outcomes and payoff in probability games

I am reading probability from AI point of view from book Artificial Intellegence A Modern approach by Russel and Norving. Below is text snippet from chapter 13.

One argument for the axioms of probability, first stated in 1931 by Bruno de Finetti (and translated into English in de Finetti (1993)), is as follows: If an agent has some degree of belief in a proposition a, then the agent should be able to state odds at which it is indifferent to a bet for or against a. Think of it as a game between two agents: Agent 1 states, “my degree of belief in event a is 0.4.” Agent 2 is then free to choose whether to wager for or against a at stakes that are consistent with the stated degree of belief. That is, Agent 2 could choose to accept Agent 1’s bet that a will occur, offering $ 6 against Agent 1’s $ 4. Or Agent 2 could accept Agent 1’s bet that ¬a will occur, offering $ 4 against Agent 1’s $ 6. Then we observe the outcome of a, and whoever is right collects the money. If an agent’s degrees of belief do not accurately reflect the world, then you would expect that it would tend to lose money over the long run to an opposing agent whose beliefs more accurately reflect the state of the world.

If Agent 1 expresses a set of degrees of belief that violate the axioms of probability theory then there is a combination of bets by Agent 2 that guarantees that Agent 1 will lose money every time.

Below shows that if Agent 2 chooses to bet $ 4 on a, $ 3 on b, and $ 2 on ¬(a ∨ b), then Agent 1 always loses money, regardless of the outcomes for a and b. De Finetti’s theorem implies that no rational agent can have beliefs that violate the axioms of probability

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My question is how we got values inf last column for example a,b column how we got -6, -7 an 2. Kindly explain.

Thanks for your time

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Why is PHP still mostly used to make browser games rather than Python or Java? [closed]

I am a Computer Science student and I have been playing to Travian for years.Travian is a browser based MMOG where you have to build your village and compete for resources. There is no animation, there is 3 main views which is the map, your village and your fields.

I was looking at some Travian clones on GitHub and I found 3 clones, all of them using PHP. Travian has itself build using PHP.

I am wondering if PHP is better in some way than Python for example for building this kind of games? And if so, why would be the reason?

What free and / or paid game master aids are available for a PC user running virtual games? [closed]

I’m running a d100 based game. Currently, we’re using Discord with DiceParser installed. I’ve poked around at www.Roll20.net in the past. What paid and/or free programs would you recommend for a game master using a PC to run a remote game? Some of my players are using android phones and some iPhones. My budget is very low but it would be great to see the high budget options too.

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What Games Are Widespread in Forgotten Realms?

I know that Three-Dragon Ante is one of the widely popular table games across Faerûn, and here’s a nice answer with some info about the Talis deck. But I am having trouble finding what other ‘table’ games are widespread throughout Forgotten Realms. Are dice games generally plentiful, and what are they usually like? Is there perhaps a common fondness for pieces-on-a-board games like baduk or checkers? Sowing games like mancala? Maybe something with a blurrier line between luck and positioning, such as nard or diced chess?

Ideally, I’d be interested in being pointed to some sort of list/compilation with descriptions and other information of the various games (comparable to, e.g., the list of semi-magical substances on the same wiki). But failing that, a direct answer is also welcome.

While I’m particularly interested in games that are widespread throughout all layers of society and common in the northern parts of Faerûn, other games are of interest too.

Spoilt for choice: helping traditional-system players adapt to narrative-control games

My group teethed on D&D 3.5 and loved 4e, but now we’re eager to take advantage of FATE’s more narrative- and character-driven philosophies. However, on our first (DFRPG) game last night, my players frequently seemed spoilt for choice: faced with “what do you want to do?” instead of “which of these options (like 4e’s power cards) would you like to use?”, we sometimes froze like deer in the headlights.

For a player trained in 4e that their choices are largely limited to a set of specific mechanical actions (eg power cards), narrative-based options seem vast and vague. The golden rule of FATE is to first decide what you want to do narratively and then figure out how to model it mechanically, and this is alien to my players’ experience. We like it conceptually, but can’t get a handle on it yet.

I know this is just new-system pains, but what can I do to make the transition easier?

Are there any PbtA games for Contemporary Fantasy and Magic?

I’m being (late) introduced to PbtA games and I’m looking for a Contemporary Fantasy and Magic option, something like Ars Magica, Mage The Ascension, Dresden Files?

Let me narrow down the question a bit…

I know we have Monsterhearts, but it is about relationships and lack Skins for magic users. What I am looking is something with more freedom (make your own spells) and combat/explosions or at least rituals.

I’m a huge fan of games likes Mage and Dresden Files, but I like how PbtA plays with conflicts and tests and I can imagine a 6- resulting in a chaotic backslash when failing to cast a spell.

Any PbtA game I can use for that?

My gaming group can’t agree on play-by-post or scheduled games

I’m currently helping out as one of the DMs of a larger gaming group that will periodically see two or three players plus a DM go on a mission, usually handled in play-by-post format.

Right now, I have a group of three that’s been having pacing problems from the start despite multiple strategies to address them:

  • When we first started, all three players had differing activity levels, and the most active player was complaining about not being able to play because they were spending all their time waiting.
  • I adopted a faster activity level myself in response, and the least active player started complaining about not being able to play because everything was happening while they were busy with real life.
  • We called a post-mortem to discuss how to handle the pacing issues. One of the players suggested moving from play-by-post to a more traditional scheduled meeting, and another player actually shot this down complaining about not being able to play because making it an obligation took too much of the fun out of it.

Unless there’s an organizational strategy I’ve missed besides play-by-post or scheduled meeting, I don’t think I’m going to be able to run a game for these players, and while I expect the answer is going to be "find better player(s)", that’s a last resort.

How do I run for this group?