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The pursuit curve assumes that the lion always moves directly towards the tamer. The better strategy for the lion is your back-to-the-wall position. The lion s
by beza1e1 15y ago
The pursuit curve assumes that the lion always moves directly towards the tamer.
The better strategy for the lion is your back-to-the-wall position. The lion should be able to get infinitesimally close to the tamer. Pragmatically and finally, the delta will be smaller the reach of the lion's pawns. Lion wins.
- amirmc 15y ago"...back-to-the-wall position." Can you expand on this? My thought was that if the lion 'zig-zagged' somewhat, it would effectively force the tamer to constantly change direction[1] and ultimately the lion would catch up. Is that what you meant by back-to-the-wall? [1] Assuming that the tamer's only strategy is to maximise distance from the lion.
- beza1e1 15y agoYes, I also have the zig-zag in mind. However, as a point, the lion will never catch him. The lion has to move further to the side than the tamer, so the tamer switches directions after each "step". This works, because within a circle the tamer with his back to the wall has to move a little towards the lion while moving sideways. The lion moves a little bit more to the side a little bit less towards the tamer. Over time the lion comes closer and the steps become smaller. When it gets really close however, the round wall looks increasingly like a flat wall. Lion and tamer end up just moving sideways without ever touching? We need some more math for this.