Advantage Tactic: Early Estimates on a Spin Banker
In the last couple of articles, I made up a bunch of numbers and games to demonstrate the value of gathering data. In this article, I’m going to use a real machine and show a subset of the real data I personally gathered.
I won’t mention the name of the machine, but I think it will be apparent pretty quickly.
This game banks spins in three buckets, let’s call them Mini, Maxi, and Mega. Any guesses on the game? Before you get too excited, this analysis is not going to give you the real break-even point on the game. It is going to show you how I approached this game and I started to narrow in on what I know today. I don’t want to sound harsh, but I’m not here to do your work for you; I’m just trying to help show you how to do the work that needs to be done.
Here is a subset of the data I recorded the first 36 times I played this machine. Notice I lost an average of 1.69 bets every time I sat down. That’s not what I wanted to happen. I’d better learn something from my mistakes.
I actually recorded a lot more data than what you see here, but I’m abbreviating the dataset because it’s all I need to get to something fun… With no more information than what you see here, I can devise a “count” to tell me where this data says the break-even point is for this machine. The math will get a little complicated, but the results will be simple and useful.
Hang on, Baby Jesus, this is gon' get bumpy! – Ricky Bobby
I learned about doing regression analysis when I was a senior in college. Because this math is on the complicated side, I’ll save you the details of doing it by hand… In fact, I think I’ve only done a single regression analysis by hand myself, and all I really learned from that is there is a definite place in the world for computers and software. With that said, I’ll show you a free tool you can use online to do this type of analysis later in this article. Before I do that, let’s talk a little about what a regression analysis is and how it applies to the problem at hand.
A regression takes data points and draws the best “line” it can through the data points by minimizing the total variance of the data points to the “line”. There are lots of different regressions you can run, but the one you want to use is called OLS (ordinary least squares). The reason you want to work with OLS is because your output will give you simple mathematical functions, specifically multiplication and addition. If you want to know more about OLS, I can recommend some junior and senior level college courses or some web sites, but I’m not going to get into all of the details here.
To do a regression analysis, you need an idea. My idea was that the banked spins would reach a point where the game would have a positive tipping point.
I wrote my idea in an OLS friendly form. Here is what my formula / idea looked like:
Break Even = Mini Spins * A + Maxi Spins * B + Mega Spins * C – the game drop
The regression analysis will tell me what values best fit A, B, and C as well as give me a conversion value to what the primary game does and how all that translates to game return.
Here is the long awaited tool for doing a regression analysis: http://www.xuru.org/rt/MLR.asp#CopyPaste
I like this tool because it is free, easy, and it works.
As soon as I put my data in the tool, it spits something out that looks like this:
Y = 2.429918446 * X1 + 1.29792787 * X2 - 1.062254166 * X3 - 82.10776899
Compare this to my theory:
Break Even = Mini Spins * A + Maxi Spins * B + Mega Spins * C - the game drop
Houston, we have a problem! My theory says mega spins should add value, the output says mega spins will take away value. That’s not right. Something is going on with the mega data that is causing a problem… I think I know what it is… I only hit one mega in the first 36 events, it was tiny, and it paid horribly. As a result, the more EV that lived in the mega was just more stored value in the machine I didn’t take down. The conclusion I’m drawing from this is that 1) I don’t have enough data on the mega and 2) that’s because the mega is hard to take down.
My solution is to say “F” the mega and revise my theory on how this machine works… New hypothesis:
Game Return = Mini Spins * A + Maxi Spins * B - the game drop (including the mega)
Now my dataset looks like this:
When I put this data into the OLS tool, I get this:
y = 3.481487604 * x1 + 1.419057454 * x2 - 155.3201563
Ok, now we have a formula that aligns with my theory. So far, so good… But I have two problems I need to deal with still.
1) What is the break-even point?
2) I can’t do this math in my head.
Let’s deal with the break-even point first.
If I set Y to 0 (no win) and I set one of the banked spin amounts to the reset value of the game, I have an algebra problem I can solve to obtain the other banked spin value. Here is what that looks like:
Before you jump on me for this being wrong, I am well aware now that this is not the real break-even point for this game. I was not well aware of that after I had played only 36 times. This analysis is the reflection of what I could figure out after a week of part time play.
On to the last problem… Now all I need to do is multiply the 7 mini spins by 3.481487604 and add that to the 92 maxi spins multiplied by 1.419057454. You can do that in your head right? No? Me either! Let’s fix it.
Fixing decimals like this is a little art and a little science. I probably need to write a whole additional article, but to save us some time if I multiply both of the long decimals by another long decimal, specifically 2.872335374. Doing so gives me this:
I’m going to go ahead and round that number that is just bigger than 4 to an even 4.
Now I have math I can do in my head… 10*Mini Spins + 4*Maxi Spins… Is this starting to sound familiar?
All that’s left is to adjust my break even spin analysis to the count I just produced.
- 7 mini spins * 10 + 92 maxi spins * 4 = 438
- 41 mini spins * 10 + 8 maxi spins * 4 = 442
You’ll notice the end numbers don’t match… That’s because I’ve been rounding everything. I’m making an executive level decision on this one and splitting the difference between the two numbers. For now, the break-even value in this analysis is 440.
If you put all the pieces together, you have:
Break Even = Mini Spins * 10 + Maxi Spins * 4 = 440
Did anyone ever mention a formula similar to this to you? I’ll bet they did… Maybe the number at the end was slightly different… That variance would have come from how much data they had and how they ran on the machine. Either way, now you know how the formula you were using came to be.
I’ll say this one more time. I know this analysis is not an accurate depiction of the break-even spot of this game. I’ve learned a lot since the first 36 times I played the game, but when I got this information I was able to start targeting machines more strategically than I could before I had this data. Funny enough, after I had this information, I stopped losing 1.69 units per play and I started making a few bucks instead.
Remember to keep growing your data set. The more data you have the closer you will get to the real break-even point.