See https://blog.ethereum.org/2015/12/28/understanding-serenity-part-2-casper/ ; essentially, it's a kind of generalization of economic consensus protocols, and one that particularly allows for us to more easily reason about secure PoS schemes.
Yes and no.
There's no way to enforce any given betting strategy in either PoS or PoW. For example, in PoW, there's no way to force miners to never mine on an attacker's chain. So, yes, a validator could be programmed to bet in any possible way.
Betting doesn't quite work this way, however. There's been multiple versions of how betting works, what exactly ...
There is precisely one validator with the right to create a block at any given height, randomly (but deterministically) chosen from the validators, weighted by their stakes. If that validator fails to do so, or their block is rejected by the rest of the network, then there is just a "hole" in the chain where that block would have been.
This can happen ...
Essentially it works like a prediction market. If you know anything about prediction markets and their abilities they do a fairly decent job of actually predicting outcomes and in the grand scope end up being right in the long run. So what this tries to do is create a system of bets that shape the chain in general.
Basically you put down a deposit from ...
You are correct assuming you (and other nodes betting on block beta) have a higher security deposit than the consensus betting on block alpha.
As long as honest nodes outnumber the dishonest nodes, the system will heavily favor honestly and discourage (by large penalties) dishonesty.
Slashed funds are the same as money wasted on energy used to mining on a fork and don't achieve becoming the largest (51% attack) .
You'll lose your founds if you behave badly as you lose Kw and CPU/GPU
cycles (which traduces in money) while mining not correct blocks or on
PoS carries some kind of bad behaviors (adopted by ...
Q1. Yes, validators can change their bet. Voting happens on every block, and validators can vote however they want. From Vlad:
Validators bet independently on blocks at every height (i.e. block number) by assigning it a probability and publishing it as a bet. Through iterative betting, the validators elect exactly one block at every height
Q2. You are ...
I'm not sure about 1) but I guess it's not possible.
About 2) and 3), referring to this post, and specifically the So how does Casper work anyway? part, it seems that you bet using a Casper contract that keeps track of 6 items, one of them being :
The current size of the validator’s deposit (note that the bets that the validator makes will increase or ...