January 30th, 2020 at 12:14:07 PM
permalink

Say you have a 2 percent constant advantage in BJ every hand. If i played 7200 hands with this advantage,what percent of the time would I be not in profit? How many hands would you need to play to bet 98 percent confident level in profit?

January 30th, 2020 at 3:15:54 PM
permalink

The game is statistically similar to a game with p=0.44 and a payout of 1.32 to 1, which gives a standard deviation of 1.15.

96 percent of results will be within 2.05 SDs of the mean, so (100 - 96) / 2 = 2 percent will fall below this range.

The expectation is n * .02 +/- 1.15 * n^.5

You want to know when n * .02 = 2.05 * 1.15 * n^.5. Rearrange and n = (2.05 * 1.15 / .02)^2 = 13,895 hands to be 98% confident of a profit. Call it 14,000 since this is a “back of an envelope” calc.

At 1000 hands per week, that will take over 3 months

96 percent of results will be within 2.05 SDs of the mean, so (100 - 96) / 2 = 2 percent will fall below this range.

The expectation is n * .02 +/- 1.15 * n^.5

You want to know when n * .02 = 2.05 * 1.15 * n^.5. Rearrange and n = (2.05 * 1.15 / .02)^2 = 13,895 hands to be 98% confident of a profit. Call it 14,000 since this is a “back of an envelope” calc.

At 1000 hands per week, that will take over 3 months

It’s all about making that GTA

January 30th, 2020 at 3:27:14 PM
permalink

For 7200 hands your expectation is 144 +/ 98.

144 / 98 is 1.47 SDs, and your result will be a loss (to the left of that grouping) about 7% of the time.

144 / 98 is 1.47 SDs, and your result will be a loss (to the left of that grouping) about 7% of the time.

It’s all about making that GTA

January 30th, 2020 at 6:16:45 PM
permalink

awesome thank you, I guessed about 5 percent, and chalking it up to bad luck. I am actually the one who is the player-dealer bank. and bj only pays 6:5. no double after splits, so I am trying to see if its really bad luck, or perhaps more players are counting vs me, but I dont think this is the case.

January 31st, 2020 at 3:07:16 PM
permalink

Ace2 looks like he gave you a good answer, let's see if my estimate can look at it from a different perspective:

OriginalSD = 1.15*AvgBet

EV(x) = (x*AvgBet)*(Advantage)

SD(x hands) = Sqrt(x) * OriginalSD

EV(7200 hands at 2% edge) = (7200*AvgBet)*(.02)

SD(7200 hands) = Sqrt(7200)*OriginalSD

...you said you're player banking, so I'm going to assume an average bet of $10 to show you the formulas and you can correct them with your real averages that I assume you know or can figure out.

EV = $1440

1SD (68% confidence) = ~$975.. 2SD (95% confidence) = $1950... 3SD (99% confidence) = $2927

So after 7200 hands you're looking at being up $1440 +/- 2927 (3SD, 99% confidence)... so quite possible to be negative.

Let's see how that plays out after 15,000 hands though:

EV = $3000

3SD = $1408

You expect to be up $3000 +/- $1408, which means it should be mathematically impossible (assuming a fare game) for you to be down at this point.

OriginalSD = 1.15*AvgBet

EV(x) = (x*AvgBet)*(Advantage)

SD(x hands) = Sqrt(x) * OriginalSD

EV(7200 hands at 2% edge) = (7200*AvgBet)*(.02)

SD(7200 hands) = Sqrt(7200)*OriginalSD

...you said you're player banking, so I'm going to assume an average bet of $10 to show you the formulas and you can correct them with your real averages that I assume you know or can figure out.

EV = $1440

1SD (68% confidence) = ~$975.. 2SD (95% confidence) = $1950... 3SD (99% confidence) = $2927

So after 7200 hands you're looking at being up $1440 +/- 2927 (3SD, 99% confidence)... so quite possible to be negative.

Let's see how that plays out after 15,000 hands though:

EV = $3000

3SD = $1408

You expect to be up $3000 +/- $1408, which means it should be mathematically impossible (assuming a fare game) for you to be down at this point.

Playing it correctly means you've already won.

February 3rd, 2020 at 5:22:27 AM
permalink

I also pay $3 collection to bank per hand. The average action is $450 per hand (spread out on about 3 hands)

- Jump to:
DEFUNCT CASINOS Bill's Gambling Hall & Saloon MonteLago O'Sheas Sahara Western FORUM INFO Announcements Help Rules GAMBLING Betting Systems Big Wins Blackjack Craps Dice Setting Gambling with an Edge Online Gambling Other Games Poker Slots Sports Betting Table Games Trip Reports Video Poker GAMBLING OUTSIDE VEGAS Asia Atlantic City California Eastern U.S. Europe/Africa Mississippi Nevada (other) Oceania The Americas Western U.S. GAMING BUSINESS Boyd Gaming Caesars Entertainment Game Inventors Corner MGM/Mirage Other Sands Station Casinos Wynn LAS VEGAS ATTRACTIONS Deals Food and Restaurants Night Clubs Other Attractions/Entertainment Relaxation and Rejuvenation Shopping Shows Strip Clubs Thrill Seeking LAS VEGAS CASINOS Aliante Casino Aria Arizona Charlie's Casinos Bally's Barcelona Bellagio Binion's Boyd Gaming Casinos Caesars Palace Cannery Casinos Casino Royale Casuarina Circus Circus Cosmopolitan D Las Vegas El Cortez Ellis Island Excalibur Flamingo Four Queens Golden Gate Golden Nugget Hard Rock Hilton Hooters Jean/Primm Casinos Longhorn Casino Luxor M Mandalay Bay MGM Grand Mirage Monte Carlo New York, New York Palms Paris Planet Hollywood Plaza Poker Palace Quad, The Rampart Rio Riviera Silver Nugget Silver Sevens Silverton Skyline Small Casinos South Point Station Casinos Stratosphere Treasure Island Tropicana Tuscany Vegas Club Venetian and Palazzo Wynn and Encore OFF-TOPIC Adult Discussions Free Speech Zone General Discussion GLBT Corner Gripes Kiosk Off-Topic Other Casinos Religion QUESTIONS AND ANSWERS Advice All Other Casual Corner Gambling Las Vegas (other than gambling) Math