What's the optimum time to enter a tournament with late registration AND a later add-on?

Question

My question is basically the same as this one, EXCEPT for one major change: there is a rather large add-on after late registration closes.

The specifics are along the lines of an initial 4,000 in chips, 15 minute levels, unlimited rebuys in the first 90 minutes, up to 1 hour late registration, but after level 6 (90 minutes after start) there is an "optional" add-on of 30,000 chips. I quote the "optional" because pretty much everybody takes the full add-on (and if you don't you are probably going to be blinded out in a couple rounds or less!) and it is uncommon that anybody has that many chips yet anyway. So, the first 90 minutes seem more like "practice" or just getting to know the tendencies of the other players at the table. On the other hand, they are also getting to know your tendencies, which you could suddenly switch up, but so could they.

So in some respects it seems kind of like a waste of time, nearly half of the whole tournament time is wasted at levels where you aren't going to get a whole lot of chips and suddenly everyone just gets a bunch more. As an example, in my most recent game I played a decent game in the first 90 minutes, doubled my chips without any rebuys and was doing better than 80% of the table, but then at the 90 minute mark my chip count suddenly increased by 475% and was only about +/- 2000 chips of anyone else at the table: barely a single big blind at the new level!

It seems like an argument could be made to enter right at the end of late registration: now you start with 4000 chips with only two levels to play until you add on 30000 more, you won't be blinded out not playing hands in this short period of time, and you save an hour of time playing for low stakes for a questionable amount of information about other players. Is this a valid argument?

Answer 1

I would wait as long as possible to buy in and focus on making it to the time of the add-on. I'd approach the question this way--how many chips do you expect to have after level 6 and what do you expect to spend for either of the following two scenarios: 1) you buy in right away or 2) you wait until as long as you can.

For the second scenario, assume that you'll play very tight and get somewhat blinded away in order to make it to the add-on. You might then end up with a total of 31k chips for 3x the initial buy-in. You could loosely then say that you 1x the initial buy-in is worth around 10k chips.

For the first scenario, you could also assume that at a minimum, you'll make it to the add-in time, having at least 30k at that point and having spent a minimum of 3x the initial buy-in. The difference is that you could have more chips and you might have spent more money on rebuys. Having played in this oddly structured tournament, you would be the best to estimate how many more chips you might have on average and how often you'd have to rebuy on average(considering that you may sometimes have to rebuy multiple times). Judging from your comment about doubling the starting stack and that being more than 80% of the field, I'm guessing that having 8k after an hour, on average, is on the optimistic side.

I have a feeling that after making these estimates and calculating (chips)/($ spent), the result will be similar to the (chips)/($ spent) for waiting out the first hour; but there's two reasons that I would lean toward waiting in that case. Firstly, as mentioned a couple times in the post you reference, the value of additional chips in tournaments is not linear--essentially "buying" chips at a fixed cost is not a good idea. As an extreme example, you could buy all the chips in a tournament and get first place but you'd be losing a ton of money by doing so. Secondly, you bring up the factor of time and whether or not it's worth spending an hour at these "low" stakes. From a $/hour perspective, you might be able to make better use of this time.