When the dealer doesn't qualify the player's bet wins the ante and the dealer's
payoff on the ante. In other words, if the dealer doesn't qualify the player is
paid even money on the bet. However, in the long run the dealer will qualify
56.3% of the time. A bluff is always an unfavorable bet. Even the best possible
bluff--where the player holds an Ace or King, another card which matches the
dealer's upcard, and a four-flush of the same suit as the dealer's upcard--is
unfavorable. This means that a player who always folds hands worse than
Ace-King will lose less in the long run than one who sometimes bluffs.
A pair or better should always be bet. A bet on even the worst possible
pair--deuces, with no Ace nor King, no card matching the dealer's upcard, and
no card of the same suit as the dealer's upcard--yields an expected profit.
This means that a player who always bets a pair of deuces or better will lose
less in the long run than one who sometimes folds such hands.
The dealer will fail to qualify 43.7% of the time, and will qualify with an
Ace-King (no pair) 6.4% of the time. The player who holds an Ace-King and bets
will win even money more than 43.7% of the time (because the player's holding
Ace-King reduces the chance of the dealer qualifying), and will be paid two to
one (1:1 bet payoff plus 0.5:1 ante plus 0.5:1 ante payoff) when the player's
Ace-King beats the dealer's. Therefore, there are some player Ace-King hands
which should be bet, depending on what other cards the player holds. For
example, if the player holds a card having the same value as the dealer's
upcard, the chance of the dealer having a pair is reduced.
The optimum strategy is to bet when the player holds:
(1) AKQJ or better (including any pair or better) or
(2a) AKQxx with any card in player's hand matching dealer's upcard; or
(2b) with both x cards having higher value than dealer's upcard; or
(2c) with a four flush of the same suit as dealer's upcard and:
at least one of the x cards being either:
8 or better (i.e., 8, 9, or 10)
or
of higher value than dealer's upcard.
or
(3) AKJ with any card in player's hand matching dealer's upcard
or
(4) AKxxx with any x card matching dealer's upcard
The results of this strategy and two simpler strategies are shown below, each
based on computer simulation of 200 million deals. "Expected loss per ante
amount per hand" is the average amount that the player will lose per hand in
the long run as a percentage of the ante amount. "Payback per $1 risked" is the
average long run total payback on each dollar wagered--on antes plus bets.
Strategy
Bet frequency
Expected loss per ante amount per hand
Payback per $1 risked
Optimum
52.0%
5.23%
$0.9743
Bet any pair or better
49.9%
5.48%
$0.9726
Bet Ace-King or better
56.3%
5.75%
$0.9729
For the casual player, "Bet any pair or better" is the recommended strategy.
The expected difference in total loss versus the optimum strategy over a couple
of hundred hands is about half of one ante. "Bet Ace-King or better" provides
more betting action at the cost of another half an ante per couple of hundred
hands.
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