International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 8, Pages 485-496

The game of Double-Silver on intervals

Gerald A. Heuer

Department of Mathematics and Computer Science, Concordia College, Moorhead 56562, MN, USA

Received 29 June 2000

Copyright © 2001 Gerald A. Heuer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Silverman's game on intervals was analyzed in a special case by Evans, and later more extensively by Heuer and Leopold-Wildburger, who found that optimal strategies exist (and gave them) quite generally when the intervals have no endpoints in common. They exist in about half the parameter plane when the intervals have a left endpoint or a right endpoint, but not both, in common, and (as Evans had earlier found) exist only on a set of measure zero in this plane if the intervals are identical. The game of Double-Silver, where each player has its own threshold and penalty, is examined. There are several combinations of conditions on relative placement of the intervals, the thresholds and penalties under which optimal strategies exist and are found. The indications are that in the other cases no optimal strategies exist.