The art of force-buying: calculation in CS:GO

This is the article of GOSU.AI. Author: Boris Litvyakov

This article will focus on economic decisions and how they affect your chances of winning a match.

Here I will describe a data approach that allows you to compare different gear buying strategies based on statistics from 6,000 recent demos on HLTV.org.

Let’s start with the simplest case and take a close look at a round. Both sides have some equipment. Below is a chart showing the probability of Ts winning in a round based on the equipment value of both sides at the start of the round:

There are a total of about 93,000 rounds in the database. For each round I record the equipment value of both CTs, Ts and the winner of that round. I divide it evenly into values ​​like “3,000-6,000”, “6,000-9,000” etc…. For the convenience of calculating the winning probability of CT for each case.

If you notice I’ve dimmed the bottom left corner because these situations are rare and there aren’t enough stats available. Theoretically, a couple of warmup rounds could leak into the database:

Furthermore, I could formulate a question like “if the Ts item value is around $21,000, how will the CTs winning ability change based on the equipment value?”

So now we have a model that predicts which side will win each round based on the initial amount. In a match is really a series of interconnected rounds, where the results of previous rounds directly affect the following rounds.

Let’s go back to the first question from the beginning of the article. The score is 14-14 and you have $2,800 plus $1,900 in case you lose this round. Your captain uses Timeout to make decisions about how to buy equipment with the above money.

In a nutshell, let’s assume that your opponent has enough money to buy $21,000 in all the remaining rounds. In case it is possible to drag the match to 15-15 and Overtime with a 50% chance of winning. Let’s compare two possible scenarios:

1. Forcebuy vs Full-buy, then
   1.1 Full-buy vs Full-buy in case of win
   1.2 Forcebuy vs Full-buy in case of loss

1. Full eco vs. Full-buy, then
   2.1 Full-buy vs Full-buy in case of win
   2.2 Full-buy vs Full-buy in case of loss

The two figures above show the possible outcomes and the probabilities of those outcomes. After doing some common math with those probabilities and assuming Overtime will give you a 50% chance to win, the result is:

1. Double forcebuy strategy : Probability of winning 35% – Losing 65%
2. Eco + buy strategy: 19% win probability – 81% lose

So, Eco + full_buy strategy at first glance seems wiser and more conservative, but in reality with Double forcebuy strategy, your team’s chances of winning are doubled! There seems to be a bit of a “wrong” feeling to me, but I think there is a reasonable explanation for this “not right”:

1. I think the $2,800 forcebuy strategy has a 34% chance of winning, that’s an average estimate, results can vary depending on the current opponent and how the game is going. However, I did work out a result based on demos at Krakow Major to double check and it was 30 – 33%
2. Yes, you’re in a situation where it’s off to a bad start, but just winning 1 more round will give you the ability to drag the game to Overtime and then the probability to win is 50%.

Conclusion and future plans

Today I showed you a method to combine equipment value in a round with the possibility of winning that round. Since CS is a series of rounds, you should be able to calculate the effect of item purchase decisions on your chances of winning.

I took a simple case of 14-14 and came up with something quite interesting. However, to get to performing more complex calculations it is necessary to create a slightly more complex model.

First of all, the number of players that survive a round affects the team’s money. So the models should be able to predict not only the winning side but also the number of players alive.

Another thing is to incorporate simulation of economic decisions. It doesn’t seem to be too difficult but it will take some time to do.

Another way to improve my analysis is more detail on weapon selection. Therefore, instead of calculating by amount, I can analyze by different cases, for example “5 AKs” or “4 AK + AWP” or “5 DE”. I think it’s also a good idea to use some of the above scenarios to find the most common weapon combinations.

What really inspired me in that model was connecting single and separate rounds into a complete sequence. So making a lot of decisions in a match (eg rush B every round :v) directly affects your money, a type of savings and also doesn’t take too much risk even sometimes increasing significantly your chances of winning.