THE MATH: Why You Can't Lose
Introduction
Game Participants: USER-A, USER-B, SYSTEM
The SYSTEM acts as a neutral judge, especially in games involving randomness, but doesn't favor any player.
Unlike games with only win or lose outcomes, we introduce a third option - Draw. This means every game has three possible results: Win, Loss, Draw.
A draw might seem meaningless at first, but we reward both players immediately with points. These points will be crucial during our future Token Generation Event (TGE).
Outcomes
We have three possible outcomes: Win, Loss, Draw.
Draw
This happens when both players make the same choice (like in Coinflip) or achieve the same score (like in 2048).
For example, in Coinflip: if USER-A and USER-B both choose "heads," it's a draw - regardless of which side the coin actually lands on.
Win
USER-A wins by:
- Making the winning choice (in Coinflip)
- Achieving a higher score than the opponent (in 2048)
Loss
USER-B loses by:
- Making the losing choice (in Coinflip)
- Achieving a lower score than the opponent (in 2048)
Outcome Probabilities
Different games have different probability distributions.
I. 25/25/50 (Example: Coinflip)
| # | USER-A | USER-B | SYSTEM | RESULT USER-A | CHANCE |
|---|---|---|---|---|---|
| 1 | HEAD | HEAD | HEAD | DRAW | 12.5% |
| 2 | HEAD | HEAD | TAIL | DRAW | 12.5% |
| 3 | TAIL | TAIL | HEAD | DRAW | 12.5% |
| 4 | TAIL | TAIL | TAIL | DRAW | 12.5% |
| 5 | HEAD | TAIL | HEAD | WIN | 12.5% |
| 6 | HEAD | TAIL | TAIL | LOSE | 12.5% |
| 7 | TAIL | HEAD | HEAD | LOSE | 12.5% |
| 8 | TAIL | HEAD | TAIL | WIN | 12.5% |
Totals:
- DRAW = 50%
- WIN = 25%
- LOSE = 25%
- CHANCE TO EARN POINTS = DRAW + LOSE = 75%
When considering only wins and losses (excluding draws), probabilities balance to:
- WIN = 50%
- LOSE = 50%
- CHANCE TO EARN POINTS = LOSE = 50%
II. 33/33/33 (Example: 2048)
Based on outcomes only (not player skill). If USER-A is more skilled, their win chance increases.
| # | USER-A | USER-B | RESULT USER-A | CHANCE |
|---|---|---|---|---|
| 1 | MORE SCORE | LESS SCORE | WIN | ~33.3% |
| 2 | EQUAL SCORE | EQUAL SCORE | DRAW | ~33.3% |
| 3 | LESS SCORE | MORE SCORE | LOSE | ~33.3% |
Totals:
- DRAW = ~33.3%
- WIN = ~33.3%
- LOSE = ~33.3%
- CHANCE TO EARN POINTS = DRAW + LOSE = ~66.7%
Considering only wins and losses:
- WIN = 50%
- LOSE = 50%
- CHANCE TO EARN POINTS = LOSE = 50%