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
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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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.
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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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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.
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Let me narrow down the question a bit…
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