Card Game Model of Ko
It is possible to model ko fights as a card game. Such a model can be both instrumental in developing intuitive terms for ko fights and possibly a tool of teaching.
Assume the ko is a pile of coins that represents the gain to be had by winning the ko fight. Each of the players Black and White has cards marked with numbers that represent values of ko threats.
Say Black starts. He puts down a card. White can either take the stake and pay Black the number on the card. Or White can play a card (in which case Black's card is out of the game), and now Black has the corresponding choice. This continues until someone takes the stake.
Naturally to apply this model to ko fights, we assume that each player can see all the cards. Then the correct strategy for this game is known, and is also something one can work out.
To this basic model one can add different cards, that represent other moves than sente moves (with no value itself, but a threat value). Gote moves elsewhere, loss-making threats, moves to enlarge the ko instead of resolving it can all be conveniently modelled as cards and be used for demonstrations of ko timing, compensation by threat + followup vs. compensation by two gote moves elsewhere.
Loss-making threats in the card game model
The card game model helps distinguishing different types of loss making threats. Additional to the pile of coins representing the ko, we may add two other piles of coins representing the score of each player.
The three types of loss-making threats can be modelled as
- cards that - in addition to the value of the threat - make you pay coins of your own to the opponent = threats losing points elsewhere
- cards that - in addition to the value of the threat - let the opponent take some coins from the pile representing the ko = local threats making the ko smaller
- cards that - in addition to the value of the threat - make you add some coins of your own to the pile representing the ko = local threats enlarging the ko
Often lumped together as loss making threats, this model can show that only the first type is always a loss, while the second and third type of loss-making threats only result in a loss when you win the ko (second type) or lose the ko (third type) respectively and can be played safely and with a gain in the opposite case.
It is inconvenient and probably not particularly useful to model typical open-ended plays (ambiguous moves, gote moves with a follow-up) that are typical for many situation in the card game model.