Matrix Chain
Minimum scalar multiplication cost associating three matrices with four dimension readings+1. Four independently uniform custom wheel readings0–7 supply the labelled inputs. This is an independent roulette-family optimization demonstration, not a European roulette paytable. The optimum is calculated automatically; the player does not choose an optimization solution. Reward powers1/2/3 each use their own exact4096-draw mean and give96% expected gross return. One whole stake10/20/50/100, no Auto/Stop/cash-out. Idle below10 manually restores1000 preserving fractional change; unfinished reload receives no refund.
S = min(a×b×c + a×c×d, a×b×d + b×c×d)
a,b,c,d ∈ {1,2,3,4,5,6,7,8}
0,1,2,3 → 1,2,3,4 → S = 18
Gross multiplier
| Reward power (p) | μp | Gross multiplier |
|---|---|---|
| 1 | 138.927734375 | 0.96 × S^1 / μ1 |
| 2 | 38477.37890625 | 0.96 × S^2 / μ2 |
| 3 | 15802812.048828125 | 0.96 × S^3 / μ3 |
4,096 · 96%
Free virtual coins · no prizes
Virtual stake
- Virtual stake (B)
- 10 · 20 · 50 · 100
- Optimized score S · M× · R coins returned.
- R = floor(B × M + carry)
carry₁ = B × M + carry₀ − R
Spin four wheels
Choose a reward power, then spin the four reading wheels.
- Reward power
- 1 · 2 · 3
- Four ordered eight-pocket readings
- 0–7 · 0–7 · 0–7 · 0–7
- Optimized score
- 2–1024
Restore balance
Balance restored to 1,000 free coins.
Free virtual coins · no prizes
Free virtual coins · no prizes
Free virtual coins · no prizes
Matrix Chain
Spin four wheels?
Choose a reward power, then spin the four reading wheels. Free virtual coins · no prizes
Reward power?
p = 1, 2, 3; M = 0.96 × S^p / μp. Free virtual coins · no prizes
Restore balance?
Balance restored to 1,000 free coins. Free virtual coins · no prizes
