"Infinite MTT" - Multi table tournament with an infinite number of players.

I came up with this when thinking of a game software concept where you could play a poker tournament endlessly ...

It's impossible to run a normal (forward) simulation of an infinite MTT for obvious reasons. But when you reverse the whole event, computer could successfully run such simulation through a special software. It's interesting because it seems to prove that poker can be used as a tool which shows that infinity can be visualized as a whole, when being visualized backwards. I can't think of a better way of visualizing the math of infinity.

So the whole simulation starts with the final showdown of the final hand where the tournament winner is decided. Then we have the last call, last bet and all the previous player actions and previous hands. The other final table players instead of leaving the table when eliminated, now appear at the table one by one. When the whole final table is full and its first hand is reversed to the beginning, the other tables start to appear one by one, and so on ...

The chip stacks instead of "$" numbers are displayed as "%". So, the tournament winner has "100%" of all chips after the final hand. Let's say the last call was a "34%" call. All bets, raises, calls, blinds and antes are displayed this way - as a "%" value.

Of course the simulation would have to be run infinitely and would require the computer to work constantly forever and we would never see the beginning of the tournament. But because the computer can calculate better than humans, it would be able to reach a simulation level that can be considered as "infinite". For example, when the simulation is too long for any human to be fully inspected within his lifetime.

Let me know what you think of it, I think it's very interesting.

It's an interesting idea. For me though I quickly run into the same trouble visualizing infinity, just in reverse. It could be interesting to calculate how many days it would take to run a tournament with the entire world population, or something like that.

The ending "100%" chip stack will help, because it visually represents 100% of infinity.

I'm sure the tournament winner should win the last hand with a Royal Flush I wonder if GTO can be reversed - when you have only the ending result of a hand (with cards and stack sizes), can you generate the previous actions using GTO and if so, is there only one (perfect) way to do it, or perhaps more ?

The chip stack would just be 100% of infinity chips though. Right? Still pretty difficult to fathom.

Your second comment reminded me of an idea I had. If there are potentially multiple GTO solutions, they could be quite different.

So my idea was that if there are multiple solutions that are at least very close to GTO, then they could potentially have very different counter strategies.

Very strong hands like aces will always be included in any range. However a lot of the reason you play the bottom of your range is to balance the top of your range.

Basically the bottom of your range is close to neutral EV. But imagine if you constructed two different bottoms of your range. Both include neutral EV hands, but maybe one is built around suited hands with the ability to semibluff a lot and make some nut combos. The other could be built around more off suit high card hands that tend to make hands with non-nut showdown value, like top pair third kicker.

Intuitively it seems like the optimal counter strategy would be different for these two different ranges. So I'm wondering if you switched between different ranges with different optimal counter strategies could you cause an opponent trying to play close to GTO to make mistakes? Even if theoretically a GTO bot could play perfectly against both strategies, would developing multiple very different strategies and not disclosing which you are playing cause human opponents to make larger average mistakes? It's an interesting thought.

Not only would you never see the start of the tournament you would never see 99.999999999+% of the tournament. After all when you reach the point where there are more players than particles in the universe you have difficulty running your program and still are in the very end stages. If all you need is your "infinite" approximation a million person tournament with details on each and every hand can be run either forward or backward and qualify.

Same thing with car design, cooking meals or football game scenarios - there are infinite possibilities for these categories and people are still interested in them, even though the humanity will never see 99,9999999999+% of all possible examples. Of course these are much more useful than my concept, but I still think it would be cool to witness something which is impossible to imagine. Even if it's only a partial look.

If you set the speed of calculating this simulation to "very low" it will probably never reach a point where the computer has trouble running the program. The program can be paused, the computer can be upgraded and you can be sure it will take longer than any human can live. All you need is to keep the simulation running, so that the user can be sure he's looking at an MTT with infinite number of players. Theoretically it can be done.

The question is how to generate backward poker MTT action. Would it have to be completely random or maybe something like a "reversed GTO" ? I have no idea.