All good points, Leif, I wondered the same questions.
What I replyed to me is:
______________________________________________________
About "Half-bet with threshold" formula:
1) First of all, Countries whose worth is higher than 10 are rare, as Oli said and you can check yourself.
2) So, being most of TO-P only 1
and the rare best positions half-price, many more people than now would be checking the Open Page looking for good deals.
3) If we set the threshold at, say, 18 then yes there's a 8
"jump" at 19, but you would be paying 9
for a CD you used to pay 19
! It looks a good deal to me, don't you think so? Would you really wait for it do drop below 19 to save further 8
? Or would you think that in the meanwhile you're waiting, someone else could snap it up? You would probably lose your good deal. Keep in mind that more people than now would be hunting for bargains.
___________________________________________________
"do we make any other step functions, say make >50
a constant 25
?"
Not easy to call. It may be useful for now, or for the next year long. But I believe it's not good in a site-growing perspective.
D-points in circulation now are very little because the site is young. You know there's a sort of Dpoints inflation due to the "Minimum Points" rule:
http://www.vdiplomacy.net/points.php
and due to newcomers signing up, so new Dpoints are constantly added to the circulation.
This lead to have people creating games with a bet higher than usual. Look at this ongoing
gameID=2855: it's starting happen here. Average Bet-size will grow.
Until a couple of years ago, I used to play on FB Diplomacy, one of the oldest sites. Since there was no RR, people used to create 101
buy-in games, to avoid newcomers, noobs and...multiaccounters. And people joined those game normally, there were a lot of points in circulation.
They also lauched challenges like "who got cohones?" with a 1,500
buy-in:
http://speedycomputing.net/phpdiplomacy/board.php?
gameID=11199Notice the pot is not 10,500
as expected, because someone paid 699
(full price) to TO a low-profile CD. (Yes! someone bet 1,500
and then CDed!).
See... 2 years ago there were already hundreds of players owning more than 1,000
, there.
Why I told you this story?
Because, yes, it will take several years for VDip to get there, but relatively soon we could have CDs whose worth is 200
(we had a 90
a few weeks ago) and make their TO-P only 25
would mean zero.
That's why I'd say no to further "steps"
_______________________________________________
"Would we need to step up slowly from 1 point? Say 13 becomes 1, 14-15 becomes 2, 16-17 becomes 3, etc?" "Or do a continous but slower increase for greater than 50? (Thus 50-53 is 25, 54-57 is 26, 58-62 is 27, "
Well, a progressive formula would probably be a bit better. What I don't know if it's worth the effort. I wondered these questions as well, because if some day there will be games with a, say, 150
buy-in, then you would say that a CD whose worth is 40 is an almost dead screwed Country and paying 20 to TO it wouldn't be very attractive. What I replied to me is the "comparison with Original Bet" formula I proposed last Monday .
TO-P = k * worth * X / 3
Where:
X = current CD worth / original bet
If X results higher than 3, then X=3
k is a discount parameter expressed in percentage. I proposed 75% but probably 60% works better
worth is the current CD worth, so until X<3 the formula is exponential, as Leif suggested
If TO-P results lower than 1, then TO-P=1. Other results are downrounded.
Does it works? Well, let's look at an example.
Say k=60% and Original Bet = 10.
These are the results the formula gives:
Current Worth.......TakeOver-Price
_________________
from 1 to 9.................1
_________________
10 - 11 - 12 ..............2
13 - 14.......................3
_________________
15...............................4
16 - 17.......................5
18...............................6
19...............................7
20 - 21.......................8
22...............................9
23.............................10
24.............................11
25.............................12
26.............................13
27.............................14
28.............................15
29.............................16
30.............................18
_________________
31.............................18
32 - 33.....................19
34.............................20
35 - 36.....................21
...
40.............................24
50.............................30
56*............................33
*Like would be a 40 SCs Country CDed in a WWIV whose Original Bet was 10.
- In the first group there are Countries whose current worth is lower than Original Bet (10). Since they're bad/screwed positions, they're basically costless;
- In the second group regular positions: very cheap! very appetizing!
- the 3rd it's the most interesting. They're basically all looking-good positions. Whether they're really good depends on the Price you ask. Well, it grows more than proportionally from 4
for a worth of 15 (4/15=26%) to 18
for 30 (18/30=60%)
- After 30, X is higher than 3, so it's put as 3 and the TO-P is always 60% of current worth. TO is always a good deal, since they're basically winning positions.
********** If you look at the results, all questions about "continous but slower increase" or "to step up slowly from 1 point" or "Will people wait for a CD to drop below [a threshold]" just DISAPPEAR! **********
How about a different Original bet?
One of the drawbacks of the simple "Half-bet with threshold" solution is this:
You would probably consider a CDed Country whose current worth is 19 (above the threshold) like a hopeless worthless position if the Original Bet was 40. Think of a 3 SCs Country in a Modern after that all Neutral SCs were conquered. It's screwed! I wouldn't pay neither 19 nor 9!
[little thought: how rare would be this occurrence?]
Let's see what the "comparison with Original Bet" formula gives.
Say k=60% again, but now Original Bet = 40.
Current Worth.......TakeOver-Price
_________________
from 1 to 19 ............1
from 20 to 24...........2
from 25 to 28...........3
29 - 30 - 31..............4
32 - 33 - 34..............5
35 - 36 - 37..............6
38 - 39......................7
________________
40 - 41 - 42..............8
43 - 44......................9
45 - 46....................10
47 - 48....................11
49 - 50....................12
________________
51 - 52....................13
...
60............................18
70............................24
80............................32
100..........................50
120..........................72
_________________
150..........................90
175........................105
200........................120
223*......................133
*Like it would be a 40 SCs Country CDed in a WWIV whose Original Bet was 40.
- In the first group there are Countries whose current worth is lower than Original Bet (40). Screwed positions are basically costless. As the position gets better, the TO-P slowly raises!
- In the second group regular positions: very cheap! very appetizing!
- In the 3rd, they're basically all looking-good positions. Whether they're really good depends on the Price you ask. Well, it grows more than proportionally from 13
for a worth of 51 (13/51=26%) to 72
for 120 (72/120=60%)
- After 120, X is higher than 3, so it's put as 3 and the TO-P is always 60% of current worth. TO is always a good deal since they're basically winning positions.
________________________________________________________
So, keeping in mind that "Half-bet with threshold" is (now) good enough for 96% of cases, if you want to have no worries for any present or future issue and to handle even rarest occurrences, I'd say that "comparison with Original Bet" formula:
TO-P = k * worth * X / 3
would be good enough for 99.7% of cases we may ever see.
- - - - - - - -
"Half-bet with threshold" - Simple and rather flawless...now. But as the time will pass, flaws will grow as Dpoints around grow and get inflated.
"comparison with Original Bet" - Almost flawless now and forever. But not simple to explain at all.
What do we do?
Thoughts?