Blackjack/Coin Flip

[Actinguy1]

Hey guys! This isn't a math homework question...it's a real-life one.

I've recently become a professional blackjack player. I want to win $87,000, and am trying to determine the best way to do so. Assume that I play basic blackjack strategy and don't count cards. Also ignore variables such as the fact that not every card is in the deck at any given moment, and splitting/doubling (which requires doubling your bet for that hand). As such, assume that my odds of winning any given hand of blackjack are approximately 50/50. A coin flip.

Strategy A: Go to the casino every day and bet $300 per hand. Continue playing until I've either won $300 or lost $2100 that day. Either way, I continue going every day.

Strategy B: Go to the casino every day and bet $1000 per hand. Continue playing until I've either won $1000 or lost $15,000 that day. Either way, I continue going every day.

Here's what I've figured so far. First, assuming I achieve my "win goal" every single day, it will take me 290 days to win $87,000 at 300 a day. It will take me 87 days at 1000 a day.

Second, my 300 walk-away strategy can be broken down...if W is win and L is lose...to W=L+1 or L=W+7. 1000 walk-away strategy is W=L+1 or L=W+15.

Assuming I have an infinite bankroll,the second strategy is clearly and vastly superior. However, I have a bankroll of about 15k. As such, a single daily loss early in strategy B will end the entire game.

So...my question:

How long, on average, will it take me to win 87,000 under each strategy? And what percentage of days will I achieve my daily "win" goal under each strategy?

Thank you so much for any help you can provide!

 

[Denis]

Why would a pro be asking us, amateurs?

 

[Actinguy1]

Ha, first, I've been a "pro" for about 22 days...but more relevantly, because it's a math question, not a how-to-gamble question.

 

[wjm11]

what percentage of days will I achieve my daily "win" goal under each strategy?

Hello, Actinguy1,

Here’s the way probability and statistics work: the rules tell us what long term (many trials/bets) outcome to expect. They offer no guarantee for results from small numbers of trials (such as the number of bets one is likely to place in a single day of gambling).

That’s what makes gambling exciting; on any given day, a gambler can be either a winner or a loser. Since the odds on various games in casinos are close to 50:50 (but are never actually 50:50), at any given moment, it might appear that there are almost as many winners as losers in a casino. This probably contributes to the belief in “luck” as a factor in betting outcomes.

How casinos work: All the games they offer have the odds shaved in favor of the house. Since the casino engages in millions of bets, the “laws” of probability and statistics are going to work very well for them. Since the odds are not 50:50 but actually favor the casinos, the many bets placed guarantee a positive return for them. There is no gambling involved for the casino. The long term outcome for them is a “sure bet.” Only the individuals placing bets are gambling.

The main idea for the individual gambler to derive from this is that he/she is playing a game that pretty much guarantees a loss in the long term. The more bets one places, the more likely that one’s results will approach the statistical predictions.

Hope that helps.