# THREE CARD 2ND CHANCE

**Introduction**

Three Card 2nd Chance is a unique three card poker variation offered by Wagerworks casinos. With optimal strategy, the game has a lower house edge per unit wagered than standard three card poker, but a higher variance.

**Rules and Play**

After placing an ante bet, the player is dealt 3 cards. He has the choice to either keep his hand or discard his hand and get a replacement. If the player discards his hand, he must make a raise bet equal to his original bet, doubling his bet size. After the player is dealt his final hand, the dealer reveals his cards. If the dealer has a queen high or less, the dealer takes a replacement hand. The final hands are compared and scored. If the dealer wins, both bets lose. If the player and dealer tie, both bets push. If the player wins, both bets pay according to the paytable below.

Hand |
Pays |

Straight Flush | 6:1 |

3 of a Kind | 4:1 |

Straight | 3:2 |

Other | 1:1 |

**Best Hand Sidebet**

Three Card 2nd Chance offers an optional Best Hand sidebet with a maximum bet of 2x the initial ante wager. Unlike nearly all other sidebets, the Best Hand sidebet is a desirable option. The sidebet pays, if either the player or dealer has a flush or better, according to the paytable below.

Hand |
Pays |

3 Aces | 35:1 |

Straight Flush | 15:1 |

3 of a Kind | 12:1 |

Straight | 3:1 |

Flush | 2:1 |

**Strategy**

As previously stated, it is to the player's advantage to make the Best Bonus sidebet. Making the sidebet reduces the house edge per wager when using optimal strategy. The maximum sidebet is 2x the initial ante wager. With this ratio, optimal strategy to minimize house edge (per hand) is to stand on unsuited AK3 or better and take a replacement hand on unsuited AK2 or worse. To minimize house edge per wager (expected loss over a fixed wagering requirement), optimal strategy changes slightly. The player should stand on unsuited AK4 or better and take a replacement hand on unsuited AK3 or worse. See the strategy calc for more specific information about the EV differences.

**House Edge**

When using the optional sidebet strategy described above, the house edge of the main game bet is 11.02%, and the house edge of the sidebet is -3.53%. Note that the sidebet has a player edge. The combined house edge between the two bets is (11.02 - 2* 3.53)/3 is 1.32%. House edge is defined in terms of initial bet. The player raises 71.9% of the time, resulting in a house edge per unit wagered of (11.02 - 2* 3.53)/3.719 = 1.07%. The later value of 1.07% corresponds to the expected loss over a wagering requirement. A forum member and I both determined the house edge per wager value of 1.07% within +/- 0.01% accuracy through independent simulation. For more detail, see this forum thread.

When not making a sidebet and using the main bet strategy of standing on KT2 or better, the house edge is 3.56%. The player raises 50.2% of the time, resulting in a house edge per unit wagered of 2.37%.

**Variance and Bet Size**

Using the optional sidebet strategy described above, the standard deviation of the main bet is 1.93 and the standard deviation of the sidebet is 2.32. When the sidebet is 2x the initial ante bet, the combined standard deviation per hand is 1.80 when expressed in terms of the 3-unit inital bet. The combined standard deviation per unit wagered is 1.62. This later value corresponds to the expected variance over a wagering requirement. So the variance over a wagering requirement with a combined bet of 3 units is roughly the same as casino hold'em with an ante bet of 3 units, and is much higher than standard 3-card poker (ante & play) with an ante bet of 3 units.

When estimating variance over a wagering requirement using the return & variance calculator, enter a bet size that is the sum of the ante bet and side bet. If you were betting 1 unit on ante and 2 units on the sidebet, you would enter a bet size of 3.

When not making a sidebet and using the main bet strategy of standing on KT2 or better, the standard deviation per hand is 1.72 and the standard deviation per unit wagered is 1.40.

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