Winners and losers

Содержание и основные понятия

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Alterna · Chapter 19 · page 19.1
Winners and losers
End-to-end analysis, L/W markup, interactive game analyser.
At the EGE 19, 20, 21 is a game of two players with stones/numbers.
End-to-end analysis
We're going to mark the loser positions (L), usually multiples (K+1). The rest are winning positions (W). In the interactive analyser, you'll see this.
GEF
PIF
EGE No. 19,20.21
01
Elements of the game
Players
- Two (Peta and Wasa, or First and Second).
Position
is the current state (e.g. the number of stones S).
Progress
- Transforming the position on the rules.
Rules
- permissible steps (e.g. +1 or x2).
Objective
To achieve a win-win situation (≥N, last move).
Strategy
- a win-win plan for every move.
Optimal game
- both players play without mistakes.
GEF PIF
The subject corresponds to the PLF's "Elements of Game Theory" for grades 10 to 11 (deep level).
02
End-to-end analysis
Marking algorithm L/W
Mark
winning final position
(S ≥ N or S=0) as
W
.
Mark position as
L (less)
if all of her moves go to W.
Mark position as
W (win)
if one move leads to L.
Repeat until all positions are marked from the end to the beginning.
EGE Key Pater
For the game "primary number S, moves 1...K, target ≥N", the losing positions are numbers
S = n × (K+1)
For example, for moves +1, +2 (K=2): 3, 6, 9, 12, 15, 18 are losers.
Formula
If the initial S position is the loser (L), it wins
Second
If W wins
First
.
03
Game with AI: "Go for the Goals"
You're playing against smart AI. Set the rules, target N first.
🎮
E-ops: game with stones.
Type
Start S
Objective ≥N
Walks (nim)
Player's Walk
Rules:
−1, −2
S =
1
Objective:
≥20
♪ Log of moves:
Начало игры. S=1, цель ≥20
04
Interactive game analyser
Enter the game parameters - see L/W table and the solution
🔬
Analyzer: L/W table
Primary S
Objective N (≥N)
Step 1
Step 2
Objective
05
Mini-test: EEG No.19, 20, 21
50 tasks at the bank · 5 per test · 1 question at a time · + 30 XP for the correct one
XP: 0
🎯
Training: Game theory