Bankroll requirement to hit a royal

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?

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.

I'm assuming, that's assuming you follow optimal strategy?

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.

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.

A "unit" means a full bet. For example, on a quarter machine it would be $1.25.

Yes, optimal strategy.

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
this is like the thread
https://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 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.

Requirements for AWAK on DDB, TDB, etc., would be interesting also as these games are pretty popular.

Very useful, and well organized, Wizard!

I think there's a paste-o at the very end, after the 25 or bust table. The short synopsis is captioned as "average bankroll needed for a royal or bust", probably copied from above and not amended....

This is great information. Thanks. I am also curious if playing multihand games affect the probability? Or do u just take the total wager per game regardless of number of hands or the denom? What about games like STP or Ultx?

If the average bankroll for DDB is 1548 units of $1.25 to hit a royal which is almost $2.000 why play when the royal only pay $1,000?

Quote: brettecantwell

This is great information. Thanks. I am also curious if playing multihand games affect the probability? Or do u just take the total wager per game regardless of number of hands or the denom? What about games like STP or Ultx?

Yes, multihand games affect the results as multihand video poker has a different variance than single line video poker. Same with STP and Ultimate X, you have to factor in multiplier wins.

Nice stuff Wiz, thanks for putting it up!

Quote: dwsblue

If the average bankroll for DDB is 1548 units of $1.25 to hit a royal which is almost $2.000 why play when the royal only pay $1,000?

Other aspects of the game make it entertaining to some. If your goal is to gain money, the casino is a tough place to do it in for many. The average loss in 40,000 hands of quarter 9/6 DDB (about the number of hands needed to hit 1 royal on average) is $510 with optimal play.