Let's compare two cryptocoins. Coin A has 10 mins between blocks, coin B has 2.5 mins between blocks. We assume they use the same hashing algo.
Let coin A has difficulty = 2000, it means that in average it's necessary to do 1000 hashing cycles to find a block. Hence, difficulty of coin B = 500 (250 cycles to find a block).
Case AAlice makes a payment in coin A. Bob waits for 2 confirmations which should take
20 mins. Alice owns 150% of hashing power (she doesn't use it for legit blockchain though). When Alice starts to hash she will get 60% of the total hashrate
150 / (100 + 150) = 150 / 250 = 60%
Odds that Alice will find 2 block in a row to fork the blockchain after Bob sees 2 confirmations
Case BAlice makes a payment in coin B. Bob waits for 8 confirmations which should take
20 mins. Alice owns 150% of hashing power (she doesn't use it for legit blockchain though).
Odds that Alice will find 8 block in a row to fork the blockchain after Bob sees 8 confirmations
60% * 60% * 60% * 60% * 60% * 60% * 60% * 60% = 4.6656%
To find 2 blocks Alice have to do
2 blocks * 1000 cycles/block = 2000 cycles.
To find 8 blocks Alice have to do
8 blocks * 250 cycles/block = 2000 cycles.
So, what do we see?
The risk of double-spending is in inverse proportion to time of waiting, no matter how many confirmations u get.
