Number Race

[Cyrus]

Alright, now I'm really confused. It seems like with what you wrote in the PS, then 10k's entrance in Round 3 seems like it got misjudged. In order for a number to in in play, it would have to be ranked, right? Then why didn't the description you outlined occur then, and cancel out both of our numbers.

In fact, the whole reason I included the default of 1,000,000 was to prevent situations like the PS from happening, which is what occurred in Round 3. I'm curious to see why that didn't happen, since I'm obviously missing some of the reasoning here.

Edit: Alydar did the same thing as both 10k and myself, so that's a third person with basically what you said, but I somehow came out ahead. Alydar's submission was especially close to your PS Situation.

[Freih]

Now that I think of it fresh, you're right and should have not ranked in game three. Back then I was considering that same thing almost an hour and decided you were legit.

Alydar's different: in the situation I described both your and the extra message would have failed. However, exactly because of that Alydar's backup clause kicks in and reverts his message to a constant (note that the backup clause in my hypothetical message is different from Alydar's).

[Alydar]

Okay, as soon as I get to writing, Freih answers... however, I'll still examine the ones you talked about, so we can get another opinion on the matter.

Feb 1, 2013 3:53:01 GMT Cyrus said:

Alright, now I'm really confused. It seems like with what you wrote in the PS, then 10k's entrance in Round 3 seems like it got misjudged. In order for a number to in in play, it would have to be ranked, right? Then why didn't the description you outlined occur then, and cancel out both of our numbers.

In fact, the whole reason I included the default of 1,000,000 was to prevent situations like the PS from happening, which is what occurred in Round 3. I'm curious to see why that didn't happen, since I'm obviously missing some of the reasoning here.

Edit: Alydar did the same thing as both 10k and myself, so that's a third person with basically what you said, but I somehow came out ahead. Alydar's submission was especially close to your PS Situation.

No, they're actually different. I'll go over them if you'd like, as the confusion that was in play Round 1 isn't applicable anymore.

So. Players have two possible outcomes: to be ranked with a number or to be unranked. Let's look at Round 3 and my post. It is [number], or one higher than the highest ranked number aside from it. It has a clause where it defaults to [number] if it would otherwise become unranked. Thus, it defaulted back to [number]. There's not much of a question there.

10k was 5 more than the highest number in play but his. Cyrus' was a complicated mess of things that took into account each player's number as well as whether they were ranked or not. Now we look at the "solution" which Freih used (I actually never paid much attention to it, assuming it was right). 10k's and Cyrus' conditions definitely come into conflict and escalate into the unranked range. If 10k is ranked, Cyrus is larger, so 10k is larger, so Cyrus is larger, etc., so both would become unranked. Now here's where the logical fallacy happened. Obviously, 10k being ranked would lead to neither 10k nor Cyrus being ranked, and Cyrus supposedly worked out a method to prevent that. So we assume 10k is unranked, and Cyrus' default kicks in, giving Cyrus a ranked number. What's not considered then is 10k's condition which is now left unfulfilled... 10k could be 5 higher than Cyrus' number, so he should not be unranked. Thus, he should be ranked, so neither is, as they come into conflict.

Now let's look at Freih's new suggestion. It concern's Cyrus' number specifically, so it ignores everything else. If Cyrus competes with another player, Cyrus is unranked, so it would default to 1. If Cyrus doesn't compete with another player, Cyrus is ranked, so this would beat Cyrus. If Cyrus competes with the highest-ranked player, both would compete with each other, so they both become unranked. The difference in wording between this and mine for Round 3 is important. Mine defaults if my own number is unranked. His defaults if another's number is unranked; it allows itself to become unranked.

It's kind of like some sort of rock/paper/scissors game where there are only two possibilities. A "maybe-ranked" decision beats out any ranked decision, assuming it's done well. However, as soon as you add a second "maybe-ranked" decision, both become unranked, so the ranked decisions win out. If it's a battle of ranked decisions, it's just whoever chose a higher number. There's a "third" decision which is really like a mix of the two. It's what I did, and it's basically "If there's no other 'maybe-ranked' decision, I go 'maybe-ranked' and win. Otherwise, I become ranked." This loses when only one other "maybe-ranked" decision is used, but if two other "maybe-ranked" decisions are used, it wins out.

So there are effectively three decisions, making it closer to rock/paper/scissors. Ranked is the weakest but safest, as it's automatically considered. Maybe-ranked is the most risky but wins as long as no one else does the same. Half-and-half is safe, as it counts as a maybe-ranked if all other decisions are ranked and counts as ranked otherwise; the problem is that it doesn't contest with maybe-ranked to force them to unranked status.

Then there's other types of half-and-half decisions, like one which focuses on a specific player. It's maybe-ranked, but it's got less of a chance of winning; it loses if the targeted player is also maybe-ranked, and it is only guaranteed to defeat the targeted player; it doesn't compete with any other player's decision.

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Let's look at the rounds in this light.

Round 1
Alydar: Maybe-ranked, self-conflicting (due to rules confusion)
Iain7: Maybe-ranked
Rise: Ranked, 0
The two maybe-rankeds conflict, ranked is set to tie with the dealer and does.

Round 2
10k: Ranked, > 0
Rise: Half-and-half, self-conflicting (due to rules confusion), becomes ranked, 0
Both are ranked, but 10k's is greater so wins.

Round 3
Alydar: Half-and-half, defaults to >0
10k: Maybe-ranked
Cyrus: Maybe-ranked
The two maybe-rankeds conflict, so the ranked >0 wins.

Round 4
10k: Ranked, > 0
Alydar: Ranked, > 0
Both are ranked, but Alydar's is greater so wins.

Round 5
N/A; game ends

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And thus I end my long spiel of explanation and go to sleep...

[Cyrus]

Yeah, that all makes sense. The main reason that I didn't include a 'if this number in unranked' clause is because I wasn't sure if that was a legal addition or not.

[Alydar]

Feb 1, 2013 6:14:35 GMT Cyrus said:

because I wasn't sure if that was a legal addition or not.

Anything's legal! ...but nothing's an assured win.