## Poll

30 members have voted

Wizard
Joined: Oct 14, 2009
• Posts: 23298
April 12th, 2016 at 8:22:41 AM permalink
Based on casual conversations, it seems to me that a lot of recreational video poker players go to Vegas, or wherever, with the goal of hitting a royal. I had a college job and my boss and his wife made frequent trips to Laughlin and it seemed to be their goal to come home with a royal story every time, at any cost.

I was wondering yesterday about how much has to lose first to hit a royal on average. That said, the table below shows the probability of hitting a royal with a bankroll of x units, in groupings of 100 up to 4000, and then by 1000. It is based on 9-6 Double Double Bonus.

For example, suppose you come to Vegas with a bankroll of 800 bet units. What is the probability of hitting a royal before you go bust? The table shows you would need exactly that last 100 3.98% of the time, and would hit a royal sometime before going bust 40.38% of the time.

In case you're wondering, the average low point before hitting a royal is 1,548 units.

 Bankroll Probability Cummulative 100 0.062638 0.062638 200 0.058518 0.121157 300 0.054999 0.176156 400 0.051686 0.227841 500 0.048380 0.276221 600 0.045309 0.321530 700 0.042473 0.364003 800 0.039799 0.403802 900 0.037233 0.441035 1000 0.035023 0.476058 1100 0.032837 0.508896 1200 0.030666 0.539562 1300 0.028847 0.568409 1400 0.027079 0.595487 1500 0.025385 0.620872 1600 0.023770 0.644642 1700 0.022227 0.666869 1800 0.020856 0.687725 1900 0.019498 0.707223 2000 0.018395 0.725618 2100 0.017145 0.742763 2200 0.016070 0.758834 2300 0.015089 0.773923 2400 0.014114 0.788037 2500 0.013240 0.801276 2600 0.012481 0.813757 2700 0.011596 0.825353 2800 0.010951 0.836304 2900 0.010233 0.846537 3000 0.009603 0.856140 3100 0.008970 0.865110 3200 0.008467 0.873577 3300 0.007910 0.881487 3400 0.007390 0.888877 3500 0.006954 0.895831 3600 0.006497 0.902328 3700 0.006113 0.908441 3800 0.005709 0.914150 3900 0.005418 0.919568 4000 0.005028 0.924596 5000 0.035789 0.960385 6000 0.018845 0.979231 7000 0.009932 0.989162 8000 0.005181 0.994343 9000 0.002689 0.997032 10000 0.001422 0.998454 11000 0.000730 0.999185 12000 0.000397 0.999581 13000 0.000196 0.999777 14000 0.000104 0.999881 15000 0.000055 0.999936 16000 0.000030 0.999966 17000 0.000015 0.999981 18000 0.000009 0.999990 19000 0.000004 0.999994 20000 0.000003 0.999997 21000 0.000001 0.999998 22000 0.000001 0.999999 23000 0.000000 0.999999 24000 0.000001 1.000000 Total 1.000000

The question for the poll is do you find this information interesting enough to make a Wizard of Odds page on it, including similar tables for other common video poker games?
It's not whether you win or lose; it's whether or not you had a good bet.
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
April 12th, 2016 at 8:28:21 AM permalink
For clarity, when you say 100, do you mean 100 credits (=20 5-credit bets) or 100 bets (=500 credits)? While rare on the LV Strip, some single-line VP games elsewhere have more than 5 credits max (e.g., 10 or 20, especially on 5c games), and sometimes it takes more than 5 credits to qualify for the 800-to-1 royal payout.

To your poll, I think it'd be interesting to do an exploration of not just the royal but other big hands -- SF, quads, bonused quads for those games (e.g., 4 A w/ 2,3,4). In other words, based on the paytable, you could provide stats on how much bankroll you'd need to hit a hand worth >=N credits with X% likelihood before busting, where N is 4000, 2000, 1000, etc.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
Ibeatyouraces
Joined: Jan 12, 2010
• Posts: 11933
April 12th, 2016 at 8:32:56 AM permalink
I'm assuming, that's assuming you follow optimal strategy?
DUHHIIIIIIIII HEARD THAT!
Romes
Joined: Jul 22, 2014
• Posts: 5514
April 12th, 2016 at 8:43:14 AM permalink
I agree, for clarity what does 1 unit mean? If it's a \$1 machine, is 1 unit \$1, or the standard \$5 bet (one game)?

I like the info though... More information is never a bad thing, and this is something I'd imagine a lot of non AP's ask. I could see this having use on your WOO page for non-AP's that search for such info.
Playing it correctly means you've already won.
RS
Joined: Feb 11, 2014
• Posts: 8623
April 12th, 2016 at 8:46:59 AM permalink
1 unit = 5x\$1

"For example, if you come with 800 bet units..."

I'd be more interested in knowing how you came up with the numbers you did than the actual answer.
Wizard
Joined: Oct 14, 2009
• Posts: 23298
April 12th, 2016 at 8:57:08 AM permalink
A "unit" means a full bet. For example, on a quarter machine it would be \$1.25.

Yes, optimal strategy.
It's not whether you win or lose; it's whether or not you had a good bet.
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
April 12th, 2016 at 3:38:19 PM permalink
Quote: MathExtremist

I think it'd be interesting to do an exploration of not just the royal but other big hands -- SF, quads, bonused quads for those games (e.g., 4 A w/ 2,3,4). In other words, based on the paytable, you could provide stats on how much bankroll you'd need to hit a hand worth >=N credits with X% likelihood before busting, where N is 4000, 2000, 1000, etc.

yes, yes
I am all for that

of course, time has to be included
http://wizardofvegas.com/forum/gambling/video-poker/19692-what-are-the-odds-of-hitting-a-royal-flush-with-a-4000-bankroll-before-going-bust/

800 units starting
9/6 JOB
prob of success = 0.53186416 (Royal B4 Ruin)

avg # of hands to either = 21,482 (hello)
I never did do the math for ruin and success separately
(maybe later)

Sally
I Heart Vi Hart
Wizard
Joined: Oct 14, 2009
• Posts: 23298
April 14th, 2016 at 6:34:40 PM permalink
I just finished my latest page, Royal or Bust, which is all about this topic. It also has tables for bankroll requirements for wins of 200 or more, and 25 or more.

As always, I welcome comments, questions, and especially corrections.

Thank you.
It's not whether you win or lose; it's whether or not you had a good bet.
Ibeatyouraces
Joined: Jan 12, 2010
• Posts: 11933
April 14th, 2016 at 7:48:47 PM permalink
Requirements for AWAK on DDB, TDB, etc., would be interesting also as these games are pretty popular.
DUHHIIIIIIIII HEARD THAT!
beachbumbabs