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3-5-7 Poker
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Introduction
3-5-7 Poker is a simple poker based game slowly finding a home in the casinos. It is actually 3 games in 1, the player can bet on a 3, 5, and 7 card hand and is paid according to the poker value of each.
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Rules
Play begins with the player making 2 or 3 wagers. The player must bet on the 3 card and 5 card hand, the 7 card hand is optional. The player may bet any amount on any hand, subject to the table minimum and maximum.
After all players have bet, the dealer will give 3 cards to each player and 4 to himself, face down. Based on his first three cards the player may surrender half his 7 card bet if he wishes, in other words the dealer gets half the 7 card bet and the player gets back the other half.
The following pay tables show what each hand pays for each bet.
3-Card Hand Pay Table
| Hand | Pays |
|---|---|
| Straight flush | 40 to 1 |
| Three of a kind | 25 to 1 |
| Straight | 6 to 1 |
| Flush | 4 to 1 |
| Pair | 1 to 1 |
| Nothing | Loss |
5-Card Hand Pay Table
| Hand | Pays |
|---|---|
| Royal flush | 500 to 1 |
| Straight flush | 100 to 1 |
| 4 of a kind | 40 to 1 |
| Full House | 12 to 1 |
| Flush | 9 to 1 |
| Straight | 6 to 1 |
| 3 of a kind | 4 to 1 |
| 2 pair | 3 to 1 |
| Pair (6's or better) | 1 to 1 |
| Nothing | Loss |
7-Card Hand Pay Table
| Hand | Pays |
|---|---|
| Royal flush | 100 to 1 |
| Straight flush | 20 to 1 |
| 4 of a kind | 7 to 1 |
| Full House | 5 to 1 |
| Flush | 4 to 1 |
| Straight | 3 to 1 |
| 3 of a kind | 2 to 1 |
| 2 pair (10's high or better) | 1 to 1 |
| Other | Loss |
Strategy
The player should never surrender. Since the 7 card hand has the lowest house edge I would recommend betting the most on that, and the least on the 5 card hand.Statistics
The following tables show the probabilities and return for each hand for all 3 bets.
3-Card Hand Return Table
| Hand | Combinations | Probability | Pays | Return |
|---|---|---|---|---|
| Straight flush | 48 | 0.002172 | 40 | 0.086878 |
| Three of a kind | 52 | 0.002353 | 25 | 0.058824 |
| Straight | 720 | 0.032579 | 6 | 0.195475 |
| Flush | 1096 | 0.049593 | 4 | 0.198371 |
| Pair | 3744 | 0.169412 | 1 | 0.169412 |
| Nothing | 16440 | 0.743891 | -1 | -0.743891 |
| 22100 | 1 | 0 | -0.034932 |
5-Card Hand Return Table
| Hand | Combinations | Probability | Pays | Return |
|---|---|---|---|---|
| Royal flush | 4 | 0.000002 | 500 | 0.00077 |
| Straight flush | 36 | 0.000014 | 100 | 0.001385 |
| 4 of a kind | 624 | 0.00024 | 40 | 0.009604 |
| Full House | 3744 | 0.001441 | 12 | 0.017287 |
| Flush | 5108 | 0.001965 | 9 | 0.017689 |
| Straight | 10200 | 0.003925 | 6 | 0.023548 |
| 3 of a kind | 54912 | 0.021128 | 4 | 0.084514 |
| 2 pair | 123552 | 0.047539 | 3 | 0.142617 |
| pair (6's or better) | 760320 | 0.292548 | 1 | 0.292548 |
| Nothing | 1640460 | 0.631199 | -1 | -0.631199 |
| Total | 2598960 | 1 | 0 | -0.041238 |
7-Card Hand Return Table
| Hand | Combinations | Probability | Pays | Return |
|---|---|---|---|---|
| Royal flush | 4324 | 0.000032 | 100 | 0.003232 |
| Straight flush | 37260 | 0.000279 | 20 | 0.00557 |
| 4 of a kind | 224848 | 0.001681 | 7 | 0.011765 |
| Full House | 3473184 | 0.025961 | 5 | 0.129805 |
| Flush | 4047644 | 0.030255 | 4 | 0.12102 |
| Straight | 6180020 | 0.046194 | 3 | 0.138581 |
| 3 of a kind | 6461620 | 0.048299 | 2 | 0.096597 |
| 2 pair (10's high or better) | 20598408 | 0.153967 | 1 | 0.153967 |
| Other | 92757252 | 0.693333 | -1 | -0.693333 |
| Total | 133784560 | 1 | 0 | -0.032795 |
The next table summarizes the house edge of each bet.
House Edge Summary
| Bet | House Edge |
|---|---|
| 3 | 3.49% |
| 5 | 4.12% |
| 7 | 3.28% |
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There is a very similar game called Side Bet City, which adds a "No Win" bet that pays if the 3-, 5-, and 7-card hands all lose.