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I am trying to understand proof of stake consensus. I found some explanation about the "nothing at stake problem at the Ethereum wiki.

Here is the part about the "Slasher"-solution i don't understand:

Note that for this algorithm to work, the validator set needs to be determined well ahead of time. Otherwise, if a validator has 1% of the stake, then if there are two branches A and B then 0.99% of the time the validator will be eligible to stake only on A and not on B, 0.99% of the time the validator will be eligible to stake on B and not on A, and only 0.01% of the time will the validator will be eligible to stake on both. Hence, the validator can with 99% efficiency probabilistically double-stake: stake on A if possible, stake on B if possible, and only if the choice between both is open stake on the longer chain. This can only be avoided if the validator selection is the same for every block on both branches, which requires the validators to be selected at a time before the fork takes place.

Can someone explain this in simpler terms and explain where those probabilities come from?

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Nothing at stake means that you lose nothing by commiting to each possible fork.

Whereas with casper your stake would get slashed if you vote on forks that don't "win"

So in nothing at stake if there are 3 forks you can sign each of the 3 1 will win and your outcome will be + 1/3 let's say

In casper you would lose your stake if you behave malicously.

Karl Floersch has some great videos on it.

I timestamped it somewhere correctly : https://youtu.be/MyDocEQfBGA?t=35m42s

Also: https://www.youtube.com/watch?v=uQ3IqLDf-oo

from the wiki https://github.com/ethereum/wiki/wiki/Problems

However, this algorithm has one important flaw: there is "nothing at stake". In the event of a fork, whether the fork is accidental or a malicious attempt to rewrite history and reverse a transaction, the optimal strategy for any miner is to mine on every chain, so that the miner gets their reward no matter which fork wins. Thus, assuming a large number of economically interested miners, an attacker may be able to send a transaction in exchange for some digital good (usually another cryptocurrency), receive the good, then start a fork of the blockchain from one block behind the transaction and send the money to themselves instead, and even with 1% of the total stake the attacker's fork would win because everyone else is mining on both.

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  • Thanks for the links, those will definitely help me to get a better overall understanding. however my question was more about the specific part I posted.
    – solaire
    Aug 25, 2018 at 10:15
  • "each individual stakeholder might only have a 1% chance of being "pivotal" (i.e. being in a situation where if they participate in an attack then it succeeds and if they do not participate it fails), and so the bribe needed to convince them personally to join an attack would be only 1% of the size of their deposit;"
    – Nico Vergauwen
    Aug 25, 2018 at 10:52

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