How to calculate ROI/expectation with BJ tournaments

gronbog said:
Sorry, for not making myself clear. I meant that as the number of rounds increases to reach a final table with the same money available, EV (meaning the amount one can expect to win by entering the tournament) would decrease exponentially. This is only an issue for events where the prize pool is capped but where a significant number of entrants beyond where the prize pool reaches the cap warrants extra rounds. I may be unnecessarily confusing the issue here since in such a situation the number of entrants also increases exponentially with each round added and so the result is reflected in the entrants/prize pool formula.
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Understood.

I had been trying to hammer home the point to tucson1972 that the only variables of any significance (in the absence of any skill-based calculations) are the amount of money on offer and the number of players competing for it. In that context you seemed to be pulling in the opposite direction by talking of rounds.:D
 
tucson1972 said:
Obviously I'm a newbie to all this. Perhaps this is the norm, guaranteeing an amount significantly less that what the tournament structure can support in case of a low turnout.
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I can't speak about the norm in the U.S., but in the handful of land-based tournaments I've played in the U.K. that's been the case. Effectively a minimum prize pool is advertised to drum up some interest, and if more than this amount is taken in entry fees, then 100% of this is paid out. (I think that may even be a legal requirement here.)

However, if the turnout is particulalry poor, and the casino managers do not mind generating some bad feeling, the minimum prize pool might prove not to be a minimum after all!


And you will have seen variations on the theme online. While SitnGos and some MTTs will have a flat rake of 10% (or whatever), some MTTs have a guaranteed prize pool or have the pot sweetened with an additional amount, over and above what the players contribute.

The most cynical example I came across was at GameAccount, where they combined a truly massive rake with an attention grabbing "£100 added" - https://www.blackjacktournaments.com/posts/42431 So what looked like a good deal was a vey bad deal on closer inspection.


tucson1972 said:
And I guess I'm talking in circles again as the original point of this thread was analyzing a games EV based on each round as you play it and based on the fact I sat with a full table for round 1, that's around a 40% house edge and that's hard to ignore.
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But that is knowledge after the fact. You can't know how many people will at be your table(s), whether you will get a wildcard, etc. in advance of deciding to play the tournament.

In truth, you generally can't even know the number of players, so if the prize pool is capped, that is the most important thing to try and get a good estimate of.
 
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$ cost and Ev

I think tucson would like to see the exact EV of the GN blackjack tournament. To do so, other than the correct formulas provided by other posters in this thread, we should use concrete format with specific numbers of players. Also, we need to clarify if one attempts to just pay the original entry fees or rebuy and superrebuy, as well.
From the link Colin provided it shows that there are 5 players per table in the semifinals.
Let’s make a model, which may be not as exact as the one of the coming tournaments but should serve as an example.
We plan on all rebuys, 4 out of 5 drawn names are present (in many tourneys it is much lower).
The format could be as follow:

1st Round
162 players – 27 Tables (all tables have 6 players, two advance)
54 players advance, 108 don’t advance
Rebuy
90-100 people rebuy, 18 tables, 6 or 5 per table (average 5.1), 36 advance
Wild Card to 2nd round: 18
total advancement to 2nd round 108

2nd round
108 players, 18 tables of 6, 36 advance
Superrebuy 66-72 players, 12 tables, mostly 6 per table, 24 advance
WC to 3rd round: 6 names
total advancement to quarterfinals around 66

Quarterfinals
66 players, 11 tables, 22 advance
WC to semis: 3 names
total in semifinals 25 players

Semifinal
25 players, 5 tables of 5, one per table advances to the final
plus 1 Wild card

We can calculate the chances of advancing for the average skill player:

to 2nd round:
1st play 33.33%
Rebuy (66.67x 39.2%) = 26.14%
WC 40.5% x (18/58) = 12.6%
Total chance 72%

to quarters:
1st play 72% x 33.33% = 24%
superrebuy (72%x.66.66%) x 33.33 = 16%
WC 60% x 6/82 = 4.4%
Total chance 44.4%

to semifinals:
44.4% x 33.33% = 14.8%
WC 85.2% x 3/112 = 2.3%
Total chance 17.1%

to final:
17.1% x 20% = 3.4%
WC 96.6% x 1/120 = 0.8%
Total chance to make the final 4.2%

As you can see making finals happens once in about 24 tournaments, which is slightly better than 6/162 (once in 27) because not all players rebuys and show for the wild cards.
The total expected value is $696 ($612 from the final table prizes).
The expected cost because of all possible rebuys is $1,073.
So, for people who pay all the entries it is 35% disadvantage.
However, I don’t know a single person who thinks that his skills are below the average player. For people who are better than average it is quite another story.

S. Yama
 
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S. Yama said:
From the link Colin provided it shows that there are 5 players per table in the semifinals.
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Does it? All I can see is that one of the available wildcards is into the final. (Which admittedly I hadn't even noticed to begin with.)

I can't see any specifics about the structure (no. of rounds, players per table, etc.). Maybe my IE browser isn't rendering the page properly:confused:

(And it's also been suggested that there is in fact one less round than Tuscon believes.)
 
Wow! Mind blown Yama. This is exactly what I was looking for. But I don't understand how you came up with certain formulas. For advancing to round 2, of course I understand the .33 with initial entry but I don't understand these numbers.

Rebuy (66.67x 39.2%) = 26.14%
WC 40.5% x (18/58) = 12.6%

With the rebuy where are you getting 66.67 and 39.2? I have no idea what these numbers represent. Same with WildCard 40.5%

Are you playing this weekend at GN? If so I gladly buy you a drink/dinner and you can explain it then. Awesome.

And Colin, I realize if you have the total number of entries that is the easiest calculation, don't have to nitpick with calculating the WC however I'm trying to figure out if a tournament is good before I enter. And I think breaking down the tournament like Yama just did does that to a T. I would be very comfortable playing in a tournament with these odds. But I appreciate your approach. It helped me see why my calculations were way off. You should visit Vegas and play the GN. It is lots of fun. Unless you re-buy twice. Then it sucks big time.
 
tucson1972 said:
however I'm trying to figure out if a tournament is good before I enter.
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That's what I'm saying is easiest done by dividing the prize pool by the estimated number of players (or entries, if accounting for rebuys - I'm beginning to confuse myself about which of those is applicable now! I think it depends on the circumstances.).

The structure does not help you get at a better estimate. The structure is the same for everybody. Just treat it as a lottery. A number of people buy tickets, some of which prove to be winning tickets.

Rebuys are a complication. I tend to think of each buyin I hand over as entry to a separate tournament. It's generally always worthwhile to rebuy, but in principle the assessment can be repeated at each opportunity to buy in.

But as Yama mentioned, if you know you will be rebuying as often as allowed, hanging around for every wildcard drawing, etc., then you may be able to get more benefit from a particular structure than the average person.
 
where do the numbers come from

Thanks for the nice words tucson. I will not play GN this weekend but perhaps we may cross paths if you play some local (Vegas) weeklies.

Where do the numbers come from?
The average player advances to the second round 33.33% (2 of 6), then he rebuys only if he lost the first try – that’s 66.67%. He advances in rebuys 39.2% because we set the assumptions, as I wrote in the format description, that there will be on average 5.1 player per table (with exactly 5 it of course would be 40%). So his cumulative chances were 33.33 + 26.14 = 59.5%. If he advanced he doesn’t need wild card, but when he was unfortunate to not advance 100% - 59.5% = 40.5% then he is a part of wild card drawing. Since 90 people advanced from first play in the first round and rebuys there could be 72 people waiting for the drawing (162-90=72). We assumed that only 80% of them shows up (this may vary, I’d witnessed 15 names called to fill 5 spots, and sometimes all called are present), so 72 x 80% = 58. If they draw 18 names the chances for the wild card are 18/58th and “our player” will be eligible when he didn’t make to the second round through first play or rebuy – 40.5%. Thus WC 40.5% x (18/58) = 12.6%.
And so it goes to the playing in the second round, he plays there 72% of the time, and advances 1/3 and not advancing 2/3rds. His superrebuy happens when he played in the second round and didn’t advance and his chances there are, once again, 1/3rd - thus we have:
1st play 72% x 33.33% = 24%
superrebuy (72%x.66.66%) x 33.33 = 16%
60 players advanced from 1st play second round and superrebuy, wild card drawing have (162-60) x 0.8 = 82 players eligible, he didn’t make to the third round 60% of the time, so
WC 60% x 6/82 = 4.4%
...and so on.

The simple formula: total prize pool divided by the numbers of players works great for simple tournaments formats for average skill player.
Even for better than average player it can be easily adjusted if he knows how much better he is for the whole tournament with that specific format (and has large enough record to justify it).
However, if there are rebuys, and especially “superrebuys”, where only players who advanced to a higher round can use them, or there are “autoqulifiers” put in by the casino into higher rounds, or wild cards are not evenly distributed because they are earned by bigger gambling or for achieving specific goals, then analysis like mine above can present approximate value of the tournament. This should be adjusted by using specific “better than average per round”.

Colin, the GN link has prize structure showing prizes for the finalist (1 to 6) and places 7 to 26 winning $500. That means there will be 5 semifinal tables of 5, one per table advances plus one wild card, and the rest (4 each on 5 semi tables = 20) gets semifinal bonus.

S. Yama
 
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S. Yama said:
Colin, the GN link has prize structure showing prizes for the finalist (1 to 6) and places 7 to 26 winning $500. That means there will be 5 semifinal tables of 5, one per table advances plus one wild card, and the rest (4 each on 5 semi tables = 20) gets semifinal bonus.
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That does sound quite likely. But I can't see a description of the $500 as a semifinal bonus. Couldn't the semi be (for example) 5 tables of 6, with last place at the table getting nothing?
 
Hey Yama, you live in Vegas? We could still meet up if so. I'm in town this weekend and other than the GN tournament I have nothing else planned.

Colin, from experience everybody at the SEMI table gets $500. The structure Yama put down is very accurate.
 
I have never seen more than 4 at a GN 100K semifinal table. YMMV.

All semifinalists get the $500. I have also never seen less than 2 advance from any table/round except for the semi. They figure things out so that it works that way, they've been doing 'em a long time and know what's going on.
 
Colin,
When I wrote this question I thought it was 6...having been to the SEMI's twice including last month I know for sure there were more than 4 people there. I would remember if it were four people. It may have been 5....if the numbers work out so that it was 5 I wouldn't disagree with that. There is another tournament this weekend and I'll do some detective work. I'll ask the staff how many players were entered, with and without rebuys and I'll make a point to see in each round the number of players playing for variance, etc. If there is anything you'd like me to ask/look into let me know. It is a great tournament, expensive but like LeftNut said...well done...and you get alot of rookies in the first round which is always a nice surprise.
 
So I guess the moral of the story is be careful of tournaments where the prize pool doesn't increase with the number of entries. Based on Yama's breakdown if the average player spends $1073 x 162 players= $173,826 and yet the prize pool is capped at $100,00. Doesn't seem like such a great tournament after all however it is much better than the terrible numbers I was coming up with.

What is an acceptable keep for a casino in your eyes? Like Yama mentioned, it requires a lot of manpower, blocking off of the casino to host an event like this so I don't expect them to payout everything.
 
tucson1972 said:
Colin,
When I wrote this question I thought it was 6...having been to the SEMI's twice including last month I know for sure there were more than 4 people there. I would remember if it were four people. It may have been 5....if the numbers work out so that it was 5 I wouldn't disagree with that.
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It's this inevitable degree of uncertainty that makes me question the value of this whole approach. We have uncertainty about the actual structure that the casino will employ if the maximum number of players enter. We don't know what that maximum number of players is. And we don't know how the structure gets modified for other numbers of players. There are just too many variables.

tucson1972 said:
There is another tournament this weekend and I'll do some detective work. I'll ask the staff how many players were entered, with and without rebuys and I'll make a point to see in each round the number of players playing for variance, etc. If there is anything you'd like me to ask/look into let me know. It is a great tournament, expensive but like LeftNut said...well done...and you get alot of rookies in the first round which is always a nice surprise.
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Alas, it's a bit too far for me to travel!:)
 
S. Yama said:
$ cost and Ev

I think tucson would like to see the exact EV of the GN blackjack tournament. To do so, other than the correct formulas provided by other posters in this thread, we should use concrete format with specific numbers of players. Also, we need to clarify if one attempts to just pay the original entry fees or rebuy and superrebuy, as well.
From the link Colin provided it shows that there are 5 players per table in the semifinals.
Let’s make a model, which may be not as exact as the one of the coming tournaments but should serve as an example.
We plan on all rebuys, 4 out of 5 drawn names are present (in many tourneys it is much lower).
The format could be as follow:

1st Round
162 players – 27 Tables (all tables have 6 players, two advance)
54 players advance, 108 don’t advance
Rebuy
90-100 people rebuy, 18 tables, 6 or 5 per table (average 5.1), 36 advance
Wild Card to 2nd round: 18
total advancement to 2nd round 108

2nd round
108 players, 18 tables of 6, 36 advance
Superrebuy 66-72 players, 12 tables, mostly 6 per table, 24 advance
WC to 3rd round: 6 names
total advancement to quarterfinals around 66

Quarterfinals
66 players, 11 tables, 22 advance
WC to semis: 3 names
total in semifinals 25 players

Semifinal
25 players, 5 tables of 5, one per table advances to the final
plus 1 Wild card

We can calculate the chances of advancing for the average skill player:

to 2nd round:
1st play 33.33%
Rebuy (66.67x 39.2%) = 26.14%
WC 40.5% x (18/58) = 12.6%
Total chance 72%

to quarters:
1st play 72% x 33.33% = 24%
superrebuy (72%x.66.66%) x 33.33 = 16%
WC 60% x 6/82 = 4.4%
Total chance 44.4%

to semifinals:
44.4% x 33.33% = 14.8%
WC 85.2% x 3/112 = 2.3%
Total chance 17.1%

to final:
17.1% x 20% = 3.4%
WC 96.6% x 1/120 = 0.8%
Total chance to make the final 4.2%

As you can see making finals happens once in about 24 tournaments, which is slightly better than 6/162 (once in 27) because not all players rebuys and show for the wild cards.
The total expected value is $696 ($612 from the final table prizes).
The expected cost because of all possible rebuys is $1,073.
So, for people who pay all the entries it is 35% disadvantage.
However, I don’t know a single person who thinks that his skills are below the average player. For people who are better than average it is quite another story.

S. Yama
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Great ides, insights etc...
 
tucson1972 said:
Thanks for the help everybody. My pea-sized brain has been absolutely consumed with this question. Quite simply yes as pointed out numerous times, take the number of spots at the final table divided by total players and you will have your odds of making the final table. For whatever reason when I tried to calculate from the bottom up (average rate of advancement starting from round one) my numbers seemed to get inflated beyond belief and I finally figured out why. Let's take the Orleans tournament for example because they are the most clear cut. What I've discovered through this thread is once they start throwing in wild card spots it REALLY screws the math up so let's keep it simple and go with the Orleans which do not offer wild card spots. The structure is the following:
Round 1: 1 of 6 advance(6:1)
Round 2: 2 of 6 advance(3:1)
Money Table: 6 players play for pot of $3000 with an entry fee of $50.

Now, doing the simple math the odds of you making it to the final table are 18:1 (6x3). However, when I tried to do it the simple way I got screwed up because I assumed the pot was close to EV neutral and took the entry fee and divided it by 3000 which tells me they expect 60 entries. 6/60 gives me a 10:1 chance of making it to the final table. Big difference than 18:1. So where was my error? Well, upon closer look I realized if the tournament was truly sold out there would actually be 108 players for a true pot of $5400...but better yet and the reason I can sleep tonight....6 divided by 108 equals 0.0555 which when you divide 1 by 0.05555=18! So my hunch was right...you should be able to calculate by round the odds of making the table or if you know the total number of players that would be easier but either way it should be the same. Obviously I'm a newbie to all this. Perhaps this is the norm, guaranteeing an amount significantly less that what the tournament structure can support in case of a low turnout. And I guess I'm talking in circles again as the original point of this thread was analyzing a games EV based on each round as you play it and based on the fact I sat with a full table for round 1, that's around a 40% house edge and that's hard to ignore.
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With analyses like this one it's easier to work with probabilities rather than odds. If of six advance your probability is 1/6 or 0.167. Your odds are 5:1, not 6:1.

Because of wild cards, re-entries, etc. the probability of cashing is the number of finalists divided by the number of entries.

As far as how the format of a tournament impacts its value for a player with above average skill, you have to consider the number and complexity of decisions that the format challenges the players with. Also, the impact that decisions have on an individual's outcome is a factor. How many hands do you have to play to get to the money? How many complex decisions do you have to make to get to the money? How strongly does the format reward dumb luck? This is more of a way to compare tournament formats rather than a way to quantify some sort of luck factor for a single tournament. And don't forget how soft the player pool is. A high buy-in open tournament populated mostly by crushers will have a bigger luck factor than one in which most of the players are clueless about strategy.
 
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