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Side Bet City
Introduction
Side Bet City is a table game by Evolution Gaming, a provider of live dealer games for Internet casinos. The game is pretty simple, the dealer deals out three cards, then another two to make a five-card hand, and then two more to make a seven-card hand. The player may bet on the poker value of any of the three hands or all three to lose. Except for the addition of the No Win bet, the game is much like 3-5-7 Poker with different pay tables.
Rules
- The game is played with a single 52-card deck.
- All hands are scored according to conventional poker rules, which I assume the reader is familiar with.
- There are four bets available, as follows:
- 3 Card Hand
- 5 Card Hand
- 7 Card Hand
- No Win
- The outcome of bets on the 3 Card Hand shall be determined by the poker value of the first three cards dealt and the pay table below.
- The outcome of bets on the 5 Card Hand shall be determined by the poker value of the first five cards dealt and the pay table below.
- The outcome of bets on the 7 Card Hand shall be determined by the poker value of all seven cards dealt and the pay table below.
- The "No Win" bet shall win and pay 0.7 to one if all three hands lose.
The following tables show what each hand pays on the 3-, 5-, and 7-Card Hand bets. Wins are on a "for one" basis.
3 Card Hand Pay Table
| Hand | Pays | |
|---|---|---|
| Royal flush | 100 | |
| Straight flush | 40 | |
| Three of a kind | 35 | |
| Straight | 5 | |
| Flush | 4 | |
| Pair | 1 |
5 Card Hand Pay Table
| Hand | Pays | |
|---|---|---|
| Royal flush | 1000 | |
| Straight flush | 250 | |
| Four of a kind | 100 | |
| Full house | 50 | |
| Flush | 40 | |
| Straight | 25 | |
| Three of a kind | 7 | |
| Two pair | 4 | |
| Pair (jacks or better) | 1 |
7 Card Hand Pay Table
| Hand | Pays | |
|---|---|---|
| Royal flush | 500 | |
| Straight flush | 100 | |
| Four of a kind | 50 | |
| Full house | 7 | |
| Flush | 5 | |
| Straight | 4 | |
| Three of a kind | 3 |
Analysis
The following table shows my analysis of the 3 Card Hand bet. The lower right cell shows a house edge of 3.31%.
3 Card Hand
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | 100 | 4 | 0.000181 | 0.018100 |
| Straight flush | 40 | 44 | 0.001991 | 0.079638 |
| Three of a kind | 35 | 52 | 0.002353 | 0.082353 |
| Straight | 5 | 720 | 0.032579 | 0.162896 |
| Flush | 4 | 1,096 | 0.049593 | 0.198371 |
| Pair | 1 | 3,744 | 0.169412 | 0.169412 |
| All other | -1 | 16,440 | 0.743891 | -0.743891 |
| Total | 22,100 | 1.000000 | -0.033122 |
The following table shows my analysis of the 5 Card Hand bet. The lower right cell shows a house edge of 4.79%.
5 Card Hand
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | 1000 | 4 | 0.000002 | 0.001539 |
| Straight flush | 250 | 36 | 0.000014 | 0.003463 |
| Four of a kind | 100 | 624 | 0.000240 | 0.024010 |
| Full house | 50 | 3,744 | 0.001441 | 0.072029 |
| Flush | 40 | 5,108 | 0.001965 | 0.078616 |
| Straight | 25 | 10,200 | 0.003925 | 0.098116 |
| Three of a kind | 7 | 54,912 | 0.021128 | 0.147899 |
| Two pair | 123,552 | 0.047539 | 0.190156 | |
| Pair (jacks or better) | 1 | 337,920 | 0.130021 | 0.130021 |
| All other | -1 | 2,062,860 | 0.793725 | -0.793725 |
| Total | 0 | 2,598,960 | 1.000000 | -0.047876 |
The following table shows my analysis of the 7 Card Hand bet. The lower right cell shows a house edge of 5.66%.
7 Card Hand
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | 500 | 4,324 | 0.000032 | 0.016160 |
| Straight flush | 100 | 37,260 | 0.000279 | 0.027851 |
| Four of a kind | 50 | 224,848 | 0.001681 | 0.084034 |
| Full house | 7 | 3,473,184 | 0.025961 | 0.181727 |
| Flush | 5 | 4,047,644 | 0.030255 | 0.151275 |
| Straight | 4 | 6,180,020 | 0.046194 | 0.184775 |
| Three of a kind | 3 | 6,461,620 | 0.048299 | 0.144896 |
| All other | -1 | 113,355,660 | 0.847300 | -0.847300 |
| Total | 133,784,560 | 1.000000 | -0.056582 |
The following table shows my analysis of the No Win bet. The lower right cell shows a house edge of 3.71%.
All Lose
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| No wins | 0.7 | 15,913,035,072 | 0.566406 | 0.396484 |
| At least one win | -1 | 12,181,722,528 | 0.433594 | -0.433594 |
| Total | 28,094,757,600 | 1.000000 | -0.037110 |
Methodology
Finding a mathematical solution was too messy, I wrote a simple looping program. Here is the logic of it:
- Loop through all 22,100 ways to choose 3 cards out of 52.
- If the three-card hand is a winner, add combin(49,2)*combin(47,2)=1,271,256 to the losing combinations. If a loser, then go to step 3.
- Loop through all 1,176 ways to choose 2 cards out of the 49 cards left in the deck, to combine with the three-card hand to make a five-card hand.
- If the five-card hand is a winner, add combin(47,2)=1081 to the losing combinations. If a loser, then go to step 5.
- Loop through all 1,081 ways to choose 2 cards out of the 47 cards left in the deck, to combine with the five-card hand to make a seven-card hand.
- If the seven-card hand is a winner, add one to the losing combinations. If a loser, then add one to the winning combinations.
External Links
- Discussion about Side Bet City in my forum at Wizard of Vegas.