible outcome, as not doing so will result in sharing equal chances of winning with player A in the range between B’s picked number and A’s picked number. Thus he has two options: 25 or 27. Both of them have equal chances, and so picking the higher number (27) would be optimal; and is consequently the choice of player B. Player C comes along having two options as well: 25 or 28. Unwilling to sacrifice chance for points, he chooses 25. Now, Player A (26) is “sandwiched” between two numbers, 25 and 27. I call this a fork. Player A now has a 1.92% chance of winning the round, as both open ends are claimed by players B and C. Note that if player C chose the number 28 instead, player B (27) would be forked between A (26) and B (28). Getting forked like this is called a tight fork as both “forkers” are exactly next to the “forked” player. A wide fork is when the opposite is true.

Putting yourself inside a fork is not recommended, unless it’s wide enough for you to cover a good area. Let’s study a case where forking yourself can actually be better than claiming an open end.

There are 4 players in this round. A and B chose 31 and 52 respectively. It’s C’s turn now.

He/She can claim an open end from 29 to 1 and get a 57.69% chance of winning; however, they know that D is after them and will, for sure, fork them and take the open end. Knowing this, C instead decides to place themselves inside of the fork between A and B – it’s a 22-wide fork, which is largely enough. But the questions is, where inside the fork? Choosing a central number inside the fork like 40 is not optimal, because if the fork’s width is an even number – like in this example – you will share a number with one of the “forkers”, in this case 36. That means, if the generated number is 36, both you and A are equally close to it and therefore have to “share” the win.

So, choosing a number right next to either of the “forkers” is the best choice, and which one to choose depends on if you want to gain more points with the possibility of losing more points. A general rule is to go for the bigger number, and so player C chooses 51. Knowing you are already half-forked (next to another player’s choice) means that D could potentially fork you between 50 and 52, but it’s unlikely as they have a much better choice, 30. (57.69% vs 38.46%). Take notes if player D hates you.

Now let’s assume A actually chose 30 instead of 31. Now, it’s a better choice to choose a central number like 41, as no numbers will be shared and you are un-forkable since you have two unoccupied ends. Increasing the number increases both the chances of you being half-forked on your wide side and the chance of losing more points potentially.

Recap
Claim open ends when you're sure you're last

Don't put yourself in a tight fork

If you're first, don't choose a central number like 26

This, kids, is why you should never have free time to spare. I literally wrote a newspaper about winning a forum game.