VPW Bankroll Calculator Question

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Mr.Dawes
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Joined: Wed Apr 15, 2015 12:05 am

VPW Bankroll Calculator Question

Post by Mr.Dawes »

Recently the IP casino in Biloxi added 9/6 JoB quarter machines. To my knowledge this is the best quarter paytable in Biloxi.I have to decided to learn the game and I am using VPW software. I used the Bankroll Calculator tool to look at risk of ruin over 50,000 hands. As my computer ran the numbers I was watching the categories "Chance of Profit" and "Chance of Loss". Initially the Chance of Loss steadily increased, then slowed around 6,000 hands when it reversed and the Chance of Loss began to decrease. It continued to decrease until about 25,000 hands when it began to increase again.At first I attributed the initial change in direction to the increased chances of catching quads, straight flushes and royals which could decrease your chance of losing. But when the chance of loss started increasing again at 25,000 hands I doubted this explanation.Does anyone know why this change in direction occurred? Since the game is -.46 shouldn't the chance of loss only increase over time?Thanks in advance for any thoughts.


Vman96
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Post by Vman96 »

Not 100% positive on this, but I want to say this is due to the "skew" of video poker payouts.

The worst you can do at any given hand is lose one betting unit. But with a royal you can win 800 units.

Let's consider your approximate expected return over time if you fail to hit a royal. The expected return without a royal is 97.56%, or an expected loss of 0.0244 units per hand.

So the expected number of betting units lost without a royal after 6k hands:
0.0244 x 6000 = 146.4 betting units

At this point, since quads are only 25 units each, you are now in a big enough hole where the most likely event to bail you out as a winner after 6000 hands is a Royal. And the more hands that you play, the probability of you hitting at least one Royal increases.

Probability of hitting at least one Royal:
1 hand: 1 in 40390 = 0.002476%
100 hands: 1 - (40389/40390)^100 = 0.2473%
1000 hands: 1 - (40389/40390)^1000 = 2.45%
6000 hands: 13.80%
10000 hands: 21.93%
15000 hands: 31.02%
20000 hands: 39.05%
25000 hands: 46.15%
30000 hands: 52.42%
35000 hands: 57.96%
40000 hands: 62.86%
45000 hands: 67.18%
50000 hands: 71.00%

75000 hands: 84.38%
100,000 hands: 91.59%

And so on...

But as you keep playing...

Expected loss without a royal after 25,000 hands:
0.0244 x 25,000 = 610 units

Now the expected hole is big enough were if you have ran below average in other categories like quads and straight flushes, there is a chance that even one royal wouldn't pull you out of the hole. The longer you play, then the house edge grinds you down. When you play an entire royal cycle of 40,390 hands, the house is expected to win:

40,390 hands x 0.0046 betting units = 186 units

So after a royal cycle of hands played you should expect to be almost a quarter of a royal in the hole. And this is even a full pay machine! Think of how it is for the 8/5 DDB players on this forum!

Mr.Dawes
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Joined: Wed Apr 15, 2015 12:05 am

Post by Mr.Dawes »


Hey Vman96 thanks for all the time and thought you put into this. It really helped clarify my thinking. In addition to the chance of loss I also have to think about the amount of loss. Since a losing hand is more likely than a winning hand, early on the chance of loss would rise. Also, the frequency of high payout hands is low and the amount of loss will likely accumulate as you play. Then, at some point in play of each different game I think there will be a point when the rising chances of hitting a high payout hand a would begin to reduce the chance of loss. But eventually the house edge will raise the amount of loss so high that you are unlikely to dig out of the hole and the chance of loss only increases.If this theory is basically correct I would think a game that offers more high payout hands would reach this initial inflection point earlier. However, since these games have higher variation the second change back to increasing chance of loss would also occur earlier. I ran the bankroll calculator on 9/5 DDB, the best quarter DDB in Biloxi. In only 50 hands the chance of loss peaks at 77%. Then the chance of loss reduces until around 5,000 hands (65.45%) where it begins to increase again continually through 50,000 hands, and I am guessing increases permanently.

Mr.Dawes
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Joined: Wed Apr 15, 2015 12:05 am

Post by Mr.Dawes »


Probability of hitting at least one Royal:
1 hand: 1 in 40390 = 0.002476%
100 hands: 1 - (40389/40390)^100 = 0.2473%
1000 hands: 1 - (40389/40390)^1000 = 2.45%
6000 hands: 13.80%
10000 hands: 21.93%
15000 hands: 31.02%
20000 hands: 39.05%
25000 hands: 46.15%
30000 hands: 52.42%
35000 hands: 57.96%
40000 hands: 62.86%
45000 hands: 67.18%
50000 hands: 71.00%

75000 hands: 84.38%
100,000 hands: 91.59%

BTW, thanks a lot for this. Don't know why I didn't realize how to figure that out myself.

FloridaPhil
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Post by FloridaPhil »




[quote=Mr.Dawes]Recently the IP casino in Biloxi added 9/6 JoB quarter machines. To my knowledge this is the best quarter paytable in Biloxi.[/quote]9/6 quarter Jacks at the IP.  That's some news.  How many machines do they have?  Are they stand up or sit down?   Thanks for the report!



Mr.Dawes
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Post by Mr.Dawes »


They have 4 sit down machines on the second floor just outside the Cove Bar. This is a non smoking area which I like. They have a sign above the machines that says best Video Poker payback in Biloxi. Which is true for the 9/6 JoB. However, all the other games on those same machines have paybacks lower than 98%.They also have 8/6 Bonus Deluxe at the quarter level against the wall upstairs in the back corner. This is about a 98.5% game. Right now the IP is really the best quarter option in Biloxi. In addition to those games they also have airport deuces at the Insomnia Bar which also has a progressive Royal payout.



alpax
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Post by alpax »

To add to what Vman contributed with regards to royal flush cycles and the noticeable change you see at the 25000 hand mark, the best way to explain to you about the change in the curve direction at around the 6000 is indeed related to the first straight flush cycle on the game (1 in 9148). The straight flush has more of an impact on Jacks or Better than it does on a DDB which quads have greater impact.

Another way to calculate odds of cycles is to use the Euler's constant (e is about 2.718) to the power of negative number of rounds divided by expected cycle.

1 - e^-( number of rounds / expected cycle)

1 - e^(-6341/9148) ~= .5
1 - e^(-9148/9148) = 1 - e^-1 ~= .64 so playing 9148 hands the exact cycle amount gives you 64% chance to hit the straight flush.

If you played 6341 hands of Jacks or Better, you have* 50% chance of hitting a straight flush and the odds of hitting it get slightly better as you play, that adds 250 credits back to your bankroll hence the shift in the curve.

I'll come back to this thread with more information/advice as I have limited time at the moment. I use the Bankroll feature quite a bit on VPW.

FloridaPhil
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Posts: 6229
Joined: Sat Jul 19, 2008 11:28 am

Post by FloridaPhil »


[quote=Mr.Dawes]Right now the
IP is really the best quarter option in Biloxi. In addition to those
games they also have airport deuces at the Insomnia Bar which also has a
progressive Royal payout.[/quote]Sounds like the thing to do is to stay at the Beau Rivage and play at the IP.  At least someone picked up where Margaritaville left off.   I read the other day where the Biloxi gambling revenue is up since the Scarlet Pearl opened, but  It's nowhere near the traffic they had before Katrina.  Players will come back if the odds are decent. 

olds442jetaway
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Post by olds442jetaway »

I have almost never hit a Royal without hitting a straight flush on job in the same session in a lifetime of playing vp. I am so sure of this that one time I bet my friend who plays only slots a fancy casino dinner that I would hit a Royal later in the session. He happened to be walking by just as I hit the straight flush. Who wouldn't take that bet....He lost. This was about ten years ago. This unusual event is still holding up even this year. Strange. I certainly cannot explain it. Somewhere along the line, I posted about this before. I just can't remember when.

Mr.Dawes
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Joined: Wed Apr 15, 2015 12:05 am

Post by Mr.Dawes »

Thanks Alpax, the info about the straight flush cycle and its importance to JoB payout makes sense. I appreciate your input.


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