An insight into Mickey Crimm’s math background

[mickeycrimm]

The video keno games I play are either banking or progressive games. This example was neither. I just used it as an example of how to do keno math. The object of doing the math is to determine if the player has an advantage.

Gambling math is pretty simple. It's just addition, subtraction, multiplication and division. There's no "stochastics" or "heuristics" or "geometic distribution." It's just simple math.

Just for fun and if anyone reading this wants another way to solve it which (imo) isn't, "Too fancy," here's how I would do it:

BASE PAYS:

Like Mickey says, just use the WoO Keno Calculator:

2/4: 0.212635465800023

3/4: 0.216239456745786

4/4: 0.199120499753411

BASE GAME TOTAL: 0.627995422299220, which we can just call 62.8%.

GETTING TO THE BONUS GAME:

The only possible mistake someone can make here is trying to come up with a bunch of ridiculous scenarios where a win on the base game impacts the probability of getting the 3/3...which in certain cases you WOULD need to know because there is at least one game where a win on the base game AND hitting the 3/3 combination is required. Fortunately, this is not one of them.

For this, I also use the WoO calculator (without attributing any pays---because just going to the bonus pays nothing) and lift the probability for 3/3, which is:

0.013875365141188

FREE GAMES RETURN:

The next step is to determine the overall return of the Free Games (as a whole) which we will then take and multiply by the probability of going to the Free Games, then having determined that, add to the base return.

Since it's a weird number of draws, we can't cheat with the WoO Calculator.

4/4 = 130
3/4 = 10
2/4 = 2

For this, I like to use an online scientific calculator you can find here:

https://web2.0calc.com/

(nCr(4,2)*nCr(76,22)/nCr(80,24)) * 2 = 0.5374878286270691

(nCr(4,3)*nCr(76,21)/nCr(80,24)) * 10 = 0.7166504381694255

(nCr(4,4)*nCr(76,20)/nCr(80,24)) * 130 = 0.8734177215189873

MickeyCrimm added them up and got 2.1276 units/game on Free Games, and:

0.5374878286270691+0.7166504381694255+0.8734177215 189873 = 2.1275559883154819

I agree with that, except I haven't rounded off yet just because I took the results the way the calculator gave them to me. Now, multiply by the number of Free Games:

2.1275559883154819*12 = 25.5306718597857828

Which is the expected return of all Free Games, so all that remains is to multiply that by the probability of Free Games:

25.5306718597857828*0.013875365141188 = 0.3542473943543810567001571019664

Which gives us our added expected return (per unit bet) that comes from Free Games, which we can call 35.4%, add to 62.8% and get 98.2%. Therefore, my results agree with those of MickeyCrimm with differences due to the way we rounded. It's not positive, anyway, so there would be very limited scenarios where I would care about this game.

Of course, if I had a multiplier day such that it came up to 2% return on the points multiplier and there was no reasonable video poker at this location (or any positive machines) this would be a good machine to know if I needed to earn points anyway...obviously I would not play this for well under a 0.5% edge alone.

Thanks for the online calculator link.

[mickeycrimm]

COMBINATORIAL FUNCTION

I also want to mention that I don't use the Combinatorial function to look fancy, or anything like that. There are a few reasons why I like it, which include:

1.) I think it's really fast for all Keno-related math and lots of playing card probability math.

2.) You can easily check your work as you go: The first numbers in each parenthesis on the left side of the multiplication symbol (*) should ALWAYS add up to total whatever is on the left side of the parenthesis on the right side of the multiplication symbol. Same thing with the right side of it, let's break this down in simple terms to see what it means in plain English:

(nCr(4,2)*nCr(76,22)/nCr(80,24)) * 2 = 0.5374878286270691

There are 4 numbers that help me and 76 that do not for a total of eighty numbers. Of 24 total balls to be drawn, I want to know how likely it is that I get 2 numbers that help me which must mean I get 22 numbers that do not help me.

And...that's it. That's all you're asking. If you wanted to know how likely hitting 5/7 is in the same scenario, you'd just do this:

(nCr(7,5)*nCr(73,19)/nCr(80,24)

For this, the left side parenthesis numbers should still always add up to be the same as the spots on the right. No double-checking needed aside from that.

3.) Very copy-pastable. You can type the equation into the calculator and copy/paste over, or type it on your sheet and move it to the calculator. At that point, you can copy/paste the answer from the calculator back to your document or post.

4.) (ADDED) Also relatively easy to do from your phone if you need Keno math on the fly.

I need to practice doing this with that calculator you put up. Today's modern video keno games are much more complicated than the old "pick ten numbers then get paid according to how many numbers out of ten you hit." The games I play at advantage are either banking or progressive.

One game in particular has run its course so I don't mind talking about it. It's a game called Gumball Falls. It has progressive free games to be won, along with progressive multipliers to be won, along with progressive extra draws to be won. At reset the meters look like this:

Free Games = 5
Multiplier = 2
Extra Draws = 3

But when I would come along and punch the game up I might see:

Free Games = 12
Multiplier = 7
Extra Draws 13

In a rare scenario I might find a highly lucrative play like:

Free Games = 21
Multiplier = 17
Extra Draws = 24



While all these meters were accumulating numbers the game would go through 4 different modes:

In mode 1 by hitting 4 out of 4 machine picks you win Free Games plus Multiplier.

In mode 2 by hitting 4 out of 4 machine picks you win Free Games plus Extra Draws.

In mode 3 by hitting 4 out of 4 machine picks you won a progressive multiple of the bet.

In mode 4 by hitting 4 out of 4 machine picks you win Free Games, Multiplier, Extra Draws.

The game would spend just about equal time among the 4 different modes. You obviously want to hit the 4-spot in mode 4 but most of the time have to settle for modes 1, 2 and 3.

The meters would reset when hit causing a reevaluation of the play after every 4-spot hit. Of course, when you hit in mode 4 the play was automatically over with the FG, M, ED meters all resetting.

Since the free game, multiplier, extra draw meters could be on so many different numbers it took me a long time going over all the various scenarios that were positive plays.

That online calc that Mission put up would have saved me a lot of time figuring that damn game out.

Overall, it was a fun game to play. Imagine playing a 6-spot with a base payscale of about 70%, you win 19 free games with a 15X multiplier for that payscale and 25 extra draws per free game.

At 20 balls drawn from 80 the freq. of hitting all six numbers is 7753. But with 45 draws the frequency is just 37.

[mickeycrimm]

Bump. It's been very interesting revisiting this old thread. Ex-AP was always trying to shame me for my gambling knowledge. Here he is striking again.

He was always talking about stochastics, heuristics, geometric distributions, shit like that, that has no bearing in determining if a play is positive or negative.

So I put up a payscale to a keno game and asked him if the game was positive or negative. It's an easy equation to figure for someone that's knowledgeable in gambling math. Takes just a few minutes.

I had put up math problems for certain games before and asked if it was positive or negative. I would devise a game that was positive by 3% or 4%.

I would get answers back like "that's obviously positive" or "looks positive to me" or "If it wasn't positive you wouldn't have put it up." But none of them ever did the math. They were just guessing. And they guessed right. That taught me a lesson.

So when I challenged Ex-AP I intentionally made the payscale slightly negative in case he tried the "looks positive to me" without putting up any math. I would have him trapped if he did that.

So I put the negative payscale up and it worked like a charm. Except it wasn't Ex-AP that bit. Ex-Ap had headed for the hills. I scared him so bad he never made another post in the thread. It was....MAXPEN that took the bait.

In post #8 maxie wrote:

"Instinctually this looks really good. You're playing about a 1/3 loser 2/3 of the time but the other 1/3 of the time you're getting about 130% at no additional cost."

Of course, maxie was wrong about the play being good. It was a 98% game. His critical mistake was he guessed the play was positive or I wouldn't have put it up. He followed with "I'm looking forward to the math lesson" that I had promised to put up.

That is very revealing. Maxie, the self professsed "most advanced AP" on VCT couldn't do the math to a simple keno game.

I kept my mouth shut in the thread about maxie's mistake because it wasn't him I was after. And since we were on good terms I didn't want to make him look bad.

After I put up the math to the play, in post #15, maxie wrote:

"But thanks for the math lesson Mickey. You actually laid out the solution in an elementary manner making it easy to understand. Seems like when you try to read some of these explanations about calculating combinations the writers always want to complicate it."

So here is maxie praising me for my work. Thats how it used to be.But that all changed when a few months later I gave my opinion that Rob Singer likely put down the double up play.

Maxie became outraged at my opinion and started delivering viscious and insulting ad hominem attacks on me.

Just a damn opinion and maxie went berserk over it.