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102

This is fair. It’s possibly even more of an incentive if for instance being joint 2nd meant you split the prize money for second place and not the prize money for 1st place, which would usually be more.

I think though form a prize pool perspective that’s something I can’t picture. Say you made a tournament with 1st place $500, 2nd place $200, 3rd place $100 only but there was a joint top place, and a joint second to top place. Calling it joint second and joint fourth suggests splitting the money like 2 -$100, 2-$100, 4-$0, 4-$0. While if you called it joint first and joint third then maybe 1 -$250, 1-$250, 3-$50, 3-$50. More resonably again would just be to call them joint first, and then joint second, 1 -$250, 1-$250 and 2 -$100, 2-$100, in which case another player or multiple could get/share third place prize.

103

I think the most reasonable is that if we have a joint “top” spot, they share evenly the combined prize from the first and the second spots. In your example, two players would get (500+200)/2 = 350 and two players would get (100 + 0)/2 = 50. The total amount is the same as if we had a clean 500 + 200 + 100 + 0.

Any other interpretation leads to lower down players caring about the specific order of the upper players in a weird way (and possibly to different amounts of money being paid out in different scenarios).

5 Likes
104

In a situation like this:

Since there are no tangible incentives, the distinction between calling B and C jointly sharing 2nd place vs jointly sharing 3rd place is quite artificial. All the rankings can directly say is that:

A > B = C > D

Let’s consider Bob’s perspective (to give player B a nickname). How might he prefer A > B = C > D versus another outcome like A > C > B > D or A > B > C > D?

With the stated objective of “rank ahead of as many players as possible”, Bob would of course prefer A > B > C > D the most, but is ambivalent about A > C > B > D vs A > B = C > D, since in either case he is still only ahead of only one. Such an objective encourages risk taking to avoid a draw, since it is anyways no worse than trying for a better rank and falling behind those you might have drawn with. Curiously, this objective says a 4-way draw is no better than finishing fourth strictly behind the rest.

An alternative objective of “rank behind as few players as possible” has the curious effect of ranking a 4-way draw the same as a solo victory, which clearly is not what we want either. This type of objective encourages risk aversion.

Ultimately, I think how people might prefer between outcomes is actually a mixture of the two objectives. Perhaps, a player would first care about ranking ahead of as many players as possible, but then secondarily, also care about ranking behind as few players as possible.

In such a perspective, Bob would strictly prefer the three outcomes discussed above in this order:

  1. A > B > C > D
  2. A > B = C > D
  3. A > C > B > D

Introducing the perspective of hypothetical cash payouts is another way to look at it, as already partially discussed above. For the sake of example, let’s pretend the nominal prizes are $500 for 1st, $200 for 2nd, $100 for 3rd, and $0 for 4th, if there are no tied rankings. However, now let’s revisit how prizes might be distributed when the outcome is A > B = C > D. With a “max ranks ahead” perspective, one might award B and C each only $100 (for being tied for 3rd), while in the “min ranks behind” perspective, one might award them each $200. However, with the third “combined” perspective (and to hold the total payout constant regardless of the outcome), one might award them both $150.

In this type of perspective, one might be faced with the strategic choice between playing safe and settling for a tie vs taking a risk to potentially rank ahead or rank below. However, whether one choose to play one way or the other depends on the specifics of the situation and one’s risk tolerance/aversion.

4 Likes
105

How about this then; Let’s make the player incentives “maximize the number of players eliminated before you minus the number of players eliminated after you”.

(Note that, if no player is eliminated in the same round, this is equivalent to the current incentive.)

1 Like
106

This would make a 3-way draw equivalent to 2nd place, which I think is wrong.

To codify the linear order described by yebellz statement in numeric terms, we could use an expression along the lines of

(players below you) + 1/(players above you + 2)

But that’s needlessly messy. This ordering would follow automatically if we had some prize pool like we discussed above (a prize pool would also make clearer how to compare different situations with probabilities assigned to outcomes). I think all that’s necessary for the prize pool to induce the “correct” preference of rankings is that it is strictly increasing between each placement. (Edit: No, I was wrong. See reply by @martin3141 in the other thread)

107

So, to be concrete: Assume a prize pool of $700 for first place, $600 for second place etc all the way down to $0 for last place. When a player is eliminated, they get the lowest prize still not given out. If N players are eliminated in the same round, they split evenly the N lowest prices still not given out.

The specific amounts can be different (as long as first place gets more than second etc) to fine tune how much risk you should take to go for first. But it’s always better to have more players eliminated before you, and if that number is the same, it is always better to get more players eliminated together with you. (Edit: still wrong :pensive:)

1 Like
108

It doesn’t have to be that complicated, and accommodating considerations of risk does not make a 3-way draw equivalent to a second place finish. They are still distinct.

Here is another way to think about it. In a game of N players, each individual player can view it as (N-1) head-to-head games against each of the other players. If you are eliminated before another particular player, then it is like you lost against them. If you are eliminated after another player, it is like you won against them. If you are eliminated in the same round, it is like you drew against that person. The aim is to win against as many players as possible. If winning against another player is not possible, then drawing is still better than losing to them.

It’s like playing a simultaneous round-robin tournament, except all of the pairwise match-ups are intertwined into a single joint competition rather than separate, independent games.

4 Likes
109

Anyone interested to fill the last spot in the upcoming game?

110

About the board size poll, I will ignore @bagelfan’s vote, since they’re not a player.

From the 1st preference votes we have 5 votes for 13x13, 2 votes for 15x15 and 1 vote for 14x14, so the latter is eliminated. Maharani’s 1st preference to 14x14 is discarded, and their 2nd preference is for 13x13. This makes the 13x13 the clear winner.

8 Likes
111

Is the plan to start today? :blush:

3 Likes
112

I think so, yes :slight_smile:

5 Likes
113

reporting in >:D

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114

Let’s go!! :slight_smile:

5 Likes