The odds are "fifty: fifty," which equals 1. 10 , then the odds are 0.
The player (punto) and banker (banco) are simply designations for the two hands dealt out in each coup, two outcomes which the bettor can back; the player hand has no particular association with the gambler, nor the banker hand with the house. The croupier will deal the cards according to the tableau and the croupier will announce the winning hand, either the player or the banker.
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