Bankroll Calculator by game

Is there a bankroll calculator on the Wizard of Odds site? I don't see it.

Can anyone direct me to one where I can put in a specific video poker game and a coin in goal to get an appropriate bankroll. I am trying to understand reasonable bankrolls for a promotion that requires $250,000 coin in. The best games they have are 8/5 Bonus poker that pays back 99.17%. They have everything from 3/5/10 play $1/$2/$5 machines and even a hundred play quarter 8/5 BP machine. I realize I have an expected loss $2,075 but don't know how much cash to take.

Quote: DRich

Is there a bankroll calculator on the Wizard of Odds site? I don't see it.

Can anyone direct me to one where I can put in a specific video poker game and a coin in goal to get an appropriate bankroll. I am trying to understand reasonable bankrolls for a promotion that requires $250,000 coin in. The best games they have are 8/5 Bonus poker that pays back 99.17%. They have everything from 3/5/10 play $1/$2/$5 machines and even a hundred play quarter 8/5 BP machine. I realize I have an expected lose $2,075 but don't know how much cash to take.

I don't know what your other considerations are, but generally speaking, you're going to reduce Variance (greater chance of approaching the ER) by betting as little as possible per play. When you say three play, I'm assuming that you still bet 5 units per hand and are therefore still betting $15/three hands on that game, is that right? That would be 16,667 plays, at that level.

I think where you might run into some trouble is that the RF represents almost 2% of your return, and the chance of hitting one in that number of plays is:

0.000025

(1-0.000025)^16667 = 0.6592317029175441--- 1-0.6592317029175441 = 0.34076829708245593 or 34.1%. Not hitting one could potentially hurt you.

If you disclude the possibility of a Royal Flush, but have everything else hit as probability dictates, then your return is:

0.991660-0.019884 = 0.971776

1 - 0.971776 = 0.028224000000000027

0.028224000000000027 * (15 * 16667) = 7056.141120000007 or a loss of $7,056.14

---

You could also subtract the 34.1% probability of hitting the Royal from the ER lost of not hitting it:

0.019884 *0.34076829708245593 = 0.006775836819187553

0.019884 - 0.006775836819187553 = 0.013108163180812445

0.991660 - 0.013108163180812445 = 0.9785518368191876

1 - 0.9785518368191876 = 0.02144816318081244

0.02144816318081244 * (15 * 16667) = $5362.15

MY CONCLUSION

There are certainly better people qualified to determine RoR than myself on here, but I noticed this post went awhile without a response. I don't like the most recent formula for expected loss because you either hit a RF or you don't. I'd assume that you don't hit it. You have a really good chance of hitting an SF in that many plays, but maybe assume you don't hit one of those either.

Just based on the RF, SF, 4Aces expected frequencies...I should think $10,000 to be a fairly safe amount. Hopefully, someone who does simulations of this stops by. This is by no means a complete analysis, nor is it even that great of an analysis on the Royal. I just kind of wanted to fill some time and bump the thread for you.

If you would like, I could move this thread to Video Poker as it may be more appropriate there, and people may follow that who do not follow General Discussion. It's fine for GD, though, so please advise.

Fwiw, I can almost guarantee to make it to $25k on $500, playing $1 8/5 BP...so I would think $5000 would hold you over...

(I can't do the math) but state the following:

Risk of ruin acceptable to you. You need a specific number, playing at 5 cents per hand for a 250k coin with 100k still has a risk of ruin. You could also start with a bankroll and ask for RoR.
Specific game including plays and unit.

I don't know of a calculator for this, but if you give maybe 2-3 different scenarios someone here might take the time to help you out. Your current question is just too vague for someone to give you a legitimate numerical answer which is what I think you're after.

Quote: ahiromu

(I can't do the math) but state the following:

Risk of ruin acceptable to you. You need a specific number, playing at 5 cents per hand for a 250k coin with 100k still has a risk of ruin. You could also start with a bankroll and ask for RoR.
Specific game including plays and unit.

I don't know of a calculator for this, but if you give maybe 2-3 different scenarios someone here might take the time to help you out. Your current question is just too vague for someone to give you a legitimate numerical answer which is what I think you're after.

I guess I am just trying to find the bankroll amount that gives me a 95% chance of not losing it while playing 8/5 BP for $250k coin in.

Quote: DRich

I guess I am just trying to find the bankroll amount that gives me a 95% chance of not losing it while playing 8/5 BP for $250k coin in.

What kinda time period are we talking?
I probably give $250k over the course of 12 months, so I spread it out, and never take more than $1000 with me and I've never lost it all...

If you have to put it in over like a weekend then I'd seriously say have a few thousand on hand...
From what you said, play 16-handed 25c ($10 a whack)...could crack it out in a good solid weekend...

Quote: TIMSPEED

Fwiw, I can almost guarantee to make it to $25k on $500, playing $1 8/5 BP...so I would think $5000 would hold you over...

I think this is a reasonable estimate and is part of my strategy for hitting 7Stars this year. But if you read my latest update, I have fallen behind, and I haven't had a royal yet which would change everything.

But I came up with $500 cash for $25,000 coin-in playing single line at $2 per coin. Does he see fewer royal flush draws playing $15 per push of the button with a three-play machine? I'm not sure what the math says about this.

Quote: DRich

Is there a bankroll calculator on the Wizard of Odds site? I don't see it.

I have not seen one.
VP for Winners has the ability to calculate Risk of Ruin for specific games, pay tables and bankroll.
It actually calculates the probabilities.
So for a 5 coin $1 bet you would need 50,000 hands played and the program will take a long time to work thru that.

It does the multi-hand games too and that would require less hands played, so it might work for you.
The program is free to use for I think 10 days, you can look into it.

http://www.beatingbonuses.com/simulator_java.htm

has a simulator (the calculator says it is not accurate for video poker)
I have not really used it much for multi-hands, I would have to read the instructions thru, they seem a little comfusing at first read.

The sim for 250000 and 1 (1 hand played) returns a 5% R0R at $6000 bankroll
a .6% ROR at $7500
and 13% at $5000
but I gather you really want to play more than one hand at a time.

Hope it helps out.
Bankroll ROR using standard deviation values for VP are really unreliable for under 500,000 hands played.

Quote: AlanMendelson

I think this is a reasonable estimate and is part of my strategy for hitting 7Stars this year. But if you read my latest update, I have fallen behind, and I haven't had a royal yet which would change everything.

But I came up with $500 cash for $25,000 coin-in playing single line at $2 per coin. Does he see fewer royal flush draws playing $15 per push of the button with a three-play machine? I'm not sure what the math says about this.

The main thing the math says is that his expected loss is over 7k if he does not hit the RF, I would not count on 5k being enough to hit 250k coin-in.

5000/0.028224000000000027 = $177154.20, which is the expected coin-in if he fails to hit a RF based on a BR of 5k.

7056.14/0.028224000000000027 = $250,004.96

In the amount of plays he is expected to make to have that kind of coin-in, he should not hit a RF, I'm fairly confident about that.

According to the Wizard

https://wizardofodds.com/ask-the-wizard/video-poker/multi-hand/

The odds of drawing a Royal are as follows, pursuant to the number of cards discarded for three hands:

5: .000008
4: .000017
3: .000185
2: .002775
1: .063830

The odds of drawing a Royal Flush in standard VP are as follows, again, pursuant to the Wizard:

https://wizardofodds.com/ask-the-wizard/video-poker/probability/

1. 1/47
2. 1/combin(47,2) = 1/1081
3. 1/combin(47,3) = 1/16215
4. 1/combin(47,4) = 1/178365
5. 4/combin(52,5) = 1/2598960 (Dealt)

OR:

1. 0.02127659574468085
2. 0.0009250693802035153
3. 0.00006167129201356769
4. 0.000005606481092142517
5. 3.8476929233231754e-7

You will see 3x as many starting hands playing one hand at a time, so we will multiply those results by three.

0.02127659574468085*3 = 0.06382978723404255
0.0009250693802035153*3 = 0.002775208140610546
0.00006167129201356769*3 = 0.00018501387604070307
0.000005606481092142517*3 = 0.00001681944327642755

Conclusion

I would have thought effect of removal would have played a factor in this, given that only one deck is used, but I guess not. For example, I would have looked at it this way for drawing one card to three hands:

1/47 + 1/46 + 1/45 = 0.06523794840168569

Which would make it slightly more likely to draw to a Royal in this situation. It would be more likely for other draws, as well, but I suppose this is incorrect for some reason.

Variance

The other thing to consider is that one is playing fewer starting hands, so as a necessary result, one should see fewer hands (playing optimal strategy) in which one is drawing to a Royal in any discard situation as opposed to just playing one hand at a time.

Quote: 7craps

http://www.beatingbonuses.com/simulator_java.htm

has a simulator (the calculator says it is not accurate for video poker)
I have not really used it much for multi-hands, I would have to read the instructions thru, they seem a little comfusing at first read.

The sim for 250000 and 1 (1 hand played) returns a 5% R0R at $6000 bankroll
a .6% ROR at $7500
and 13% at $5000
but I gather you really want to play more than one hand at a time.

Hope it helps out.
Bankroll ROR using standard deviation values for VP are really unreliable for under 500,000 hands played.

7Craps, you are and will forever be the man!

http://www.beatingbonuses.com/simulator_java.htm

It basically says to use the amount you wish to play per hand on the wager, which is $5.00.

DATA

Deposit: $7060
Wagering: $250,000
Bet Size: $5
Runs (Simulations): 100,000

RoR at $7,060 coin-in = 23.94%

RoR at $5,000 coin in = 46.23%

RoR at $10,000 coin-in = 5.03%

RoR at $15,000 coin-in = 0.02%

RoR at $12,500 coin-in = 0.56%

I am now running a simulation in which I have changed the pay on an RF to 0 in order to determine your RoR at $5.00/hand assuming you do not hit the RF:

$5000 = 85%

$7060 = 57.20%

$10,000 = 14.66%

$15,000 = 0.07%

$12,500 = 1.83%

Ok Good.
I had run VP for Winners and got the same results for the $5k bankroll
that is good for the sim


I also ran 3Play at $15 total hand, $250,000 coin in at 16,667 hands played
I set $25000 to quit so the program would run faster.

At a 10K bankroll bust rate is 7.74%
So probably $11k would be 5% or so.


VP for Winners actually calculates the probabilities instead of doing just sims. It does take longer to run.
At least it can be used to check the results from the simulation site.

Good Luck

Thank you 7Craps and Mission. I was thinking $10k should be enough if i did it at $1 Triple Play but i guess I should take another couple thousand just in case. I think I will try and do it over two ten hour days. If I get too tired I can extend it another day.

a 12K bankroll returns a 2.12% chance of ruin
or about 1 in 48 at $1 3Play

Lots of Luck to you

Quote: DRich

Thank you 7Craps and Mission. I was thinking $10k should be enough if i did it at $1 Triple Play but i guess I should take another couple thousand just in case. I think I will try and do it over two ten hour days. If I get too tired I can extend it another day.

Man, I'm going to be honest with you..play the 25c 50-play (but only set it at 8 hands per shot)
TRUST ME! $5000 should be enough...
When I play fast on a multi-play (10 play or 50-play) I can get through 1000 hands per hour...so that's basically $5000 (or $10,000) per hour...if you have three days, it would be better...just hit like three 8-hour days, no problem...
I really hope you have a helluva bonus coming...cuz $250k is a LOT of action...and for that kind of action my casino (spread out over a year) would give you the house! (like 3 nights per week, $1000 a month cashback, tons of comps, etc)

Very interesting post. Good luck to you! Give us an update after your weekend. I would love to do the same thing some time.

ZCore13

DRich,

You're welcome!

I also figured out my error in determining the probability of drawing to a RF in Three-Play when drawing one card:

1/47 * 46/46 * 45/45 = 0.02127659574468085

46/47 * 1/46 * 45/45 = 0.02127659574468085

46/47 * 45/46 * 1/45 = 0.02127659574468085

0.02127659574468085 * 3 = 0.06382978723404255

The problem was simply one of known results. If one card makes the Royal, then the other two cards cannot possibly make it. My calculation from yesterday was giving each hand a 1/x chance of making the RF and I just summed those. Completely wrong. If you hit it on the first hand, you can't possibly make it on the next two. If you hit it on the second hand, then you already missed it on the first and cannot make it on the third. If you hit it on the third, then you've already missed it on the first two.