It's the only machine from that era that I know of, that uses static RAM, and no refresh.

After the host throws open the empty door (let’s say C), which he always knows beforehand as empty (due to the placing of the prize behind a certain door and the player choosing a door for himself), the choice involving two remaining doors (A or B) for the prize and by the player in terms of two sides of coin can be considered as the head H (corresponding to door A) and the tail T (corresponding to door B). These choices are mutually exclusive in terms of H and T, implying that the player or the prize can’t be both at door A and door B.

Consider also that the prize and the player are represented now by two coins, coin 1 and coin 2, respectively.

We can then represent all the possible choices involving prize, player and the two remaining doors A and B (after the host has opened the empty door with the prior knowledge about the door being empty) in terms of coins 1 and 2 and their heads and tails.

From the above, prize at door A will be designated as 1H (head in the case of coin 1) and the player at door A as 2H. Similarly, prize at door B will be 1T and the player at door B as 2T.

The conditions for switch to work (leading to a win), i.e. either the prize is at door A (1H) and the player at door B (2T), or the prize at door B (1T) and the player at door A (2H): which in terms of probability, the probability for the switch to work,
P(s) = P(1H)*P(2T) + P(1T)*P(2H) ………….. (Eq. 1)

Similarly, the conditions for the switch to not work (i.e. failing to win), either the prize is at door A (1H) and the player at door A (2H), or the prize at door B (1T) and the player at door B (2T), which in terms of probability for switch not producing a win,
P(f) = P(1H)*P(2H) + P(1T)*P(2T) ……………(Eq. 2).

Since the probability for head or tail for any coin is 1/2, i.e. P(1H) = P(1T) = P(2H) = P(2T) = 1/2.

The probability therefore for the switch leading to a prize (from Eq. 1), P(s) = 1/2;

And the probability switch leading to no win (using Eq. 2), P(f) = 1/2

In other words, there is no advantage in the player making a switch

I did actually try a universal remote first, but didn't have any success with it - perhaps that universal remote also got its codes from the LIRC database.

IR serial between Spectrums would certainly be a fun hack!

The CGA isn't responsible for refreshing the system RAM, but as you said it does have its own VRAM which is also DRAM and does need to be refreshed. That RAM doesn't partake in the system refresh and the CGA card doesn't have any dedicated refresh circuitry so it must be refreshed by the display addresses. Fortunately the 6845 continues to generate addresses even in the non-display areas, so works fine for this task.

The C64 can't use the display address for refresh because the data would decay during vertical blanking as you said. However, it's simpler to refresh constantly (even in the active display area) than to add circuitry to turn off the refresh during the active time. It doesn't slow the system down either, since the Vic-II does a memory read every clock cycle anyway.

Anyway, my question was in fact wondering why it wasn't possible to capture codes with your own kit, instead of trying to "discover" them or hunt them out another way, when commercial remotes can do it easily enough ;) ... 2-way infrared-to-serial-header doodads are pretty cheap if you go to the right places (...the wrong places will charge £10+ just for the tranceiver)

Bizarrely I actually have a couple of those IR beads hanging around here, too - I think they must have come either from someone's long-since-dead VC card, or are spares from a pro room control system - but I have no idea what we could use them for. There's not much they can connect to as-is, and the whole "run it through a sound card" thing would be a fun project but impractical for any real application, especially as you'd then need a bespoke program to receive and interpret the data and do something with it.

Maybe it could be used to set up line-of-sight wireless communication between a pair of Sinclair Spectrums or the like?

Tile-based displays may be more problematic though, as you can't predict the access pattern except for the relatively much smaller and lower frequency tile array block...

As for the CGA, I was considering that as being entirely separate to the main computer anyhow, as it doesn't use system RAM; hence the computer needs its own refresh anyhow. The CGA card doesn't do much other than taking stuff off the bus, putting it into the onboard VRAM, then repeatedly and sequentially reading it out into the monitor port (and/or whatever passes for a DAC on the composite video line...).

The Amiga I guess needs separate refresh, now I think about it, because of the "fast RAM". Perhaps it doesn't have to bother when it comes to "chip RAM", as that gets buzzed through by the vidchip, but the fast RAM is purely for the CPU's use, much like a PC's system memory... The C64 I'm not familiar enough with, but I coulda sworn the background is bitmap and a large proportion of the bus time is given over to sequentially reading the video field data from RAM to VIC-II even though it has sprites as well? Is the separate refresh just for Vblank, or does it also run during the display time for some reason?

Certainly such a capability is technically possible. And I have heard of games adapting themselves to the players strengths to give more of a challenge to stronger players and to make themselves less frustrating to weaker players. An online component is not necessary though - offline games have been doing that for a long time.

> If it does, then cheating is involved.

I don't think that necessarily implies cheating, though - if it's part of the way the game works, then it's part of the way the game works.

> So, no matter how good math I have, I will still lose, just they are watching how I play.

Well, either it's a game of skill (in which case the computer has no influence) or a game of luck (in which case you can lose no matter how good your math is anyway). What kind of game are you talking about here anyway?

> can you tell me how to prevent this?

Yes, there is an absolutely foolproof way to prevent this. Don't play games which you find frustrating.

> If games software does not function well, would that mean the online games software lose the storage memory and the chance of winning is higher.

Not necessarily. Bugs in games can make the game easier, more difficult or have effects orthogonal to difficulty.