Gambling your way to New York: A story of expectation
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Scenarios 1 and 2 assume the player only plays the one game to turn over the required $10,000. If a player had a good run in the first $5,000 turnover in Casino War, he or she may be inclined to switch to 3 Card Stud Poker. Likewise, if a player had a bad run in the first $5,000 turnover in 3 Card Stud Poker, he or she may be inclined to switch to Casino War. A player’s choice to switch between 3 Card Stud Poker and Casino War is dependent on his or her current bankroll and how many hands are left to play to wager the required $10,000.
The minimum bet for both games has always been applied. A player may choose to speed up the process by betting higher than the minimum. This may again depend on the player’s current bankroll and how many hands are left to play. In general, increasing the size of the bankroll in any casino game increases the variance and skewness. This would amount to increasing the probability of losing the initial $200 before wagering the initial $5,000 (i.e., a greater chance of having to deposit more money into the casino account).
Is the offer worthwhile? The cost of a return flight to New York from Australia is around $2,000, excluding taxes. The expected cost for the player in 3 Card Stud Poker is $88 and $32 in Casino War. Therefore, on average, the offer is worthwhile in the sense of having a positive expected value once one accounts for the value of the flight from Australia.
Which is the best game to play? We identified two games in which the playing strategies were straightforward and had relatively low percent house margins. The best game to play depends on the player’s objective toward the offer. A professional gambler, for example, may be more inclined to play 3 Card Stud Poker because it has a lower %HM, whereas an individual who gambles only to take advantage of these promotional offers may be more inclined to play Casino War, as it minimizes the probability of having to deposit more than $200 into an account.
There is evidence to show that Casino War is the preferred game if a player is trying to minimize the probability of depositing more than the minimum $200. This is interesting, as a player is willing to spend an extra $56 to reduce risk.