OK, here is, how the game goes. The game has a small set of numerical parameters, I just describe them together with their "standard" values:
Numfield is a game for any number of players, probably more interesting for 5 and above. And actually more interesting for people to design strategies and program them, than to play it themselves.
A game of Numfield consists of rounds. The number of rounds is not restricted, but players drop out of the game and game should probably stop when no real changes happen any more.
All players start with a certain initial amount of points (typical 200) .
At every turn a player eithers passes (bets nothing) or bets a certain amount of its points. The amount must be a whole number, an integer below a certain limit (typical less than 100) .
All bets are payed in the pot. Additional points are added to the pot (I prefer only 1 to be added every round) .
The pot is divided between all playes who did not pass.
The part a player gets is proportional to the number of players which have bet the same or a lower amount than themselves, including themself. Payments are only whole numbers, the remainder is carried over and added to the pot next round.
Players who end at zero or below after a round drop out of the game. I usually call them dead or extinct.
Oops, maybe the scoring part was a bit fast. So here are few example with four players. Note, no carry over, but only a basic bonus of one point in the pot is assumed...
player
bets
pot
players below or equal
total parts
share
payment (truncated)
net effect
A
5
15
4
10
4*15/10
6
+1
B
4
3
3*15/10
4
+-0
C
3
2
2*15/10
3
+1
B
2
1
1*15/10
1
-1
Now the low players act cooperative and play different, while the high player stays:
player
bets
pot
players below or equal
total parts
share
payment (truncated)
net effect
A
5
9
4
13
4*9/13
2
-3
B
1
3
3*9/13
2
+1
C
1
3
3*9/13
2
+1
B
1
3
3*9/13
2
+1
Note that one point is carried over to the next round.
In case the cooperation of the low players had failed (due to whatever) and one of them had played higher, what would have happened?
player
bets
pot
players below or equal
total parts
share
payment (truncated)
net effect
A
5
11
4
11
4*11/11
4
-1
B
2
3
3*11/11
3
+1
C
2
3
3*11/11
3
+1
B
1
1
1*11/11
1
+/-0
Mixed remarks
Yes a strategy which passes all the time, cannot drop out of the game, but since the expectation of the game is positive, such a strategy cannot be optimal!
Note that ones own bid is counted as an equal. So every bidder gets at least one part, but of how many total parts?! You get a different, more aggressive variant of Numfield , if you do not count your own bid when counting lower or equal bids. I'd gladly agree to explore that game either!
If you have any other question, wishes or ideas, strategies or even class files please send an email to info@doris-frank.de .