score/gains/cost
I was beginning to suspect that this is a fabrication - but for the moment I will play along.
Actually, the consistent peculiarity makes the post believable, but purposed or personal fragmentation makes it unappealing. I don’t care if it is written in proper English if the author’s native language is not English, but what makes it really hard to comprehend is the mixing of incomplete facts with subjective analysis.
Do they randomly select and assign players into two groups and the group with more chips after playing two rounds receives bonus of $21K ($3K to each member of the group), but seven players with the best scores get to play in the “final” for the top three cash prizes? Yes?
If so, then, for the average player the expected payout, expressed in thousands of dollars, would be
[3+(50+20+10)/7]/2=7.214
To calculate the Expected Value of the tournament we need to deduct from the expected payout the average cost of reentries and add possible rewards of future tournaments that participation in this tournament would entitle us to.
Of course, the EV for player with good playing plan and knowledge of tournament strategy would be much higher.
You would want to figure out how much you would be willing to pay (in form of reentry fees) for a chance to improve your score. This directly relates to the size of the EV.
One way to understand process better is to exaggerate the situation.
If the value of this tournament was one million dollars for the average player then having score in the top seven would be worth two millions. It should be worth three millions if you get to be invited for the next one, or maybe even more if there would be more tournaments. So, even if you needed to reenter three times in both rounds, to be almost guaranteed top seven scores, which could cost you up to $6,000 , your expected value still would be “almost four millions”.
Giving up any chance of being the top seven would be very costly. Resignation of even one percent would mean giving up $40K in profits. The cost of reentries becomes insignificant and your right way of play is to maximize you chances to be in the top seven players. Your goal would not be a fixed number as you chances for achieving “the goal” would change based on you initial results. The bigger the EV- the closer you need to play to maximizing your score without regard to reentries.
Back to reality. Notice that the higher the goal, the more likely you would need to reenter.
Let’s compare the difference in obtaining final goal of 5,000 and 6,000 and the related cost and rewards.
First, let’s see what happens when you try to shoot for the total of 6,000. In the first round you would try to get to 4,000 and make no bets in the second round. Or you would try to get to 6,000 in the second round if you rebought three times in the first round and busted out. You have almost fifty percent chance of getting to 4K without rebuys, then another 50% with your first and subconsequent rebuys.
(The numbers would be slightly smaller because you may end up in a “limbo” not being able to achieve your goal or bust out – this is very important but not “huge” and the main mechanics remain the same. At this time let’s assume that you would be able to resolve this within the 21 hands you get to play in every round.)
You achieve the goal of 4,000 with one rebuy 25% of the time for total chance of success of 75%; and so on.
Your chances of success, with three rebuys in the first round, are 93.8% at the average cost of $688 and total chances (reaching the goal using reentries in both rounds) are 98.8% at the cost of $920.
Setting goal at 5,000 (3,000 in the first round and then betting minimum in the second round, or going for 5,000 in the second round if you busted out in the first round) would be: success 99.8% at the cost of $490.
By having the goal at 5,000 instead of 6,000 you would increase your chance of reaching the goal by one percent and it would be $430 cheaper. But now you have to counter-balance it with a decreased chance of making the cut (top seven).
If you increase your chances of being in the top seven (because of one thousand higher score) by only one percent (and I am certain of that, and actually think it would be a significantly higher) you regain double of what we calculated as the average payout, plus there is a value of possible future tournaments- all that for $430.
Getting to 4,000 in the first round is also more beneficial when seeing other players’ scores makes you raise up the goal score. For example, if you determine in the middle of playing the second round that the goal is 7,000, you would have 2/3rds chance of achieving it if you ended up the first round with 4,000 and only ½ chance with score of 3,000 in the first round.
I would be even tempted to shoot for 7,000 total score. Assuming that you bust or reach the goal, you reach it 96.6% of the time at cost of $1,263. For the score of 8,000 the numbers are 93.8% and $1,523.
S. Yama
