Lucky Lucky
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- Appendices
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Introduction
Lucky Lucky is a side bet based on the player's first two cards and the dealer's up card. As far as I know, it is the first side bet to be based on the player's first two cards and the dealer's up card. Since it came out, there have been many imitators.
Through the years I have seen four pay tables, which I refer to on this page as numbers 1 to 4. Pay table 1 was the original one and seen at casinos all over the United States and Canada. Pay table 2 was a double-deck version, omitting the pay for a suited 7-7-7, which is impossible in a double-deck game. Pay table 3 came along around 2014 as an apparent effort to increase what was a low house advantage for a side bet. Pay table 4 can be found at Internet casinos using Felt Gaming software.
The following table shows the various pay tables.
Lucky Lucky Pay Tables
| Event | PT 1 | PT 2 | PT 3 | PT 4 | PT 5 | PT 6 | PT 8 | PT 8 |
|---|---|---|---|---|---|---|---|---|
| Suited 7-7-7 | 200 | 0 | 200 | 200 | 200 | 200 | 100 | 500 |
| Suited 6-7-8 | 100 | 100 | 100 | 100 | 100 | 100 | 50 | 200 |
| Unsuited 7-7-7 | 50 | 50 | 50 | 50 | 50 | 50 | 30 | 100 |
| Unsuited 6-7-8 | 30 | 30 | 30 | 25 | 30 | 30 | 10 | 25 |
| Suited total of 21 | 15 | 10 | 10 | 15 | 15 | 10 | 3 | 15 |
| Unsuited total of 21 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 3 |
| Total of 20 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| Total of 19 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 |
Analysis — Pay Table 1 — Six Decks
Following is my analysis of pay table 1 using six decks. The lower right cell shows a house edge of 2.66%, which is quite low for a side bet.
Lucky Lucky — Pay Table 1 — Six Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Suited 7-7-7 | 200 | 80 | 0.000016 | 0.003191 |
| Suited 6-7-8 | 100 | 864 | 0.000172 | 0.017234 |
| Unsuited 7-7-7 | 50 | 1,944 | 0.000388 | 0.019388 |
| Unsuited 6-7-8 | 30 | 12,960 | 0.002585 | 0.077553 |
| Suited total of 21 | 15 | 26,568 | 0.005299 | 0.079492 |
| Unsuited total of 21 | 3 | 406,296 | 0.081043 | 0.243130 |
| Total of 20 | 2 | 377,568 | 0.075313 | 0.150626 |
| Total of 19 | 2 | 364,320 | 0.072670 | 0.145341 |
| All other | -1 | 3,822,720 | 0.762513 | -0.762513 |
| Total | 5,013,320 | 1.000000 | -0.026556 |
Analysis — Pay Table 2 — Two Decks
Following is my analysis of pay table 2 using two decks. The lower right cell shows a house edge of 5.39%.
Lucky Lucky — Pay Table 2 — Two Decks
| Event | Combinations | Probability | Pays | Return |
|---|---|---|---|---|
| Suited 6-7-8 | 100 | 32 | 0.000176 | 0.017572 |
| Any 7-7-7 | 50 | 56 | 0.000308 | 0.015376 |
| Unsuited 6-7-8 | 30 | 480 | 0.002636 | 0.079076 |
| Suited total of 21 | 10 | 936 | 0.005140 | 0.051399 |
| Unsuited total of 21 | 3 | 14,904 | 0.081843 | 0.245530 |
| Total of 20 | 2 | 13,792 | 0.075737 | 0.151474 |
| Total of 19 | 2 | 13,344 | 0.073277 | 0.146554 |
| All other | -1 | 138,560 | 0.760884 | -0.760884 |
| Total | 182,104 | 1.000000 | -0.053903 |
Analysis — Pay Table 2 — One Deck
Following is my analysis of pay table 2 using one deck. The lower right cell shows a house edge of 5.05%.
Lucky Lucky — Pay Table 2 — One Deck
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Suited 6-7-8 | 100 | 4 | 0.000181 | 0.018100 |
| Any 7-7-7 | 50 | 4 | 0.000181 | 0.009050 |
| Unsuited 6-7-8 | 30 | 60 | 0.002715 | 0.081448 |
| Suited total of 21 | 10 | 108 | 0.004887 | 0.048869 |
| Unsuited total of 21 | 3 | 1,836 | 0.083077 | 0.249231 |
| Total of 20 | 2 | 1,688 | 0.076380 | 0.152760 |
| Total of 19 | 2 | 1,640 | 0.074208 | 0.148416 |
| All other | -1 | 16,760 | 0.758371 | -0.758371 |
| Total | 22,100 | 1.000000 | -0.050498 |
Analysis — Pay Table 3 — Six Decks
Following is my analysis of pay table 3 using six decks. The lower right cell shows a house edge of 5.31%.
Lucky Lucky — Pay Table 3 — Six Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Suited 7-7-7 | 200 | 80 | 0.000016 | 0.003191 |
| Suited 6-7-8 | 100 | 864 | 0.000172 | 0.017234 |
| Unsuited 7-7-7 | 50 | 1,944 | 0.000388 | 0.019388 |
| Unsuited 6-7-8 | 30 | 12,960 | 0.002585 | 0.077553 |
| Suited total of 21 | 10 | 26,568 | 0.005299 | 0.052995 |
| Unsuited total of 21 | 3 | 406,296 | 0.081043 | 0.243130 |
| Total of 20 | 2 | 377,568 | 0.075313 | 0.150626 |
| Total of 19 | 2 | 364,320 | 0.072670 | 0.145341 |
| All other | -1 | 3,822,720 | 0.762513 | -0.762513 |
| Total | 5,013,320 | 1.000000 | -0.053054 |
Analysis — Pay Table 4 — Six Decks
Following is my analysis of pay table 4 using six decks. The lower right cell shows a house edge of 3.95%.
Lucky Lucky — Pay Table 4 — Six Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Suited 7-7-7 | 200 | 80 | 0.000016 | 0.003191 |
| Suited 6-7-8 | 100 | 864 | 0.000172 | 0.017234 |
| Unsuited 7-7-7 | 50 | 1,944 | 0.000388 | 0.019388 |
| Unsuited 6-7-8 | 25 | 12,960 | 0.002585 | 0.064628 |
| Suited total of 21 | 15 | 26,568 | 0.005299 | 0.079492 |
| Unsuited total of 21 | 3 | 406,296 | 0.081043 | 0.243130 |
| Total of 20 | 2 | 377,568 | 0.075313 | 0.150626 |
| Total of 19 | 2 | 364,320 | 0.072670 | 0.145341 |
| All other | -1 | 3,822,720 | 0.762513 | -0.762513 |
| Total | 5,013,320 | 1.000000 | -0.039482 |
Analysis — Pay Table 5 — Six Decks
Following is my analysis of pay table 5 using six decks. The lower right cell shows a house edge of 9.96%.
Lucky Lucky — Pay Table 5 — Six Decks
Lucky Lucky Kh2
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Suited 7-7-7 | 200 | 40 | 0.000014 | 0.002763 |
| Suited 6-7-8 | 100 | 500 | 0.000173 | 0.017267 |
| Unsuited 7-7-7 | 50 | 1,100 | 0.000380 | 0.018994 |
| Unsuited 6-7-8 | 30 | 7,500 | 0.002590 | 0.077704 |
| Suited total of 21 | 15 | 15,300 | 0.005284 | 0.079258 |
| Unsuited total of 21 | 3 | 234,900 | 0.081123 | 0.243368 |
| Total of 20 | 2 | 218,200 | 0.075355 | 0.150710 |
| Total of 19 | 1 | 210,600 | 0.072731 | 0.072731 |
| All other | -1 | 2,207,480 | 0.762351 | -0.762351 |
| Total | 2,895,620 | 1.000000 | -0.099557 |
Analysis — Pay Table 6 — Six Decks
Following is my analysis of pay table 6 using six decks. The lower right cell shows a house edge of 12.60%.
Lucky Lucky — Pay Table 6 — Six Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Suited 7-7-7 | 200 | 40 | 0.000014 | 0.002763 |
| Suited 6-7-8 | 100 | 500 | 0.000173 | 0.017267 |
| Unsuited 7-7-7 | 50 | 1,100 | 0.000380 | 0.018994 |
| Unsuited 6-7-8 | 30 | 7,500 | 0.002590 | 0.077704 |
| Suited total of 21 | 10 | 15,300 | 0.005284 | 0.052838 |
| Unsuited total of 21 | 3 | 234,900 | 0.081123 | 0.243368 |
| Total of 20 | 2 | 218,200 | 0.075355 | 0.150710 |
| Total of 19 | 1 | 210,600 | 0.072731 | 0.072731 |
| All other | -1 | 2,207,480 | 0.762351 | -0.762351 |
| Total | 2,895,620 | 1.000000 | -0.125976 |
Analysis — Pay Table 7 — One Deck
Following is my analysis of pay table 7 using one deck. The lower right cell shows a house edge of 5.05%.
Lucky Lucky — Pay Table 7 — One Deck
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Suited 6-7-8 | 100 | 4 | 0.000181 | 0.018100 |
| Any 7-7-7 | 50 | 4 | 0.000181 | 0.009050 |
| Unsuited 6-7-8 | 30 | 60 | 0.002715 | 0.081448 |
| Suited total of 21 | 10 | 108 | 0.004887 | 0.048869 |
| Unsuited total of 21 | 3 | 1,836 | 0.083077 | 0.249231 |
| Total of 20 | 2 | 1,688 | 0.076380 | 0.152760 |
| Total of 19 | 2 | 1,640 | 0.074208 | 0.148416 |
| All other | -1 | 16,760 | 0.758371 | -0.758371 |
| Total | 22,100 | 1.000000 | -0.050498 |
The following table is an analysis of pay table 8 with six decks.
Lucky Lucky — Pay Table 8 — Six Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Suited 777 | 500 | 80 | 0.000016 | 0.007979 |
| Suited 678 | 200 | 864 | 0.000172 | 0.034468 |
| Unsuited 777 | 100 | 1,944 | 0.000388 | 0.038777 |
| Unsuited 678 | 25 | 12,960 | 0.002585 | 0.064628 |
| Suited 21 | 15 | 26,568 | 0.005299 | 0.079492 |
| Unsuited 21 | 3 | 406,296 | 0.081043 | 0.243130 |
| Any 20 | 2 | 377,568 | 0.075313 | 0.150626 |
| Any 19 | 1 | 364,320 | 0.072670 | 0.072670 |
| All other | -1 | 3,822,720 | 0.762513 | -0.762513 |
| Total | 5,013,320 | 1.000000 | -0.070743 |
Lucky Lucky Kh2
House Edge Summary
Following is a summary of the house edge by pay table and number of decks.
House Edge Summary
| Decks | Pay Table 1 | Pay Table 2 | Pay Table 3 | Pay Table 4 | Pay Table 5 | Pay Table 6 | Pay Table 7 | Pay Table 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 2.61% | 5.95% | 6.66% | 6.41% | 7.31% | 8.67% | 9.56% | 8.67% |
| 2 | 2.82% | 5.21% | 6.02% | 5.97% | 6.85% | 8.17% | 9.03% | 8.17% |
| 3 | 2.77% | 4.65% | 5.5% | 5.52% | 6.39% | 7.7% | 8.54% | 7.7% |
| 4 | 2.72% | 4.32% | 5.18% | 5.24% | 6.1% | 7.4% | 8.25% | 7.4% |
| 5 | 2.68% | 4.1% | 4.98% | 5.05% | 5.92% | 7.21% | 8.05% | 7.21% |
| 6 | 2.66% | 3.95% | 4.83% | 4.92% | 5.78% | 7.07% | 7.91% | 7.07% |
| 7 | 2.63% | 3.84% | 4.72% | 4.82% | 5.68% | 6.97% | 7.81% | 6.97% |
| 8 | 2.63% | 3.84% | 4.72% | 4.82% | 5.68% | 6.97% | 7.81% | 6.97% |