Theoretical Value of Playing Satellites in Poker
Satelliting into big tournaments is incredibly popular among online poker players. Ever since Chris Moneymaker won the WSOP Main Event after qualifying in a $30 satellite, online satellites constitute a big part of the poker economy.
Of course it's appealing to enter an expensive tournament by paying a smaller amount of money and play it out for the seats. But is satelliting a profitable strategy? Let's take it down in pieces and see what we find.
We'll use the following notation:
B = buy-in to the target tournament
s = satellite buy-in
a = your ability, see below
n = number of satellites played
In a poker tournament, we'll assume that the average player's probability of winning equals his share of the total buy-in. For example, in a ten player sit-and-go, the average player has 10% of winning.
Likewise, in a satellite, the average player has the following probability of winning a seat:
P = 1 / (Number of players per seat)
This is the same as:
P = s/B
where, I repeat, s is the satellite buy-in and B the buy-in to the target tournament.
For if you pay $10 to play a satellite to a $100 tournament, it doesn't matter if there are 10 or 200 players. In the first case there's one seat to win, in the second there are 20. If you're average, your chances are 1/10 in both cases.
If you're above average you will win more often, maybe 20 percent as often or twice as often as the average player. We will express your ability as that factor, and write the probability of winning a seat depending on your ability as:
P = as/B
For example, a = 2 if you win a seat twice as often as the average player, and a = 1.3 if you win 30% more often.
There are some very specific limits for this value, but we'll not go into those details here. Also , this factor varies from tournament to tournament. We'll use a fixed value for our calculations, but you should keep in mind that in reality, 'a' depends on the specific conditions in every tournament.
Expected cost of qualifying
With your probability of winning a seat in an individual satellite being P = as/B, the expected number of satellites you need to play before qualifying is:
EV(n) = B/(as)
Since the cost for each satellite is s, your expected cost of qualifying is:
EV(cost) = B/a
This gives us a few interesting results right away.
Average players = no gain
For average players, satelliting has no value, it turns out. When a = 1, the expected cost of qualifying equals B, the direct buy-in.
So instead of wasting time in satellites, go ahead and buy a seat. You'll be saving time and also some additional fees connected to playing in the satellites (more on this below).
Bad players = bad idea
For bad players, with below average ability, satellites are a losing proposition.
You'll probably be an underdog in the target tournament as well, but by playing satellites you're just exploring a new way of losing money.
In this context it's worth repeating that your ability is expressed as a comparison to the opponents in the specific tournament, so if you play cheaper satellites, your 'a' is likely to go up.
In this way, if you're a long-term loser in $40 satellites, you may still be a winner in $3 satellites, assuming that the opposition is softer in the cheaper satellites.
Good players = good value
If you're above average, however, satellites become interesting. The better you are, the more you gain from playing satellites.
For example, if you expect to win a seat twice as often as the average player, the expected cost for qualifying equals half the buy-in to the target tournament.
For the WSOP Main Event this amounts to $5,000, not a bad deal in any way.
If you're 30% better than average, a = 1.3 and you can expect to save 23% of the target tournament buy-in. And so on.
Involving tournament fees
In reality, satellites come with a fee, typically a certain percentage of the satellite buy in. This increases the expected cost of qualifying.
With tournament fees 'q' expressed as a part of the buy-in, the expected cost of qualifying becomes:
EV(cost) = (1+q)*B/a
For satelliting to be profitable, we get the following requirement on your ability:
a > 1 + q
So if the tournament fee for satellites is 1/5 of the satellite buy-in, q = 1/5 and your ability 'a' must be at least 1.2, that is, 20% better than average.
Taking a shot
Then again, playing a few satellites to a big event may still be motivated, even if the expected value is zero or negative. After all, it gives you a chance to a fantastic adventure.
Maybe you're ready to pay something for that.
If you've decided to play the target tournament anyway
However, if you're going to play the tournament anyway, things get more complicated, and satelliting naturally becomes less attractive. We'll attack this topic in Part II of this installation.
Also see our article on how expensive satellites you should play in should be.