ꯔꯨꯂꯦꯠ ꯇꯝꯕ · ꯑꯍꯧꯕꯒꯤꯗꯃꯛ · ꯃꯤꯅꯤꯠ 8

ꯔꯨꯂꯦꯠ ꯄꯦꯑꯥꯎꯠꯁꯤꯡ

ꯔꯨꯂꯦꯠ ꯄꯦꯑꯥꯎꯠꯁꯤꯡꯅ ꯅꯤꯌꯝ ꯑꯃꯈꯛ ꯆꯠꯂꯤ: 36ꯕꯨ ꯌꯥꯎꯕ ꯃꯁꯤꯡꯅ ꯌꯦꯟꯗꯨꯅ, ꯑꯃꯥ ꯂꯧꯊꯣꯀꯄ꯫

ꯊꯨꯅ ꯄꯥꯎꯈꯨꯝ

ꯄꯦꯑꯥꯎꯠ = 36/n − 1꯫ ꯃꯁꯤꯡ ꯑꯃꯅ 35:1 ꯄꯤꯏ, ꯑꯅꯤꯅ 17:1 ꯄꯤꯏ, ꯇꯔꯥꯅꯤꯄꯥꯟꯅ 1:1 ꯄꯤꯏ꯫ ꯐꯣꯔꯃꯨꯂꯥ ꯑꯁꯤꯅ ꯄꯣꯀꯦꯠ 36 ꯂꯩ ꯍꯥꯌꯅ ꯂꯧꯏ; ꯑꯁꯦꯡꯕꯗꯤ 37 ꯂꯩ꯫

ꯅꯤꯌꯝ
36/n − 1
ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ
35:1
ꯆꯞ ꯃꯥꯟꯅꯕ ꯁꯦꯜ
1:1
ꯑꯦꯖ, ꯕꯦꯠ ꯄꯨꯝꯅꯃꯛ
2.70%

ꯔꯨꯂꯦꯠ ꯄꯦꯑꯥꯎꯠ ꯆꯥꯔꯠ

ꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠꯇꯃꯈꯜꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ ꯆꯛꯔ, ꯄꯣꯀꯦꯠ 37, ꯍꯥꯎꯁ ꯑꯦꯖ 2.70%꯫ ꯋꯦꯕꯁꯥꯏꯠ ꯑꯁꯤꯒꯤ ꯃꯔꯨꯑꯣꯏꯕ ꯃꯑꯣꯡꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯈꯦꯠꯅꯕ ꯄꯦꯑꯥꯎꯠꯁꯦꯜꯄꯦꯑꯥꯎꯠꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯍꯜꯂꯛꯄ ꯁꯦꯜ, ꯍꯜꯂꯀꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯊꯛꯇ “X ꯗꯒꯤ 1” ꯍꯥꯌꯅ ꯍꯥꯌꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯇꯔꯦꯠ ꯈꯛꯇꯃꯛ ꯂꯩ, ꯌꯥꯎꯕ ꯌꯥꯕ ꯃꯑꯣꯡ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯥ; ꯃꯈꯥꯒꯤ ꯇꯦꯕꯜ ꯑꯁꯤꯅ ꯔꯨꯂꯦꯠꯀꯤ ꯑꯣꯗꯁ ꯑꯃꯁꯨꯡ ꯄꯦꯑꯥꯎꯠꯁꯤꯡ ꯃꯅꯥꯛ ꯃꯅꯥꯛꯇ ꯊꯝꯂꯤ꯫ ꯅꯤꯌꯝ ꯑꯁꯤ ꯇꯃꯂꯕꯗꯤ ꯇꯦꯕꯜ ꯑꯁꯤ ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯃꯊꯧ ꯇꯥꯔꯣꯏ; ꯇꯦꯕꯜ ꯑꯁꯤ ꯇꯃꯂꯕꯗꯤ ꯅꯤꯌꯝ ꯑꯁꯤ ꯃꯁꯥꯃꯛꯅ ꯃꯌꯦꯛ ꯁꯦꯡꯂꯛꯀꯅꯤ꯫

ꯌꯥꯎꯕ ꯃꯁꯤꯡꯕꯦꯠꯄꯤꯕꯆꯨꯝꯃꯤꯟꯅꯕ ꯑꯣꯏꯔꯕꯗꯤꯍꯟꯊꯕ
1ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ35:136:11/37
2ꯁ꯭ꯞꯂꯤꯠ17:117.5:11/37
3ꯁ꯭ꯇ꯭ꯔꯤꯠ11:111.33:11/37
4ꯀꯣꯔꯅꯔ, ꯕꯥꯁ꯭ꯀꯦꯠ8:18.25:11/37
6ꯁꯤꯛꯁ ꯂꯥꯏꯟ5:15.17:11/37
12ꯗꯖꯟ, ꯀꯂꯝ2:12.08:11/37
18ꯑꯉꯥꯡꯕ, ꯑꯃꯨꯕ, ꯕꯤꯖꯣꯔ, ꯖꯣꯔ, ꯑꯋꯥꯡꯕ, ꯑꯅꯦꯝꯕ1:11.06:11/37
ꯆꯨꯝꯃꯤꯟꯅꯕ = 37/n − 1꯫ ꯍꯟꯊꯕ ꯑꯁꯤ ꯂꯥꯏꯟ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯃꯥꯟꯅꯩ: ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ 2.70%꯫

ꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠ

ꯃꯐꯝ ꯈꯨꯗꯤꯡꯗ ꯑꯦꯖ ꯀꯔꯤꯒꯤ ꯃꯥꯟꯅꯕꯒꯦ

ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 37ꯒꯤ ꯃꯅꯨꯡꯗ n ꯌꯥꯎꯕ ꯕꯦꯠ ꯑꯃꯒꯤ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯄꯦꯑꯥꯎꯠ ꯑꯁꯤ (37 − n)/n : 1 ꯑꯣꯏꯒꯗꯕꯅꯤ꯫ ꯀꯦꯁꯤꯅꯣꯅ (36 − n)/n : 1 ꯄꯤꯏ꯫ ꯂꯧꯊꯣꯛꯂꯕꯗꯤ ꯈꯦꯠꯅꯕ ꯑꯁꯤ ꯃꯥꯏꯄꯥꯛꯄ ꯈꯨꯗꯤꯡꯗ ꯆꯨꯝꯅ 1/n ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯣꯏ; ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → n/37ꯅ ꯃꯜꯇꯤꯞꯂꯥꯏ ꯇꯧꯔꯕꯗꯤ, ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯍꯟꯊꯒꯗꯕ ꯑꯁꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ 1/37ꯅꯤ꯫ ꯃꯔꯝ ꯑꯁꯤꯅ ꯕꯦꯠꯁꯤꯡꯒꯤ ꯀꯔꯤꯒꯨꯝꯕ ꯌꯥꯃꯗꯅꯕ ꯑꯃꯠꯇꯅ ꯑꯦꯖꯗꯒꯤ ꯂꯥꯄꯊꯣꯛꯄ ꯉꯃꯗꯦ: ꯅꯍꯥꯛꯅ ꯅꯦꯒꯦꯇꯤꯕ ꯃꯁꯤꯡꯁꯤꯡ ꯄꯨꯟꯁꯤꯟꯂꯤꯕꯅꯤ꯫

ꯌꯥꯎꯕꯒꯥ ꯆꯥꯡꯗꯝꯅꯕꯗ ꯄꯦꯑꯥꯎꯠꯄꯦꯑꯥꯎꯠ, 1ꯗ
ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ (1/37)
35:1
ꯁ꯭ꯞꯂꯤꯠ (2/37)
17:1
ꯁ꯭ꯇ꯭ꯔꯤꯠ (3/37)
11:1
ꯀꯣꯔꯅꯔ (4/37)
8:1
ꯁꯤꯛꯁ ꯂꯥꯏꯟ (6/37)
5:1
ꯗꯖꯟ / ꯀꯂꯝ (12/37)
2:1
ꯆꯞ ꯃꯥꯟꯅꯕ ꯁꯦꯜ (18/37)
1:1
ꯄꯦꯑꯥꯎꯠ, 1ꯗ
017.5035:1
ꯄꯦꯑꯥꯎꯠ = 36/n − 1꯫ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯑꯣꯏꯔꯕꯗꯤ 37/n − 1꯫ ꯃꯥꯡꯈꯤꯕ ꯌꯨꯅꯤꯠ ꯑꯗꯨ ꯍꯥꯎꯁ ꯑꯦꯖꯅꯤ꯫

“ꯇꯨ” ꯑꯃꯁꯨꯡ “ꯐꯣꯔ”

35 ꯇꯨ 1 ꯍꯥꯌꯕꯁꯤ ꯃꯥꯏꯄꯥꯛꯂꯕ $1ꯒꯤ ꯆꯤꯞꯁꯦꯜꯆꯤꯞꯂꯦꯞꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯃꯜ ꯇꯥꯛꯄ ꯇꯣꯀꯟ, ꯕꯦꯠ ꯊꯝꯅꯕ ꯂꯦꯑꯥꯎꯠꯇ ꯊꯝꯃꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯆꯦꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯅ ꯃꯥꯏꯄꯥꯛꯇꯨꯅ ꯐꯪꯂꯕ ꯁꯦꯜ $35 ꯄꯤꯔꯤ ꯑꯃꯁꯨꯡ $1 ꯑꯗꯨ ꯅꯍꯥꯛꯅ ꯊꯃꯖꯤꯜꯂꯤ꯫ 35 ꯐꯣꯔ 1, ꯑꯃꯦꯔꯤꯀꯥꯒꯤ ꯂꯦꯑꯥꯎꯠꯈꯨꯠꯂꯥꯏꯂꯦꯑꯥꯎꯠꯇꯦꯕꯜꯗ ꯏꯔꯕ ꯕꯦꯠ ꯊꯝꯕꯒꯤ ꯒ꯭ꯔꯤꯗ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯇꯦꯕꯜ, ꯐꯦꯜꯠ, ꯀ꯭ꯂꯣꯊ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯈꯔꯗ ꯑꯃꯁꯨꯡ ꯁ꯭ꯂꯣꯠ ꯃꯦꯁꯤꯟꯁꯤꯡꯗ ꯎꯕ ꯐꯪꯕ ꯋꯥꯍꯩ ꯑꯃꯅꯤ, ꯃꯁꯤꯒꯤ ꯑꯔꯊꯗꯤ $1 ꯑꯗꯨ $35ꯒꯤ ꯃꯅꯨꯡꯗ ꯌꯥꯎꯔꯤ, ꯃꯔꯝ ꯑꯁꯤꯅ ꯑꯁꯦꯡꯕ ꯄꯦꯑꯥꯎꯠ ꯑꯁꯤ 34:1ꯅꯤ꯫ ꯔꯨꯂꯦꯠꯅ ꯃꯐꯝ ꯌꯥꯝꯅ ꯃꯔꯣꯂꯗ “ꯇꯨ” ꯁꯤꯖꯤꯟꯅꯩ꯫ ꯔꯨꯂꯦꯠ ꯇꯦꯕꯜ ꯑꯃꯒꯤ ꯄꯦꯑꯥꯎꯠ “ꯐꯣꯔ” ꯍꯥꯌꯅ ꯏꯔꯕꯗꯤ, ꯕꯦꯠ ꯑꯗꯨꯒꯤ ꯍꯥꯎꯁ ꯑꯦꯖꯃꯦꯊꯃꯦꯇꯤꯛꯁꯍꯥꯎꯁ ꯑꯦꯖꯊꯝꯂꯕ ꯁꯦꯜ ꯈꯨꯗꯤꯡꯗꯒꯤ ꯀꯦꯁꯤꯅꯣꯅ ꯑꯦꯚꯔꯦꯖꯗ ꯊꯃꯖꯤꯜꯂꯤꯕ ꯁꯔꯨꯛ: ꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠꯇ 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯎꯕꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯋꯥꯡꯏ꯫

ꯔꯨꯂꯦꯠꯅ ꯀꯌꯥ ꯄꯤꯕꯒꯦ? ꯊꯤꯗꯣꯛꯂꯕ ꯈꯨꯗꯃꯁꯤꯡ

ꯃꯥꯏꯄꯥꯛꯂꯕ ꯀꯣꯔꯅꯔꯕꯦꯠꯀꯣꯔꯅꯔꯂꯦꯑꯥꯎꯠꯇ ꯀꯣꯟꯅꯥ ꯑꯃꯥ ꯁꯦꯌꯔ ꯇꯧꯅꯔꯤꯕ ꯃꯁꯤꯡ ꯃꯔꯤ, 8:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ ꯗꯣꯂꯥꯔ ꯇꯔꯥ: 8 × $10 = ꯃꯥꯏꯄꯥꯛꯇꯨꯅ ꯐꯪꯂꯕ ꯁꯦꯜ $80, ꯊꯝꯂꯕ ꯁꯦꯜ ꯌꯥꯎꯅ $90 ꯍꯜꯂꯛꯏ꯫ ꯃꯥꯏꯄꯥꯛꯂꯕ ꯗꯖꯟꯕꯦꯠꯗꯖꯟ1–12, 13–24 ꯅꯠꯔꯒ 25–36, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ ꯗꯣꯂꯥꯔ ꯇꯔꯥ: ꯃꯥꯏꯄꯥꯛꯇꯨꯅ ꯐꯪꯂꯕ ꯁꯦꯜ $20, $30 ꯍꯜꯂꯛꯏ꯫ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯥ ꯂꯩꯕ ꯌꯨꯝꯂꯣꯟꯅꯕꯕꯦꯠꯌꯨꯝꯂꯣꯟꯅꯕ ꯕꯦꯠꯆꯛꯔꯗ ꯃꯁꯤꯡ ꯑꯃꯥ ꯑꯃꯁꯨꯡ ꯃꯗꯨꯒꯤ ꯅꯥꯀꯜ ꯑꯅꯤꯃꯛꯇ ꯂꯩꯕ ꯄꯣꯀꯦꯠ ꯑꯅꯤ ꯑꯅꯤ, ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯆꯤꯞ ꯃꯉꯥ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯕꯦꯠ ꯑꯃꯗ ꯗꯣꯂꯥꯔ ꯇꯔꯥ ($2ꯒꯤ ꯆꯤꯞ ꯃꯉꯥ): ꯆꯤꯞ ꯑꯗꯨꯅ 35 × $2 = $70 ꯄꯤꯏ, ꯑꯇꯣꯞꯄ ꯃꯔꯤꯅ $8 ꯃꯥꯡꯏ, ꯅꯦꯠ +$62꯫ ꯚꯣꯌꯥꯖꯦꯟ ꯗꯨ ꯖꯦꯔꯣꯗꯐ꯭ꯔꯦꯟꯆ · ꯁꯦꯛꯇꯔꯚꯣꯌꯥꯖꯦꯟ ꯗꯨ ꯖꯦꯔꯣ“ꯖꯤꯔꯣꯒꯤ ꯌꯨꯝꯂꯣꯟꯅꯕꯁꯤꯡ”: ꯆꯛꯔꯗ 22 ꯗꯒꯤ 25 ꯐꯥꯑꯣꯕ ꯃꯁꯤꯡ ꯇꯔꯥꯇꯔꯦꯠ, ꯆꯤꯞ ꯃꯥꯄꯟꯅ ꯕꯦꯠ ꯊꯝꯃꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯗꯣꯂꯥꯔ ꯇꯔꯥ (ꯆꯤꯞ ꯃꯥꯄꯟ, ꯃꯔꯝ ꯑꯁꯤꯅ ꯑꯁꯦꯡꯕꯗ ꯈꯨꯗꯤꯡꯗ $1.11, ꯇꯦꯕꯜꯒꯤ ꯁ꯭ꯇꯦꯄꯇ ꯔꯥꯎꯟꯗ ꯇꯧꯔꯒꯥ) ꯑꯁꯤꯅ ꯀꯅꯥꯒꯤ ꯄꯣꯀꯦꯠ ꯊꯣꯀꯄꯒꯦ ꯍꯥꯌꯕꯗ ꯌꯨꯝꯐꯝ ꯑꯣꯏꯗꯨꯅ +$10ꯗꯒꯤ +$16.67ꯒꯤ ꯃꯔꯛꯇ ꯄꯤꯏ, ꯃꯔꯃꯗꯤ ꯕꯦꯠ ꯑꯁꯤꯅ ꯄꯣꯀꯦꯠ ꯈꯔꯗ ꯑꯃꯨꯛ ꯑꯅꯤ ꯊꯝꯃꯤ꯫

  • ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, 35:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, $10: ꯃꯥꯏꯄꯥꯛꯂꯕꯗꯤ +$350, $360 ꯍꯜꯂꯛꯏ꯫
  • ꯁ꯭ꯞꯂꯤꯠꯕꯦꯠꯁ꯭ꯞꯂꯤꯠꯌꯨꯝꯂꯣꯟꯅꯕ ꯃꯁꯤꯡ ꯑꯅꯤ, 17:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, $10: +$170꯫
  • ꯁ꯭ꯇ꯭ꯔꯤꯠꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯤꯠꯂꯦꯑꯥꯎꯠꯀꯤ ꯂꯥꯏꯟ ꯑꯃꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯑꯍꯨꯝ, 11:1 ꯄꯦꯑꯥꯎꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯇ꯭ꯔꯥꯟꯁꯚꯔꯁꯥꯜ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, $10: +$110꯫
  • ꯀꯣꯔꯅꯔ, $10: +$80꯫
  • ꯁꯤꯛꯁ ꯂꯥꯏꯟꯕꯦꯠꯁꯤꯛꯁ ꯂꯥꯏꯟꯌꯨꯝꯂꯣꯟꯅꯕ ꯂꯥꯏꯟ ꯑꯅꯤꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯇꯔꯨꯛ, 5:1 ꯄꯦꯑꯥꯎꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯁꯤꯖꯦꯟ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, $10: +$50꯫
  • ꯗꯖꯟ ꯅꯠꯔꯒꯥ ꯀꯂꯝꯕꯦꯠꯀꯂꯝꯂꯦꯑꯥꯎꯠꯀꯤ ꯊꯣꯡꯅꯥꯡꯒꯤ ꯀꯂꯝ ꯑꯃꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, $10: +$20꯫
  • ꯆꯞ ꯃꯥꯟꯅꯕ ꯁꯦꯜ, $10: +$10꯫

ꯔꯨꯂꯦꯠ ꯌꯨꯝꯂꯣꯟꯅꯕ ꯕꯦꯠꯚꯣꯌꯥꯖꯦꯟ ꯗꯨ ꯖꯦꯔꯣ ꯔꯨꯂꯦꯠ ꯕꯦꯠ

ꯕꯦꯠ ꯀꯌꯥ ꯄꯨꯟꯅ ꯊꯝꯂꯕꯗꯤ ꯔꯨꯂꯦꯠꯅ ꯀꯌꯥ ꯄꯤꯕꯒꯦ?

ꯕꯦꯠꯁꯤꯡ ꯇꯣꯉꯥꯟꯅ ꯂꯣꯏꯁꯤꯜꯂꯤ ꯑꯃꯁꯨꯡ ꯃꯇꯨꯡꯗ ꯄꯨꯟꯁꯤꯜꯂꯤ꯫ ꯑꯉꯥꯡꯕꯗꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → $5, ꯑꯃꯨꯕꯗꯕꯦꯠꯑꯃꯨꯕꯑꯃꯨꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯅꯣꯌꯥꯔ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → $5 ꯑꯃꯁꯨꯡ ꯖꯤꯔꯣꯗꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → $1: ꯑꯉꯥꯡꯕ ꯅꯠꯔꯒꯥ ꯑꯃꯨꯕ ꯃꯁꯤꯡ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯗ ꯅꯍꯥꯛꯅ $5 ꯃꯥꯏꯄꯥꯀꯏ ꯑꯃꯁꯨꯡ $5 ꯃꯥꯡꯏ, ꯅꯦꯠ −$1 (ꯖꯤꯔꯣꯒꯤ ꯆꯤꯞ)꯫ ꯖꯤꯔꯣꯗ ꯅꯍꯥꯛꯅ $10 ꯃꯥꯡꯏ ꯑꯃꯁꯨꯡ $35 ꯃꯥꯏꯄꯥꯀꯏ, ꯅꯦꯠ +$25꯫ ꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯦꯊꯃꯦꯇꯤꯛꯁꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯇꯝ ꯁꯥꯡꯅ ꯌꯦꯡꯂꯕꯗ ꯕꯦꯠ ꯑꯃꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ꯫ ꯃꯔꯨꯑꯣꯏꯕ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯍꯧꯖꯤꯀꯁꯨ ꯊꯝꯂꯕ $11ꯒꯤ −2.70%ꯅꯤ, ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ −$0.30ꯒꯤ ꯃꯅꯥꯛꯇ, ꯃꯔꯃꯗꯤ ꯁꯔꯨꯛ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯁꯥ ꯃꯊꯟꯇ −2.70%ꯅꯤ꯫

ꯇꯦꯕꯜꯗ ꯔꯥꯎꯟꯗ ꯇꯧꯕ

ꯀꯦꯁꯤꯅꯣ ꯑꯃꯗ ꯔꯨꯂꯦꯠ ꯇꯦꯕꯜꯒꯤ ꯄꯦꯑꯥꯎꯠꯁꯤꯡ ꯆꯤꯞꯀꯤ ꯃꯃꯂꯁꯤꯡꯅ ꯄꯤꯏ, ꯃꯔꯝ ꯑꯁꯤꯅ ꯀꯣꯜ ꯕꯦꯠꯁꯤꯡꯗꯇꯦꯕꯜꯀꯣꯜ ꯕꯦꯠꯈꯨꯠꯅ ꯊꯝꯗꯅ ꯗꯤꯂꯔꯗ ꯂꯥꯑꯣꯊꯣꯛꯄ ꯕꯦꯠ, ꯌꯥꯝꯅ ꯚꯣꯌꯥꯖꯦꯟ ꯅꯠꯔꯒ ꯇꯤꯌꯦꯌꯔꯒꯨꯝꯕ ꯆꯛꯔꯒꯤ ꯁꯦꯛꯇꯔ ꯕꯦꯠ ꯑꯃꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: “ꯂꯥꯑꯣꯊꯣꯛꯄ ꯕꯦꯠ”꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯥꯟꯅꯗꯕ ꯊꯝꯂꯕ ꯁꯦꯜ ꯔꯥꯎꯟꯗ ꯇꯧꯏ꯫ ꯑꯣꯟꯂꯥꯏꯟ ꯇꯦꯕꯜꯁꯤꯡꯅ ꯁꯦꯟꯇ ꯐꯥꯑꯣꯕ ꯄꯤꯏ꯫ ꯔꯥꯎꯟꯗ ꯇꯧꯕ ꯑꯁꯤ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯆꯠꯂꯕꯗꯤ (ꯈꯨꯗꯝꯅ $0.333ꯒꯤ ꯆꯤꯞ ꯑꯃꯥ $0.33 ꯑꯣꯏꯅ ꯄꯤꯔꯕꯗꯤ), ꯃꯁꯤꯒꯤ ꯃꯍꯩ ꯑꯁꯤ ꯅꯍꯥꯛꯀꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯁꯔꯨꯛ ꯑꯄꯤꯛꯄ ꯑꯃꯒꯤ ꯄꯔꯁꯦꯟꯇꯀꯤ ꯁꯔꯨꯛ ꯑꯄꯤꯛꯄ ꯑꯃꯅꯤ, ꯑꯃꯁꯨꯡ ꯃꯤꯁꯤꯡꯅ ꯍꯪꯂꯤꯕꯅꯥ ꯃꯔꯝ ꯑꯣꯏꯗꯨꯅ ꯃꯐꯝ ꯑꯁꯤꯗ ꯏꯔꯤꯕꯈꯛꯇꯅꯤ꯫

ꯀꯣꯜ ꯕꯦꯠꯁꯤꯡꯒꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜ

ꯀꯔꯤꯒꯤ 36

36 ꯑꯁꯤ 1, 2, 3, 4, 6, 9, 12, 18 ꯑꯃꯁꯨꯡ 36ꯅ ꯌꯦꯟꯕ ꯌꯥꯏ, ꯃꯔꯝ ꯑꯁꯤꯅ ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯔꯨꯂꯦꯠ ꯄꯦꯑꯥꯎꯠ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯄꯨꯡ ꯐꯥꯕ ꯃꯁꯤꯡꯅꯤ꯫ ꯔꯨꯂꯦꯠꯀꯤ ꯏꯇꯥꯂꯤꯒꯤ ꯏꯄꯥ-ꯏꯄꯨ ꯑꯃꯥ ꯑꯣꯏꯔꯤꯕ ꯕꯤꯔꯤꯕꯤꯗ ꯃꯁꯤꯡ 70 ꯂꯩꯝꯃꯤ ꯑꯃꯁꯨꯡ ꯃꯈꯣꯌꯒꯤ ꯑꯃꯗ 64 ꯐꯣꯔ 1 ꯍꯜꯂꯛꯄꯤꯔꯝꯃꯤ; 64ꯒꯤ ꯃꯊꯛꯇ ꯁꯥꯕ ꯄꯦꯑꯥꯎꯠ ꯅꯤꯌꯝ ꯑꯃꯅ ꯃꯁꯤꯡ 1, 2, 4, 8, 16 ꯑꯃꯁꯨꯡ 32ꯒꯤꯗꯃꯛ ꯆꯨꯝꯅ ꯌꯦꯟꯕ ꯌꯥꯏ ꯑꯗꯨꯕꯨ 3, 5 ꯅꯠꯔꯒꯥ 6ꯒꯤꯗꯃꯛ ꯌꯥꯗꯦ, ꯃꯔꯝ ꯑꯁꯤꯅ ꯕꯦꯠ ꯀꯌꯥꯗ ꯔꯥꯎꯟꯗ ꯇꯧꯕ ꯃꯊꯧ ꯇꯥꯔꯝꯂꯒꯅꯤ꯫ ꯌꯥꯝꯅ ꯈꯟꯅꯥ ꯊꯣꯀꯄ ꯕꯦꯠ ꯑꯅꯤꯅꯁꯨ ꯑꯇꯣꯞꯄꯁꯤꯡꯒꯨꯝꯅ 36/n − 1 ꯅꯤꯌꯝ ꯑꯗꯨ ꯆꯠꯂꯤ: ꯃꯁꯤꯡ 24 ꯌꯥꯎꯕ ꯑꯃꯁꯨꯡ ½ : 1 ꯄꯤꯕ ꯗꯕꯜ ꯀꯂꯝ ($10ꯒꯤ ꯃꯥꯏꯄꯥꯛꯂꯕ ꯕꯦꯠ ꯑꯃꯅ $5 ꯄꯤꯏ), ꯑꯃꯁꯨꯡ ꯏꯂꯦꯛꯠꯔꯣꯅꯤꯛ ꯑꯃꯁꯨꯡ ꯀꯥꯔꯗꯀꯤ ꯒꯦꯝ ꯈꯔꯅ ꯄꯤꯔꯤꯕ 3:1ꯒꯤ ꯃꯁꯤꯡ 9ꯒꯤ ꯕꯦꯠ ꯑꯃꯥ꯫ ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ ꯆꯛꯔꯗ ꯑꯅꯤꯃꯛꯀꯤ ꯃꯃꯜ 2.70%ꯅꯤ, ꯑꯇꯣꯞꯄ ꯄꯨꯝꯅꯃꯛꯒꯨꯝꯅ꯫

ꯔꯨꯂꯦꯠꯀꯤ ꯏꯄꯥ-ꯏꯄꯨ ꯑꯃꯥ ꯑꯣꯏꯔꯤꯕ ꯕꯤꯔꯤꯕꯤ: ꯕꯦꯉ꯭ꯀꯔꯅ ꯕꯣꯔꯗꯀꯤ ꯃꯊꯛꯇ ꯈꯥꯎ ꯑꯃꯗꯒꯤ ꯂꯧꯊꯣꯀꯏ꯫

ꯔꯨꯂꯦꯠ ꯀꯅꯥꯅ ꯁꯦꯃꯈꯤꯕꯒꯦ? ꯔꯨꯂꯦꯠꯀꯤ ꯍꯧꯔꯛꯐꯝ

ꯐꯣꯔꯃꯨꯂꯥ

ꯄꯦꯑꯥꯎꯠ = 36/n − 1
ꯆꯨꯝꯃꯤꯟꯅꯕ = 37/n − 1
ꯌꯨꯅꯤꯠ ꯈꯨꯗꯤꯡꯒꯤ EV = (n/37)(36/n − 1) − (37 − n)/37 = −1/37

ꯋꯥꯍꯪꯁꯤꯡ

ꯖꯤꯔꯣꯗ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯑꯃꯅ ꯍꯦꯟꯅꯥ ꯈꯔꯥ ꯄꯤꯕꯔꯥ?

ꯄꯤꯗꯦ꯫ ꯖꯤꯔꯣ ꯑꯁꯤ ꯑꯇꯣꯞꯄ ꯄꯣꯀꯦꯠꯁꯤꯡꯒꯨꯝꯅ ꯄꯣꯀꯦꯠ ꯑꯃꯅꯤ: 35:1꯫

35:1ꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯄꯤꯕ ꯕꯦꯠ ꯑꯃꯥ ꯂꯩꯕꯔꯥ?

ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯇꯦꯕꯜ ꯑꯃꯗ ꯂꯩꯇꯦ꯫ ꯒꯦꯝ ꯁꯣꯒꯤ ꯃꯈꯂꯁꯤꯡꯅ ꯃꯜꯇꯤꯞꯂꯥꯏꯌꯥꯔꯁꯤꯡ ꯍꯥꯄꯆꯤꯜꯂꯤ, ꯃꯔꯨꯑꯣꯏꯕ ꯄꯦꯑꯥꯎꯠ ꯑꯗꯨ 29:1 ꯐꯥꯑꯣꯕ ꯍꯟꯊꯍꯟꯗꯨꯅ ꯃꯗꯨꯒꯤ ꯃꯃꯜ ꯁꯣꯜꯂꯤ꯫

ꯕꯥꯁ꯭ꯀꯦꯠꯅ 8:1 ꯑꯃꯁꯨꯡ ꯑꯃꯦꯔꯤꯀꯟ ꯃꯁꯤꯡ ꯃꯉꯥꯒꯤ ꯕꯦꯠꯅ 6:1 ꯀꯔꯤꯒꯤ ꯄꯤꯕꯒꯦ?

ꯌꯨꯔꯣꯄꯤꯌꯟ ꯕꯥꯁ꯭ꯀꯦꯠꯅꯕꯦꯠꯕꯥꯁ꯭ꯀꯦꯠꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ ꯆꯛꯔꯗ: ꯆꯤꯞ ꯑꯃꯅ 0, 1, 2, 3, 8:1 ꯄꯦꯑꯥꯎꯠ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯑꯍꯥꯅꯕ ꯃꯔꯤ, ꯀꯥꯠꯔ ꯄ꯭ꯔꯦꯃꯤꯌꯦ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 37ꯒꯤ ꯃꯅꯨꯡꯗ 4 ꯌꯥꯎꯏ ꯑꯃꯁꯨꯡ ꯐꯣꯔꯃꯨꯂꯥ ꯆꯠꯂꯤ꯫ ꯑꯃꯦꯔꯤꯀꯟ 0-00-1-2-3ꯅ 38ꯒꯤ ꯃꯅꯨꯡꯗ 5 ꯌꯥꯎꯏ ꯑꯃꯁꯨꯡ 36/5 − 1 ꯑꯁꯤ 6.2ꯅꯤ, ꯃꯈꯥ ꯊꯥꯗꯨꯅ 6 ꯑꯣꯏꯍꯜꯂꯤ: ꯑꯦꯖ 7.89%, ꯔꯨꯂꯦꯠꯇ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯠꯇꯕ ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯕꯦꯠ꯫

ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

36/n − 1꯫ ꯊꯕꯛ ꯄꯨꯝꯅꯃꯛ ꯑꯃꯥ ꯑꯗꯨꯅ ꯇꯧꯔꯤ꯫

36/n − 1꯫ ꯊꯕꯛ ꯄꯨꯝꯅꯃꯛ ꯑꯃꯥ ꯑꯗꯨꯅ ꯇꯧꯔꯤ꯫

ꯍꯧꯔꯛꯐꯃꯁꯤꯡ

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010꯫ ꯆꯦꯞꯇꯔ 13, ꯔꯨꯂꯦꯠ꯫
  2. Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
  3. Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette. CRC Press, 2021꯫ ꯆꯦꯞꯇꯔ 2, ꯔꯨꯂꯦꯠ꯫
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