My Math Forum $40,000 vs$50,000 at casino problem

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 April 9th, 2018, 05:13 AM #1 Newbie   Joined: Apr 2018 From: Connecticut Posts: 1 Thanks: 0 $40,000 vs$50,000 at casino problem Okay so let's see who can figure this one out. Hypothetically, let's say you are going to a casino with a goal to walk out with your original money plus \$30,000. You can either bring \$40,000 or \$50,000 to the blackjack table, where you are a novice card counter, and the chance of winning a hand is exactly 48% of the two different amounts of money to bring, being 40k or 50k which option is seen as less risky and also quicker to get to a \$30k profit. I first thought \$50,000 because you would have an extra \$10,000 that would act as "extra ammo" in a way, but you would also have an extra \$10,000 to make up in case you were down, so I'm not sure. Anyway, it's for a story I am writing, so any and all help is most appreciated. Thank you for reading! Last edited by skipjack; April 9th, 2018 at 06:31 AM.  April 9th, 2018, 06:34 AM #2 Global Moderator Joined: Dec 2006 Posts: 18,841 Thanks: 1564 How much (in relation to your stake) is paid out when you win a hand?  April 9th, 2018, 04:38 PM #3 Senior Member Joined: Oct 2013 From: New York, USA Posts: 595 Thanks: 81 I assume 2/1 odds, meaning your profit equals your bet. With a 48% chance at winning, 2/1 odds would make the expected payout 96% of what is bet. Having an expected payout a little less than 100% is common.  April 10th, 2018, 02:51 AM #4 Global Moderator Joined: Dec 2006 Posts: 18,841 Thanks: 1564 Yes, but making a \$30,000 profit is then unlikely. Is there a house limit on the amount of each stake?
April 10th, 2018, 03:51 AM   #5
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Quote:
 the chance of winning a hand is exactly 48% of the two different amounts of money to bring
doesn't make sense. 48% of $50,000 is$24,000 and 48% of $40,000 is$19,200. Both are amounts of money, not "chances" (percentages). Did you mean the expected value of your return on your bet? To calculate the probability of winning $30,000 more than you brought, you would need to know more about the probability distribution than just the expected value. (But it will, of course, be very very low!)  Tags$40, \$50, 000, casino, chance, probability, problem

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