本研究針對台灣彩劵三星彩投注進行獎號隨機性卡方檢定，資料收集從2005年12月19日至2018年12月31日共3,795期之三星彩獎號，分別針對個位數與拾位數及佰位數之球號出現次數、總體球號出現次數、偶數球號、大號碼球號、相同球號連續出現、三組彩中獎球號組合、六組彩中獎球號組合、對彩中獎球號組合等八個方向進行卡方隨機性檢定，檢定結果均滿足隨機性。本研究進一步將上述資料進行分析，找尋三組彩、六組彩、對彩等出現次數較少的獎號組合，進行之三年模擬投注，模擬投注時間從2019年1月1日至2021年12月31日共940期之三星彩獎號，本研究以三組彩獎號出現次數最少的六個獎號進行模擬投注，總平均獲利為-12.234，略優於期望值-13。六組彩以出現次數最少的九個獎號進行模擬投注，總平均獲利為-12.94319，略優於期望值-13。對彩以出現次數最少的十二個獎號進行模擬投注，平均總平均獲利為-10.43882，明顯優於期望值-16.75。研究結果顯示三種模擬投注均未能達到正值報酬，原因應該是投注時間不夠長遠以及三組彩、六組彩、對彩均具有隨機性。但因三組彩與六組是以出現較少次數的獎號進行，故平均模擬獲利還是略優於期望值，對彩則同時選取前面兩個與後面兩個獎號出現最少次數的加總方式來進行模擬投注，才能導致平均模擬獲利遠優於期望值，同時也優於三組彩與六組彩模擬投注方式。本研究是國內首次對於台灣彩劵公司三星彩獎號進行具學術性的隨機性檢定及較長期的模擬投注實驗，對於未來研究台灣彩劵具有一定的參考價值。

This research focused on the chi-square random test for the award numbers of Taiwan 3-Star Lottery. Data collected from December 19, 2005 to December 31, 2018. Total including 3795 times award numbers. We aimed on the chi-square random test for singles, tens, hundreds of ball numbers, totals ball numbers, even ball numbers, big ball numbers, same ball numbers appear continuously, award numbers of three sets betting, award numbers of six sets betting, award numbers of pair set betting. All of the test results satisfied randomness. We further searched the least happen award numbers of three sets betting, six sets betting, pair set betting to conduct three years betting simulation. Betting simulation from January 1, 2019 to December 31, 2021. Since the randomness of 3-Star Lottery and the simulation was not long enough, all of three kind simulation results showed that have no positive rewards. For the three sets betting and six sets betting, we searched the least happen award numbers. Therefore, the simulation results were a little bit better than exception. For pair set betting, we used the combination with the least happen award numbers of front and rear. The pair set betting simulation was much better than exception. The reward for pair set betting simulation also much better than three sets betting and six sets betting. This research is the first academic random analysis for Taiwan 3-Star Lottery and can provide a good reference for the research of Taiwan Lottery.