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頂部、底部、左側、右側和邊緣基諾
簡介
上下基諾 (Top Bottom Keno) 是一種基諾遊戲，玩家選擇 1 到 40 或 41 到 80 之間的數字。玩家將根據所選半區中出現的號碼數量獲得賠償。有時，玩家還可以投注左側、右側和邊緣號碼，這些號碼也已標註。
規則
- 玩家必須選擇“上”或“下”。如果玩家選擇“上”，則必須覆蓋 1 至 40 之間的數字。如果玩家選擇“下”，則必須覆蓋 41 至 80 之間的數字。
- 遊戲將從編號 1 至 80 的球池中隨機且不重複地抽取 20 個球。
- 玩家將根據20個球抽籤中落入其所選半區的球數獲得賠付。這被稱為“接球數”。賠付表示例如下。
下表列出了我所知的三種賠償表 (PT)。最下面一行顯示的是玩家回報率 (RTP)。
支付表
| 漁獲量 | 第一部分 | PT 2 | PT 3 | 第四部分 |
|---|---|---|---|---|
| 0 或 20 | 12500 | 12500 | 12500 | 12500 |
| 1 或 19 | 5000 | 5000 | 5000 | 5000 |
| 2 或 18 | 492 | 434 | 558 | 1000 |
| 3或17 | 122 | 125 | 180 | 200 |
| 4 或 16 | 二十八 | 三十 | 三十二 | 40 |
| 5或15 | 11 | 12 | 12 | 10 |
| 6或14 | 3 | 3 | 3 | 3 |
| 7或13 | 2 | 2 | 2 | 1 |
| 12 | 1 | 1 | 1 | 0 |
| 返回 | 88.32% | 90.32% | 94.32% | 72.29% |
例子
下圖中，我押注了後40個號碼。我投注1個積分，20個號碼中了16個，贏了32個。
分析
下表顯示了賠付表 1 中所有可能的捕獲次數（從 0 到 20）的機率及其對回報的貢獻。右下角單元格顯示回報率為 88.32%。
薪資表1分析
| 漁獲量 | 支付 | 組合 | 可能性 | 返回 |
|---|---|---|---|---|
| 0 | 12,500 | 137,846,528,820 | 0.00000004 | 0.000487 |
| 1 | 5,000 | 5,251,296,336,000 | 0.00000149 | 0.007427 |
| 2 | 492 | 88,436,604,204,000 | 0.00002502 | 0.012307 |
| 3 | 122 | 876,675,902,544,001 | 0.00024798 | 0.030253 |
| 4 | 二十八 | 5,744,053,569,793,500 | 0.00162476 | 0.045493 |
| 5 | 11 | 26,468,598,849,608,400 | 0.00748691 | 0.082356 |
| 6 | 3 | 89,077,015,359,259,200 | 0.02519634 | 0.075589 |
| 7 | 2 | 224,342,112,756,653,000 | 0.06345744 | 0.126915 |
| 8 | - | 429,655,207,020,554,000 | 0.12153233 | 0.000000 |
| 9 | - | 632,136,396,535,987,000 | 0.17880619 | 0.000000 |
| 10 | - | 718,528,370,729,238,000 | 0.20324303 | 0.000000 |
| 11 | - | 632,136,396,535,987,000 | 0.17880619 | 0.000000 |
| 12 | 1 | 429,655,207,020,554,000 | 0.12153233 | 0.121532 |
| 十三 | 2 | 224,342,112,756,653,000 | 0.06345744 | 0.126915 |
| 14 | 3 | 89,077,015,359,259,200 | 0.02519634 | 0.075589 |
| 15 | 11 | 26,468,598,849,608,400 | 0.00748691 | 0.082356 |
| 16 | 二十八 | 5,744,053,569,793,500 | 0.00162476 | 0.045493 |
| 17 | 122 | 876,675,902,544,001 | 0.00024798 | 0.030253 |
| 18 | 492 | 88,436,604,204,000 | 0.00002502 | 0.012307 |
| 19 | 5,000 | 5,251,296,336,000 | 0.00000149 | 0.007427 |
| 20 | 12,500 | 137,846,528,820 | 0.00000004 | 0.000487 |
| 全部的 | 3,535,316,142,212,170,000 | 1.00000000 | 0.883189 |
下表顯示了賠付表 1 中所有可能的捕獲次數（從 0 到 20）的機率及其對回報的貢獻。右下角單元格顯示回報率為 90.32%。
薪資表2分析
| 漁獲量 | 支付 | 組合 | 可能性 | 返回 |
|---|---|---|---|---|
| 0 | 12,500 | 137,846,528,820 | 0.000000 | 0.000487 |
| 1 | 5,000 | 5,251,296,336,000 | 0.000001 | 0.007427 |
| 2 | 434 | 88,436,604,204,000 | 0.000025 | 0.010857 |
| 3 | 125 | 876,675,902,544,001 | 0.000248 | 0.030997 |
| 4 | 三十 | 5,744,053,569,793,500 | 0.001625 | 0.048743 |
| 5 | 12 | 26,468,598,849,608,400 | 0.007487 | 0.089843 |
| 6 | 3 | 89,077,015,359,259,200 | 0.025196 | 0.075589 |
| 7 | 2 | 224,342,112,756,653,000 | 0.063457 | 0.126915 |
| 8 | - | 429,655,207,020,554,000 | 0.121532 | 0.000000 |
| 9 | - | 632,136,396,535,987,000 | 0.178806 | 0.000000 |
| 10 | - | 718,528,370,729,238,000 | 0.203243 | 0.000000 |
| 11 | - | 632,136,396,535,987,000 | 0.178806 | 0.000000 |
| 12 | 1 | 429,655,207,020,554,000 | 0.121532 | 0.121532 |
| 十三 | 2 | 224,342,112,756,653,000 | 0.063457 | 0.126915 |
| 14 | 3 | 89,077,015,359,259,200 | 0.025196 | 0.075589 |
| 15 | 12 | 26,468,598,849,608,400 | 0.007487 | 0.089843 |
| 16 | 三十 | 5,744,053,569,793,500 | 0.001625 | 0.048743 |
| 17 | 125 | 876,675,902,544,001 | 0.000248 | 0.030997 |
| 18 | 434 | 88,436,604,204,000 | 0.000025 | 0.010857 |
| 19 | 5,000 | 5,251,296,336,000 | 0.000001 | 0.007427 |
| 20 | 12,500 | 137,846,528,820 | 0.000000 | 0.000487 |
| 全部的 | 3,535,316,142,212,170,000 | 1.000000 | 0.903248 |
下表顯示了賠付表 3 中所有可能的捕獲次數（從 0 到 20）的機率及其對回報的貢獻。右下角單元格顯示回報率為 94.32%。
薪資表3分析
| 漁獲量 | 支付 | 組合 | 可能性 | 返回 |
|---|---|---|---|---|
| 0 | 12,500 | 137,846,528,820 | 0.000000 | 0.000487 |
| 1 | 5,000 | 5,251,296,336,000 | 0.000001 | 0.007427 |
| 2 | 558 | 88,436,604,204,000 | 0.000025 | 0.013958 |
| 3 | 180 | 876,675,902,544,001 | 0.000248 | 0.044636 |
| 4 | 三十二 | 5,744,053,569,793,500 | 0.001625 | 0.051992 |
| 5 | 12 | 26,468,598,849,608,400 | 0.007487 | 0.089843 |
| 6 | 3 | 89,077,015,359,259,200 | 0.025196 | 0.075589 |
| 7 | 2 | 224,342,112,756,653,000 | 0.063457 | 0.126915 |
| 8 | - | 429,655,207,020,554,000 | 0.121532 | 0.000000 |
| 9 | - | 632,136,396,535,987,000 | 0.178806 | 0.000000 |
| 10 | - | 718,528,370,729,238,000 | 0.203243 | 0.000000 |
| 11 | - | 632,136,396,535,987,000 | 0.178806 | 0.000000 |
| 12 | 1 | 429,655,207,020,554,000 | 0.121532 | 0.121532 |
| 十三 | 2 | 224,342,112,756,653,000 | 0.063457 | 0.126915 |
| 14 | 3 | 89,077,015,359,259,200 | 0.025196 | 0.075589 |
| 15 | 12 | 26,468,598,849,608,400 | 0.007487 | 0.089843 |
| 16 | 三十二 | 5,744,053,569,793,500 | 0.001625 | 0.051992 |
| 17 | 180 | 876,675,902,544,001 | 0.000248 | 0.044636 |
| 18 | 558 | 88,436,604,204,000 | 0.000025 | 0.013958 |
| 19 | 5,000 | 5,251,296,336,000 | 0.000001 | 0.007427 |
| 20 | 12,500 | 137,846,528,820 | 0.000000 | 0.000487 |
| 全部的 | 3,535,316,142,212,170,000 | 1.000000 | 0.943228 |
下表顯示了賠付表 4 中所有可能的捕獲次數（從 0 到 20）的機率及其對回報的貢獻。右下角單元格顯示回報率為 72.29%。
薪資表4分析
| 漁獲量 | 支付 | 組合 | 可能性 | 返回 |
|---|---|---|---|---|
| 0 | 12,500 | 137,846,528,820 | 0.000000 | 0.000487 |
| 1 | 5,000 | 5,251,296,336,000 | 0.000001 | 0.007427 |
| 2 | 1,000 | 88,436,604,204,000 | 0.000025 | 0.025015 |
| 3 | 200 | 876,675,902,544,001 | 0.000248 | 0.049595 |
| 4 | 40 | 5,744,053,569,793,500 | 0.001625 | 0.064991 |
| 5 | 10 | 26,468,598,849,608,400 | 0.007487 | 0.074869 |
| 6 | 3 | 89,077,015,359,259,200 | 0.025196 | 0.075589 |
| 7 | 1 | 224,342,112,756,653,000 | 0.063457 | 0.063457 |
| 8 | - | 429,655,207,020,554,000 | 0.121532 | 0.000000 |
| 9 | - | 632,136,396,535,987,000 | 0.178806 | 0.000000 |
| 10 | - | 718,528,370,729,238,000 | 0.203243 | 0.000000 |
| 11 | - | 632,136,396,535,987,000 | 0.178806 | 0.000000 |
| 12 | - | 429,655,207,020,554,000 | 0.121532 | 0.000000 |
| 十三 | 1 | 224,342,112,756,653,000 | 0.063457 | 0.063457 |
| 14 | 3 | 89,077,015,359,259,200 | 0.025196 | 0.075589 |
| 15 | 10 | 26,468,598,849,608,400 | 0.007487 | 0.074869 |
| 16 | 40 | 5,744,053,569,793,500 | 0.001625 | 0.064991 |
| 17 | 200 | 876,675,902,544,001 | 0.000248 | 0.049595 |
| 18 | 1,000 | 88,436,604,204,000 | 0.000025 | 0.025015 |
| 19 | 5,000 | 5,251,296,336,000 | 0.000001 | 0.007427 |
| 20 | 12,500 | 137,846,528,820 | 0.000000 | 0.000487 |
| 全部的 | 3,535,316,142,212,170,000 | 1.000000 | 0.722862 |
邊緣
2023年6月13日，我在拉斯維加斯廣場酒店看到了一場邊緣投注。投注金額為3美元。下表顯示了邊緣每次接球的賠率（基於3美元的投注）、機率和回報。回報基於3美元的投注。右下角單元格顯示預期報酬率為71.38%。
邊緣分析
| 漁獲量 | 支付（3 美元賭注） | 組合 | 可能性 | 返回 |
|---|---|---|---|---|
| 0 | 15000 | 16,735,679,449,896 | 0.000005 | 0.023669 |
| 1 | 1800 | 369,339,132,687,360 | 0.000104 | 0.062683 |
| 2 | 180 | 3,625,679,152,547,580 | 0.001026 | 0.061534 |
| 3 | 18 | 21,052,330,563,179,500 | 0.005955 | 0.035729 |
| 4 | 6 | 81,084,366,934,746,100 | 0.022936 | 0.045871 |
| 5 | 3 | 220,156,341,737,977,000 | 0.062273 | 0.062273 |
| 6 | 0 | 437,075,090,215,102,000 | 0.123631 | 0.000000 |
| 7 | 0 | 649,368,705,462,438,000 | 0.183681 | 0.000000 |
| 8 | 0 | 732,794,546,094,764,000 | 0.207278 | 0.000000 |
| 9 | 0 | 633,768,256,081,958,000 | 0.179268 | 0.000000 |
| 10 | 0 | 421,956,233,654,567,000 | 0.119355 | 0.000000 |
| 11 | 3 | 216,387,812,130,547,000 | 0.061207 | 0.061207 |
| 12 | 9 | 85,202,701,026,403,000 | 0.024100 | 0.072301 |
| 十三 | 三十 | 25,576,795,805,299,200 | 0.007235 | 0.072347 |
| 14 | 120 | 5,785,227,622,627,200 | 0.001636 | 0.065456 |
| 15 | 600 | 968,689,276,346,880 | 0.000274 | 0.054801 |
| 16 | 6000 | 116,958,222,286,200 | 0.000033 | 0.066166 |
| 17 | 30000 | 9,784,740,165,120 | 0.000003 | 0.027677 |
| 18 | 40000 | 531,779,356,800 | 0.000000 | 0.002006 |
| 19 | 75000 | 16,673,932,800 | 0.000000 | 0.000118 |
| 20 | 100000 | 225,792,840 | 0.000000 | 0.000002 |
| 全部的 | 3,535,316,142,212,170,000 | 1.000000 | 0.713840 |