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Power 8's
Introduction
Power 8's is a baccarat side bet based on the number of eights in the Player and Banker cards. This side bet can be found in some casinos in South Africa.
Rules
- Standard baccarat rules are followed, which I assume the reader is familiar with. For this analysis, eight decks are assumed.
- The game pays based on the number of eights dealt between the Player and Banker hand, according to the pay table below. For the top award, the four eights must be in the initial four cards. For all other awards, they can include the draw cards.
- If any progressive jackpot is won, it shall be shared among all players who made the power 8's bet.
- The three progressives are independent of each other. I do not know the seed amounts or meter contribution rates.
Power 8's Pay Table
| Event | Pays |
|---|---|
| Four eights in initial deal | Top jackpot |
| Four eights | Middle jackpot |
| Three suited eights | Bottom jackpot |
| Three eights | 20 for 1 |
| Two eights | 4 for 1 |
Please do not write to me saying that the bottom two pays are on a "to 1" basis, quoting TCS John Huxley game literature. I have it on good authority that this literature is in error.
Analysis
The following table shows the probability of each event and the return of the awards with a fixed pay. The total return does not include any wins from the progressive jackpots.
Power 8's Return Table
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Four eights in initial deal | ? | 146,140,289,280 | 0.000029 | ? |
| Four eights | ? | 356,815,257,600 | 0.000071 | ? |
| Three suited eights | ? | 666,369,134,592 | 0.000133 | ? |
| Three eights | 20 | 14,088,947,417,088 | 0.002819 | 0.056374 |
| Two eights | 4 | 212,157,913,151,488 | 0.042445 | 0.169781 |
| Loser | 0 | 4,770,982,090,253,310 | 0.954502 | 0.000000 |
| Total | 4,998,398,275,503,360 | 1.000000 | 0.226155 |
The table above shows the player can expect to get back 22.62% of his wager, before considering the progressives. Thus the return is highly dependent on the three jackpots. The return per player is also very dependent on the number of other players making the side bet, due to jackpot sharing. The following formula shows the return for any given three jackpot amounts:
(((0.000029 × TJ) + (0.000071 × MJ) + (0.000133 × BJ))/NP) + 0.226155, where:
TJ = Top Jackpot
MJ = Middle Jackpot
BJ = Bottom Jackpot
NP = Number of other players making the side bet (not including yourself)
To reach break-even, the return would need to be exactly one.
Here is another way to express the return:
(TJ + (2.441594 × MJ) + (4.559791 × BJ))/(24919 × NP) + 0.226155
When the above formula returns a value greater than one, the bet is positive.
Strategy
Use one of the formulas above to calculate the return at any given time.
Also, it is not difficult to see that this side bet would be very vulnerable to card counters. I'll leave the details of that up to the reader.
External Links
TCS John Huxley — Company literature on Power 8's.