You should link to some graphics then.

-- Simon

Hi,

(This has github issue #391: Handicaps in Multiplayer.)



If you're a brand-new player at golf, go, or chess, it's already an achievement when you beat a strong opponent at queen odds, or at nine stones, or at three more strokes per hole. Next time, can you do it at rook odds? You can easily see your personal progress in how the handicap shrinks over time. I'd like to have this in Lix.

Per game: In Lix's networking lobby, I'd like to offer handicap options next to the color picker. Between games, you can adjust the handicap. The default is no handicap for either side.

Choosing a handicap puts you at a disadvantage. The stronger side should handicap itself and thus start with a weaker position. I'd like the new player to start with the level's normal, unhandicapped-but-also-unimproved position; this makes it easier for him to learn how the map usually plays. Also, as I wrote in 2017: A strong player with 50 lix can beat a novice with 500, but a strong player with 5 lix must play enourmously well to beat a novice with 50 on a map with batters.

---

In IRC, geoo and I have considered some types of handicap.

Divisor handicap: You pick a number ≥ 1. Your initial number of lix is divided by it, and every skill count in your panel is divided by it. Options for divisor handicap could be 1 (= no handicap), 1.2, 1.5, 2, 3.3, 5, 7, and 10.

We'll always round up non-integer results. If the map gives 2 builders, you'll start with 2 builders at handicap 1.2 or 1.5, and you'll start with 1 builder at any bigger handicap.

Previously, I've expressed this as a multiplier handicap, and values were 100% (= no handicap), 70%, 50%, ..., but this design has a downside: Lower numbers mean stronger handicaps. It's nice when higher numbers mean stronger handicaps, to avoid confusion when people say "high handicap" or "you can lower it".

If you're in a team, the team's total divisor handicap can be the average of the team's players. Should "average" be the arithmetic mean or the harmonic mean? I'll have to ponder, and Proxima will be happy. Harmonic makes sense because it's a divisor handicap.



Delay handicap. You pick a number of seconds ≥ 0. Your first lix spawns later than other players' first lix, at this delay. Afterwards, your remaining lix continue to spawn at the normal spawn interval after each previous lix. Options for delay handicap could be 0, 5, 10, 20, 30 seconds. Anything more than 30 seconds is probably too boring for the experienced player.

Again, if you're in a team, the team's total delay is the average of the individual player's delay.

Asymmetric levels. If you choose a divisor and/or delay handicap, you always start in the first seat, and other players are randomly distributed amongst the remaining seats. This doesn't matter in a symmetric level, but if the author wants to build an asymmetric map, the author can put the seat-to-be-disadvantaged always in the first position. As long as we have any kind of handicap option, or even just a checkbox, we can add this seating rule at little exta UI cost in the lobby dialog -- it needs an explanation, but no extra pickers.

Level-specific handicap. Instead of offering concrete values to pick, you merely have a checkbox: Do you want to be handicapped or not? Or you have a choice of handicap strengths; which handicap strength do you want? It's the task of the level author to define the handicap in terms of delays or divisors or seats.

The downside of such level-specific handicap is that most authors won't bother to define handicaps for their levels. The few levels that have author-defined handicaps won't be consistent, e.g., you can play at strength 1 on this map, but it's hard to win against strength 3 on that other map. If it's not consistent anyway, I feel it's better to just offer concrete values, and let the players pick.

Ideas?

-- Simon

I'll play this Sunday. Message me on IRC, or I'll message you on IRC.

Regular games on weekdays are hard to fit in my schedule.

-- Simon

Thanks! Great session with great maps.

Please post the new maps here on the forums or send them via PM. I'll add them to the next release.

-- Simon

Lana: Thanks for joining and building maps! Sorry for the crash in 0.9.43. Dullstar and I found that crash on sending chat messages, and I've released 0.9.44 that fixes that crash. Looking forward to the next session!

Flopsy: I can't play on Easter Sunday, but I'll certainly join on the 24th; I'll reply there.

-- Simon

I'm sitting on the Lix central server. Everybody is welcome to join!

-- Simon

Hi,

Rampoina asked on IRC: Are there replays of two-player Lix games between strong players? How can we learn more about multiplayer strategy?

I've attached two replays:

• Stepping Stones 2v2. It shows a common principle in multiplayer: Higher and faster routes are better. Even though the purple team loses, pay attention to purple's initial relentless attacking of the orange bunch. The orange bunch is weakest while the top route is nearly prepared, but not completely done, and the bunch hasn't yet ascended to the top level.
• A close and eventually drawn endgame at the bottom of the towers: Both geoo and I want to fight for a win in a drawn position. This shows micromanagement of single lixes that have to attack a bunched enemy crowd.

To watch replays:

• Either put them into your replay directory, then navigate there from Lix's replay browser.
  
• Or, on Windows, drag them on the Lix icon.
  
• Or, on all OSes, run Lix with the replay filename as a command-line argument.
  

Ah, if you watch these replays: Lix versions since mid-2021 have a bug: Lix will re-save a watched multiplayer replay, even though you haven't changed it. This is a regression of the new end-of-game dialog. I'll fix this in the next version, 0.9.44.

-- Simon

More cute graph theory.

Let G be an undirected graph with n ≥ 2 nodes, with only simple edges, i.e., no multiple edges. Prove the following statement or construct a counter-exeample: There exist two nodes in G that have exactly the same number of edges.

Example: In the picture, both A and B have two edges each.

Example: if G contains only n = 2 nodes, they're either connected (and both have 1 edge) or not (and both have 0 edges); in either case, G contains two nodes with the same number of edges. Thus, the statement is true at least for two-node graphs.

-- Simon