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Double Bonus supplement 2: Ace / high card versus single ace

In Double Bonus it's often correct to hold a single ace and discard an unsuited high card. The difference between the two plays is extremely small, and if you were to follow Jacks Or Better strategy and always hold both ace and high card you would be giving up very little value. Here are some illustrations of the precise rules:

Kh, 9c, Ad, 7s, 6c

The correct Double Bonus play is to hold the single ace; in Jacks Or Better, both ace and off-suit king are held. In Double Bonus, the discards - marked in blue above - determine which play is correct. There are three factors involved: straight ace-low (ace, 2, 3, 4, 5), straight ace-high (10, jack, queen, king, ace) and a flush of the same suit as the ace. If any of these cards figure amongst the discards they affect the play, because their absence from the remaining pack means that straights both ace-high and ace-low, and flushes, are less likely to result in the final hand. As such, they are known as "penalty cards", because their presence in the initial hand "penalises" the value of certain plays.

• If none of the three discards is a 2, 3, 4, 5 or 10 penalty card, then the correct play is to hold the single ace, as in the initial example. The large payoff on four aces in Double Bonus is the deciding factor:

Kh, 9c, Ad, 7s, 6c

• If there is a 10 in the initial hand, this "penalises" an ace-high straight and reduces the value of holding the other high card, since there are now less ace-high straights for the high card to figure in. In this case, the correct play is to discard the high card again:

Kh, 9c, Ad, 7s, 6c

• If 2, 3, 4, or 5 figures amongst the discards, the ace-low straight is now "penalised" but an ace-high one is clear; in this case it's correct to hold the high card as well:

Qh, 9c, Ad, 7s, 3c

• If there are penalty-cards to both an ace-low AND an ace-high straight, then it's correct to hold just the ace, for the same reason as when there are no penalty cards - the value of four aces tips the scales in favour of the single ace:

Kh, 10s, Ad, 7s, 5c

• If there is a FLUSH penalty card, a discard suited with the ace, it's correct to hold the high card whether or not there's a 10 card penalising the ace-high straight, both...

Qc, 10s, Ad, 7d, 5c

...and without the 10 penalty card...

Qc, 9h, Ad, 8d, 6c

It bears repeating again that these various exceptions to the Jacks Or Better play of always holding ace plus unsuited high card are very inexpensive. If you don't want to learn the above exceptions, go ahead and always hold the two high cards - the cost is approximately one cent for every $300 wagered.

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