How to Calculate When a Game Becomes +EV

In my opinion, it is extremely difficult (if not impossible) to completely deconstruct a game mathematically, especially a complicated game like Hexbreaker or Buffalo Ascension. Update: Check out this Buffalo Link calculator for an example of a simple game where creating a mathematical model is possible.

I’ve seen APs share mathematical formulas for “solving” Hex. There are just way too many variables to solve a game that complicated with a simple formula. And unless you know the exact RTP of the specific machine you are playing, even a perfect formula wouldn’t be accurate.

I recently had a conversation with an AP who was trying to solve Buffalo Ascension. He spent many hours counting spins and tracking the data to try to determine how fast the reels would grow. But he completely missed how it states in the game rules that the reel height and specific prizes affect how quickly the reels move up. So to track it accurately, you would need to track spins separately for each reel based on its current height and prize above. This introduces way too many variables to make this a useful approach. Also, the number of spins to move a reel likely depends on the RTP of the particular machine you are playing. And some games actually have different metrics based on the bet level as well, so that introduces a whole other set of variables. So again, that is just way too many unknowns and too many variables for a single person to be able to track.

Here is another example...

There is an AP that I have shared many long emails with who claims to use “stochastic calculus” to solve games. He once claimed to have “solved” a game that wasn’t even an AP game (if he had read the rules screen, he would have realized this). When he started losing money on the play, he claimed the game must have gotten “nerfed” and that it was no longer profitable. He likely just experienced good variance at the beginning and then his luck caught up with him. He was too smart for his own good and made assumptions about a game that weren’t true. He spent more time solving the math of the game than actually playing it in the real world.

Another issue with solving a game mathematically is that it introduces situations where the EV might be more theoretical rather than realizable. If you need to play thousands or tens of thousands of sessions of a game to realize the EV, then that is worthless in the real world. You need to be able to make a profit on a game over a reasonable number of sessions. That is why factoring in super rare events like hitting a grand jackpot should be thrown out of your data.

So I think the best strategy is to just track plays and network with other APs. At the end of the day, the only thing that matters is your entry point and profit. When you track plays, you aren’t making any assumptions and there is nothing theoretical. And if you track plays on a specific machine, that is an even better approach because the exact RTP of that machine will be taken into account.

Here is a good strategy:

1. Read the entire rules screen. I like to take photos of every page and then study the rules when I get home. Most AP games will have caveats about how the persistent state features function.

2. Make a hypothesis about when the game might become +EV. You can usually make a decent guess based off what you know about other similar games. Most games aren’t completely new. Most borrow ideas from other games and have similar math and functionality behind them.

3. Play conservatively at first and see if you can consistently make a profit.

4. From there, you can start playing more loosely. Keep tracking plays to see how early you can get in and still profit. Narrow things down to figure out where you are breaking even. You can actually figure out MHBs using this method without doing any spin tracking, getting the meter, using a formula, etc (I don’t recommend doing it this way—I’m just saying that it is possible).

5. If you network with other APs and you are all reaching similar conclusions, then that is a good indication you are on the right track.