“Sit and Go” Tournaments are an increasingly popular form of play. The typical structure is that 10 people ‘buy a seat’ at an online poker tournament. Once the tenth person has signed up the tournament begins – as opposed to conventional tournaments which just begin at a specified time with whatever entrants are already present.
The entry amount usually consists of two components – an administration fee which goes to the site owners (as a fee for running the tournament) and a contribution to the prize pool. The most common balance between the two is 20% fee (e.g. $5+$1), typically used for very small buy-in tournaments, and 10% fee (e.g. $20+$2), used for most others. For very large tournament fees there may be a slightly smaller fee (e.g. $200+$15 – equating to a 7.5% fee).
"The tournament is based around an elimination format, with blinds rising to put pressure on players"
Prize money is normally distributed in the ratio 50%, 30%, 20% for first, second and third finishing position respectively. The tournament is based around an elimination format, with blinds rising to put pressure on players, i.e. 10 players play, gradually eliminating entrants until only 3 are left. The next person eliminated gets 3 rd place and the remaining two play off for the winner and runner-up spot.
The strategy for tournament play, including STT (single table tournament) play, is different to optimal strategy for cash games, but that is a topic for another article. In this article I want to focus on the impact of the administration fee – specifically to look at how good you have to be in comparison to the other players to break even, or make a specified level of profit. What one has to remember of course, is that win or lose, the administration fee is taken from you (and all players), while the prize pool is redistributed among the players at the table. Therefore it is necessary to be better than average just to break even. How much better is of course determined by the fee (and the prize structure).
To examine the problem we need to make number of assumptions, viz:
- That all players other than yourself can be considered to be statistically equal – i.e. on average they are as good as each other, but not necessarily as good (or bad!) as you are. In practice some will be much weaker and some may be stronger, but overall, this shouldn’t bias our calculations too much.
- That the chance of finishing second is independent of who finishes first – i.e. the battle for second place can be considered as a battle for ‘first’ between the remaining players. While this isn’t strictly true, and certainly the game dynamics in any individual game will not reflect this, overall it is probably not too inaccurate. Similar methods can be used in horse racing to estimate place odds from win odds.
" It is more difficult to calculate the chance of finishing second, as it depends on you NOT finishing first of 10 WHILE finishing first of the remaining 9. "
If the average player at your table has an X% chance of winning, then you have a (1-9X)% of winning. It is more difficult to calculate the chance of finishing second, as it depends on you NOT finishing first of 10 WHILE finishing first of the remaining 9. You have a 9X% chance of NOT winning, while you have a (1-9X)/(1-X) chance of finishing first of the remaining 9.
Winning a tournament returns an amount equal to 5 buy-ins. The net profit is therefore 4 times the buy in, minus the admin fee. If we denote the admin fee as a percentage, f, of the buy in, we can say that:
Profit for a tournament win = 4-f buy-ins
Finishing second or third gives returns of 2-f and 1-f respectively, while losing (i.e. finishing outside of the top three) has a return of -1-f.
If we multiply the probability of each of the above results by the return, we get the expectation – the amount of money we expect to make, on average, in any tournament. The graph below shows the expected percentage profit for two different tournament fee structures versus the ‘edge’ we have over the average player at our table (i.e. a 100% edge means we are twice as likely to win as he is, a 10% edge would mean we win 11 times for every 10 he wins etc)
"In general therefore you should look to play at a slightly higher level than the lowest buy-in,"
The break-even figures show us that to break even at the ‘standard’ fee rate requires us to be 12.5% better than the average player at our table, while at the larger ‘rake’ common to small buy-in tournaments we need to be 25% better. Now while the standard of (the average) player tends to decrease with smaller rakes, it is unlikely for example that if you are 25% better than the average player at a $5 buy-in, you will not be more than 12.5% better than the average at $10 buy-in.
In general therefore you should look to play at a slightly higher level than the lowest buy-in, although you do also have to consider the increasing skill-level, as well as the size of bank needed to cope with the fluctuations in fortune which are part of this great game!
BBC
