With this in mind, will Joe and Billy be able to reach their goal of doubling their money? What is the probability of this? Even if some bets are not in their favorable outcomes, they think that if they keep the sequence going and take turns betting on the tie and increasing it by $5 every turn (which they think takes away the house edge), in addition to hoping the higher
Billy and Joe are buddies that think they can outsmart the casino by splitting each other’s profits. They decided to play a game by the name of Baccarat. They both have $1200 and their goal is to leave once they double their money. In Baccarat, the Banker's or Player’s hand will win 45% of the time. Ties win 10% of the time. The goal in baccarat is to have the hand you’re betting on, either the player or the banker, be the best hand of the two dealt. The winning hand is the one with a score where the final digit is the closest to nine. Face cards are worth zero, and aces count as one. There are 8 decks in a shoe.
Billy and Joe came up with a betting strategy/sequence and assigned “teams”. Billy will ALWAYS bet on “Player” whereas Joe will always bet on “Banker”.
The sequence goes as follows: Billy: 12113 Joe: 21221
Billy: $100, $200, $100, $100, $300 = $900
Joe: $200, $100, $200, $200, $100 = $900
The remaining $300 that Billy and Joe have will go towards taking turns on betting $5 on the Tie (side bet). Here’s the catch. Billy and Joe will take turns betting on the Tie increasing their bet by $5 each time. (Ex. $5 Billy, then once it’s the next turn/bet, $5 Joe, $10 Billy, then $10 Joe, $15 Billy, so on and so forth). The rest of the $900 will follow the sequences of bets (Ex. 1st turn, Billy will bet $100 on player whereas Joe will bet $200 on banker). If Billy or Joe happen to run out of the $300 dedicated to the Tie side bet, they will withdraw $300 from the money that supposed to go towards betting on either player or banker. If they happen to win on the Tie side bet, they will reset to betting $5 on the Tie side bet, and have the money won go towards betting on the tie side bet. (Ex. If Billy or Joe is at a point where they are betting $20 on the Tie and win, that would equal $160, which would go towards betting on the tie side bet). Joe is also really hoping that Billy will win the $300 bet at the end of the sequence so they can make more profit.
Hypothetically, if Joe won the first bet, he would now have won $200, leaving Billy losing $100. Joe would then give Billy $150 so they can split the profits, leaving Billy and Joe $50 each, but in reality, Joe has $50 in profit whereas Billy has $45 in profits since he put $5 on the Tie side bet that pays 8:1. (Player & Banker bets pay 1:1). In contrast, if Joe lost the first bet, Billy would now have won $100, leaving billy at -$55 (due to the side bet) and Joe at -$50. If the game happened to be a tie, Billy and Joe win $20 each since the Tie bet of $5 pays 8:1.
With this in mind, will Joe and Billy be able to reach their goal of doubling their money? What is the
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