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If I select any two tips randomly, without a full knowledge of the tangle, will it change the probability that my transaction will be selected by other transactions?

Selecting 2 random tips will impact negatively the probability for your transaction to be confirmed by others. There are multiple reasons for that:

1. There is a chance that 2 randomly selected tips are inconsistent. (i.e. your transaction would approve a double spend and will never be selected by any other transactions selected by the recommended GTTA algorithm). This situation is impossible with the recommended GTTA.




2. There is a chance that one of the randomly selected tip is not solid and will never be solid because one of it's branch or trunk simply don't exists. Therefore your transaction will never be solid and will never be approved by anyone else. This situation is impossible with the recommended GTTA.




3. Most importantly, the recommended GTTA algorithm is more likely to select tips to approve in the main tangle branch. If you select 2 tips completely randomly: the probability that they are in the main branch is lower than with the recommended GTTA algorithm. As a direct consequence : the probability for your transaction to be approved by others decrease.

I think those 3 points are relatively simple to understand and should give you the intuition that selecting 2 tips completely randomly will never increase your probability to be confirmed.

How much does it decrease is a more complex problem and the most efficient way to estimate this is probably by running simulations/real world measurement.

As a side note researchers from the IF already run tangle simulations and published the results, not directly answering your question, but at least giving you an idea of how the random walk parameters impact the probability to be confirmed.

Related links :

Alpha: playing with randomness (for an explanation of the random walk and how it can be fine tuned)

Confirmation rates in the Tangle (presenting the results of various simulations)

The Tangle is a DAG and the issues inherent in it are independent of the tip selection and MCMC walk methods selected.

As such, whether the tip selection is random or constrained, given that all nodes follow the same protocol, the chances of any transaction getting included in any transaction is the same.

Even if the most stringent criteria is used to restrict tip selection, the fundamental nature of a DAG and an asynchronous network means:

• Nodes will never have a complete view of the entire network or of all issued transactions at the same time.

I would also like to note here that the current GTTA breaks essential Tangle functionality of allowing for Tangle partitioning and offline Tangles. It is detrimental and ultimately goes against one of the main advantages of Tangle.

Although adopted since v 1.5, this restriction to depth of a certain Milestone, and the presence of a Coordinator, explains why certain situations are impossible with the current software.

If Solidity means that all a transactions parents are known, then the DAG will grow wider as more old transactions will get built upon than new transactions. If random new tips are selected, then there will be more Blowballs and a greater chance of creating a partitioned DAG.

I argue, in the absence of the Milestones, it will be impossible to create a tip selection restriction that is liberal enough to include a high percent of new network transactions and simultaneously restricted enough to constrain the width of the Tangle DAG.

As a result, the DAG will grow wider and the confirmation time will grow unreasonably long as the software in each node will be required to evaluate the entire path of every transaction path.

So, my answer is that, whether the two tips are randomly selected or not, ultimately makes no difference in the absence of the Coordinator.