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Question of the Day - 17 January 2024

Q:

I had a guy tell me that my money will last longer playing 3-2 blackjack for $25 than if I play 6-5 for $15. Mathematically speaking, true or false? 

A:

Assuming 6 decks, dealer hits soft 17, double down allowed after splits, and resplit aces, the casino edge against perfect basic strategy when naturals pay 3-2 is .57%, while the same game paying 6-5 on naturals jumps all the way up to 1.93%. That works out to a per-hand expected loss of 14¢ on the $25/3-2 game compared to 29¢ on $15/6-5.

In terms of the expected result, you’ll certainly do better over time playing $25 on a 3-2 game, losing less even though you’re betting more.

What’s not taken into consideration in assessing this statement literally is fluctuation. If you have very limited funds — maybe you buy in with just $50 — and things go badly from the start, you could lose your stake faster at the better game because of the bigger bets.

Despite this dynamic, however, the spirit of the statement that your "money will last longer” is correct and punctuates the need to seek out the games with the smallest edges for the casino.

 

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Comments

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  • David Miller Jan-17-2024
    There You Have It
      There is a reason Blackjack has changed from 3/2 to 6/5 -- more money for the casino. Anyone playing 6/5 Blackjack must hate money, and the casinos love you for it. 

  • Thomas Dikens Jan-17-2024
    Roulette
    I believe Roulette has the same odds dynamic.  I guess that even a logarithmic difference in bet sizing, $100 vs $10 and you will last longer at a $100 one zero table than a 3 zero. I  once did a "back of the envelope" calculation that at a 3 zero table one would last 2 hours with a certain bank roll and bet size, while at a  2 zero wheel one would last 4 hours and six hours at a one zero wheel. I would love to know what an expert would say on this.  I don't have the right skill set.  To vent a bit, I get annoyed when I see a group betting big on a 3 zero wheel at the Mandalay Bay, while just a few yards away a fine high-rollers room has the one zero wheel setting idle. The fact that the majority of casual gamblers just don't seem to care.  Dare we call them stupid?  Their illogical decisions damage the environment, at least on the strip.  Reminds me of the adage that "A Fool and his money are soon parted" how did the Fool get the money in the first place. Am I  just jealouse?

  • Thomas Dikens Jan-17-2024
    BOAT
    Just to complete my diatribe.... If I had the money, time, expertise and political connections, (that is a lot if If's!!), I would buy a strip casino, change the name to Better Odds At Tom's (inevitably called The BOAT) and make a fortune.  I would be hoping to attract a lot of  LVA members!

  • Jack Gruber Jan-17-2024
    Minimums
    "long-term"is a luxury reserved for the casinos, as most of us do not have the bankroll for "long-term".   Long-term we will all be dead. The casinos now are blatantly all about soaking us as opposed to before where certain perks and game-rules gave the illusion of a fair gamble.  It is entertainment and I will not play the ridiculous minimums and the $10/pull slots.  The fun ends too quickly that way.  I will accept the scraps they throw at me for my comfortable play and will not engage until things loosen up a bit(next recession).

  • Stewart Ethier Jan-17-2024
    Formula
    There is a formula for how long your money will last, on average, when the game is an even-money (win or lose the amount that you bet) game of independent trials.  Blackjack is a bit more complicated, because of doubling, splitting, and naturals, and because of sampling without replacement, but the simplifying assumptions will give a good approximation.  Let H be the house advantage at each trial, and let L be the number of betting units you start with.  The expected time until ruin is L/H.  Let's apply this to the two scenarios.  Say you begin with $150.  In the 3-to-2 case, L=6 and H=0.0057.  The ratio is 1053.  In the 6-to-5 case, L=10 and H=0.0193.  The ratio is 518.  Your bankroll lasts twice as long in the 3-to-2 game.

  • jay Jan-17-2024
    Roulette math
    The odds of landing on any one number:
    Single 0 1/36 = 2.77%
    Double 0 1/37 = 2.70%
    Triple 0 1/38 = 2.63%
    Seems very little variance between the 3 games until you factor in the payback.
    
    Roulette pays 35:1 and with 36 spots if you bet on all the spots but one you would break even most of the time. However 1/35 = 2.8% loss when you occasionally didn't get it right. No one would want to play to break even so you don't bet on 2 spots, that means you would make something as long as those 2 spots didn't hit. Now you are losing 5.7% of the time. A decent slot pays back between 95-98% (2-5% loss). Go to your classic double zero game and your losing 8.57% and Triple zero your losing 11.4%. Those are big numbers
    
    If you bet $5 on Red & Black, a single zero still loses you 5.8%

  • Sandra Ritter Jan-17-2024
    Fluctuation
    WAY back when I started playing BJ, I went to a $1 table, with $10. The dealer was nice enough to say beware, I'm really hot right now. 10 hands later playing $1/hand, I left with $0. She definitely was on a hot streak and I definitely was not.

  • Rosemarie Jan-17-2024
    What's This About?
    I found this on Yahoo News this morning.
    
    LAS VEGAS (AP) — Standing or stopping is now banned on pedestrian bridges on the Las Vegas Strip where visitors often pause to take photos amid the glittery casino lights or to watch street performers.
    
    Violators of the ordinance that took effect Tuesday could face up to six months in jail or a $1,000 fine.

  • Bob Jan-17-2024
    Rosemarie
    The new ordinance has nothing to do with tourists stopping to take photos. it's to be able to clear out all the hucksters, homeless panhandlers, scam artists etc. that congregate/camp out on the pedestrian bridges. 99% of the bogus articles make it sound like they are out to arrest tourists who stop to see the sights or take a photo.  Metro has their hands full, they aren't going to hassle anyone minding their own business.  

  • Anthony Curtis Jan-17-2024
    Stewart's Formula
    Excellent contribution to this answer. Please chime in anytime.

  • O2bnVegas Jan-17-2024
    written to purposely mislead?
    I saw it somewhere and, like Rosemarie, wondered WTH?  I went back and re-read the quote.  
    
    Good example of something easily mis-interpreted, whether purposely written to mislead or not:  "Standing or stopping...where visitors often pause to take photos amid the glittery casino lights or to watch street performers." That part is, of course, true.  
    
    Thanks, Bob, for the clarification.
    
    Candy

  • Cyclone99 Jan-17-2024
    Roulette
    Even single-zero roulette has a larger house edge than 6:5 blackjack. If you're concerned about house edge, you shouldn't be playing roulette at all.

  • Raymond Ray Jan-18-2024
    6-5 BLACKJACK
    JUST SAY NO!!!!!!

  • Raymond Jan-18-2024
    New Ordinance
    Sure, it's designed to clear the pedestrian bridges of panhandlers, hustlers, etc.  What it will be used for may be somewhat or entirely different.  I'm not saying it will be misused, but I can see bad cops using this as an excuse to hassle people they don't like or people their friends in the casinos don't like.  To use an old term, "loitering" statutes are a great way to harass people.