How to calculate ROI/expectation with BJ tournaments

Hello all,
I'd like to think I'm pretty good with math but I tried to calculate my odds and anticipated ROI with various tournaments and it's driving me crazy. For example, lets talk about the Golden Nugget tournament. All things being equal odds of making the final table is 1 in 162. Calculations are from the following:
1st round: 2 of 6 advance (1 in 3 chance)
2nd round: 2 of 6 advance (1 in 3 chance)
QTR Final: 2 of 6 advance (1 in 3 chance)
SEMI Final: 1 of 6 advance (1 in 6 chance)

3x3x3x6=162

Now....assuming the final table chops the pot each player at the final table will take home around $14,000. Ok, if the average player will make the final table every 162 times they play at $500 a shot that means they are spending $81,000 for every $14,000 they make which doesn't make sense at all. My calculations must be off somewhere but I'm not sure how. I assumed tournaments where fairly decent with ROI assuming the tournament payouts close to what they bring in. HELP!!!

 

If you hunt around, there are some past threads on this topic that you might find interesting.

If you aren't attempting to factor in your own, personal edge (i.e. your assessment of how much better you are than an average player), then the calculation is simply total_prize_pool / number_of_entrants.

In practice it can still be complicated because both of the above terms may have to be estimates, particularly if rebuys are permitted (in which case we are concerned with the number of entries, not entrants, and you generally want to rebuy as many times as possible).

Is this the tournament you are talking about? - https://www.blackjacktournaments.com/oldtourn/viewtourn.php?infoID=2260

If so, then -

The guaranteed prize pool is 100K, but presumably all entries go into the prize pool, so if there are more than 200 (including rebuys) then the prize pool will be over 100K.

(Or if it should be the case that the prize pool is fixed at 100K, with the casino keeping any excess, then you don't want there to be too many entrants, or there will come a point where it is not worth playing.)

[Also note that not all the prize pool goes to the final table, and the small amount that does not appears to be promo chips, rather than cash. So the total value of the prize pool is a bit less than the advertised 100K.]

I can't see where you got the multi-round breakdown from, but this will also depend on the number of entries. There may be less rounds, and tables of various sizes, to accomodate the actual numbers. For the breakdown you have given to actually occur in full there would have to be 6 x 162 = 972 entries into the first round, meaning a prize pool of 972*$500 = $486K, if all the entries go into the prize pool. (Or the sort of utterly non-worthwhile return you indicated if the prizepool is in fact capped at $100K.)

 

Golden Nugget in Vegas

I had the same thought re: which BJT - one of the GN 100K events. If so, there's another factor to include in the calculations. Making the semifinal round gets you the $500 entry fee paid back.

Also, the majority of players in those are comped. There aren't very many paid entries, one must fall in a narrow range of being between a comped player and not being allowed to enter at all.

 

You should make the final table one 1 in 27 attempts.

 

But-------

boneheaded errors like I make at times, can really throw off the theoretical expectations.:laugh::laugh::laugh:

Billy C

 

Thanks for the quick responses. I know the round breakdown because I've played the tournament numerous times and am at a crossroads whether or not to continue. In other tournaments you are correct (London), number of rounds, number of players at the table, number advancing all depend on the number of players, number of rebuys etc. However this tournament is different because they do give out so many comped entries, etc that pretty much I know what to expect every round. Maybe reduce the number of players at the table by 1 max in round 2 and 3 but every time I've played the tables are pushed to 6 and unfortunately no, the payout is capped at 100k regardless of number of entries.

LeftNut is correct, you do get $500 for making the SEMI round however just to keep the calculations simple I didn't want to factor that in. 25 players will get the $500 SEMI final payout which doesn't really make a dent in the final calculation.

Moses, I think you should make the SEMI table one in every 27
1st round 33% chance of advancing
2nd round 33% chance of advancing
QTR FINAL round 33% chance of advancing

There is your 1 in 27. You still need to get past the SEMI take which only 1 in 6 will do.

Ok, perhaps Golden Nugget was a bad example because the pot does NOT increase, there are so many comped players, and so many rounds. Here is a simpler example with the same bad results. London, perhaps these calculations get thrown off with the re-buy option compared to tournaments where you can't re-enter. I'm familiar with the formula you gave me however I would think you could use the odds of making it past each round to also determine whether a tournament is a good one to play or not.

This example is based off the Orleans weekend tournaments.
$50 entry fee, 3 round tournament
1st round: 1 in 6 advance
2nd round: 2 in 6 advance
Money Table: 1st place $2000, 2-5 earn $500 each for a total of $3000. The pot does increase depending on the number of players/buy-ins.

Ok, based on my calculations you have a 1 in 18 chance to make the money table. On average each player at the money table gets $500. At $50 a shot x 18 each player should be making $900 or the pot should be closer to $5400. I can tell you the pot does increase but nowhere near $5400. This past weekend I think the total pot was $3300.

One last by the way, London Colin, now that 5 Dimes doesn't offer BJT anymore, where are you playing? Thanks everybody!

 

Factor in Your Own Experience

Tuscon, you can do a little better with your calculations, given that these appear to be tournaments that you have personal experience with. Instead of using the average advancement rate, use your actual advancement rate. This is one way to factor in your own skill level, which is important, because most tournaments are not +EV based on the prize pool and the number of entrants alone.

Keeping detailed records, of course, makes this easier. Just as most advantage players keep detailed records of their play, tournament players should keep detailed records of their advancement rates. In my records, I factor in the ratio of the maximum and minimum bet to the starting bankroll, the number of hands in the round, the number of players and advancers at the table (the actual numbers, not the ratio), a rating of the typical aggression level of the other players and a rating of the average skill level of the other players. For accumulation rounds, I keep stats regarding the required goal as well as my advancement rates.

Over time, this allows me to gather advancement rates for various "table types" which not only helps me to evaluate the regular events that I play, but also allows me to have some idea about how I might do at a new event.

 

Thanks Gronbog,
I do keep track of my advancement rates compared to the average but that is another thread entirely. With this thread I was trying to determine if one could calculate the value of a tournament based on average advancement and payout alone. I realize that BJT don't offer +EV tournament unless something really out of the ordinary happens (like poor turnout) and that it is a player's skill that will tip the scale into their favor HOWEVER what I'm realizing is that even tournaments that increase the pot with the number of entries the "vig" is really high....unless I'm missing something but the calculations to me seem pretty straight forward.....and going back to the Orleans example....$900 dollars in entry fees (1 in 18 at $50 a shot) for every $500 in winnings doesn't sounds like the casino is paying out anywhere close to what it is taking in based on the structure it uses. Roulette is the worst game in the casino with a house edge of 5% but if I bet $50 on an 1 in 18 wager and got paid $500 (instead of $900 which would be the true odds) that gives a walloping house edge of 44%.

I guess my point is have I got it terribly wrong? Is there some calculation that is for whatever reason I keep missing? Or...do I have to admit that these BJT are not the +EV you would think because the payouts just aren't there when you assess it like you would any other casino game. And I have calculated my skill based on average advancement rates and have even been banned from casinos but I can tell you a house advantage of 44% it still a tough pill to swallow. Please somebody tell me I have it all wrong. I like playing blackjack tournaments but what I'm slowly realizing is even though I'm better than the average play...I'm not so good that it makes up for a crappy payout on the casino's end.

 

EV is over $500

If the Golden Nugget had exactly 200 entries including all rebuys, the EV would be exactly $500. They almost never have 200 entries (not in over two years). Discounting skill, the EV for every entry in the tournament is over $500. Comped entries do not matter, because the Golden Nugget pays out the full guaranteed purse in each tournament.

 

No, I don't see that you've got it terribly wrong. What I am seeing in your examples (Golden Nugget and Orleans) are two tournaments with underfunded prize pools and, in the case of the Nugget, a tournament with too many rounds (EV decreases exponentially with the number of rounds).

Maybe I've just been lucky, but the events I've played (mainly in Ontario, Quebec, Michigan, New York and Pennsylvania) have all had prize pools scaled to the number of entrants regardless of whether entries have been comped or not and have returned almost all (if not all) of the (theoretical) entry fees to the prize pool. As such, the "vig" has been minimal and, factoring in my advancement rate, I have been able to show that they are +EV for me.

What you have shown is that it is essential to figure out at least a ballpark EV for any event before you decide whether to enter.

 

If we discount skill, which we can't accurately estimate, the EV for any tournament is the total prize purse divided by the number of entries (original and rebuys). If the EV is greater than the cost of an entry, then the tournament is a "good" value. It doesn't matter how many rounds there are. Everyone has an equal chance of advancing through however many rounds there are.

 

1 in 162 would be correct for the rounds as described; 1 in 27 would be to the semi.

Unless they give out a total of 972 entries, you cannot expect the situation to be as you described it. If you want to know the probability of reaching the final table; it is six divided by the total number of players. You don't need to worry about the structure, unless you are trying to factor in your skill level. (Which does then start to get tricky. As I said, there are some old threads kicking around somewhere which cover this topic.)

I briefly looked at the casino website and got the impression that these $500 payments were part of the $100K total (and also that they were promo chips, not cash). By dividing the $100K by the number of players, all payouts are factored in, regardless of where in the structure they occur. But you do lose any distinction between cash and promo chips, unless you mark down the value of the promo chips to begin with, I suppose.

I may have misread the casino information, though.

If they pay out all the money they take in, then the EV is zero for an average player, regardless of the number of players or the structure.

I'm not, unfortunately. GameAccount is now the only site I'm aware of that offers any form of elimination BJT (but Americans, and indeed Canadians for some reason, are not allowed). I haven't played there in quite a while.

I tried to point out where you went wrong in my first post, but probably hid the answer among too much wittering. Moses put it a lot more succinctly.

To come at this from a slightly different direction -

For every player to have the same 1 in 162 chance that you calculated for the Nugget, they must each have to play the same number of rounds, with the same number of players at each table in a given round. That is, they must each be faced with the same path to the final.

For that to happen, the tournamnet must be 'full'. -

For each of the 6 finalists, there will have been 6 semi-finalists, making 6*6=36 players at the semi stage.
For each semi-finalist, there will have been 3 quarter-finalists, making 36 * 3 = 108 players at the quarter stage.
For each quarter-finalist, there will have been 3 round-two-ists, making 108 * 3 = 324 players in round two.
For each round-two-ist, there will have been 3 round-one-ists, making 324 * 3 = 972 players in round one.

In reality there are nowhere near this number of players. So long as everyone is treated equally when it comes to how the structure is jigged around to cope with the numbers on any given day (that is, everyone should have an equal chance of getting a rebuy, of finding themselves at a short table, with a bye to the next round, or whatever, without the casino playing favourites with anybody), then all the matters is the number of players.

Assume 200 players, bidding for 6 seats at the final table. So they each have a 6/200 chance of getting there. Once at the final table, they have an EV of $100K / 6. Which means their initial EV was 6/200 * $100K/6 = $500. Q.E.D. [Reverting to the assumption that all the payouts go to the final table, just for the purposes of this example.]

 

I thought EV went UP with the number of rounds (for a given number of players and a given prize pool).

[To clarify, I mean EV in the sense of a player's personal edge, derived from above-average skills, rather than EV in the sense I've previosly been using it - the average amount returned to each player. The latter would not change at all.]

 

I have a flyer from one of these BJT'S that I attended earlier this summer. The $500 for making the semifinals is cash. Final table players have a choice of cash, slot credits (works for video poker, too), or the "good" promo chips.

Also, the semifinal prizes are, indeed, part of the 100K prize pool, as is a $5,000 wristwatch given out at a drawing.

 

Yeah, I got it wrong. This is what I was looking at - http://goldennugget.com/specials/eblasts/great_american_blackjack.html

So it seems everyone can take cash, but the top 6 are offered the choice of something less valuable; presumably in the hope that they will take it!

 

The number of rounds does increase variance, however, since one would cash in less often. This could be a consideration for some players.

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.

 

Where the error might be

Hi Tuscon
You calculating one extraround. The 2nd round is the quarter final. So if you win every time, you go 1st round, 2nd round, semi and then final.

 

Taking the cash option also means accepting a love note from the I.R.S.

 

more aspects of EV

Hey tucson1972 and others,

Interesting questions. I think the subject matter is much more complicated and to get “mathematical” answers to you pondering the EV of GN bj tournament we need to have specific details.

Let me address a few things before we get to the EV numbers.

We need to keep in mind that casino tournaments are strictly business. They (casinos) have to make money. From what I know, we can see them work for two and half days. There are about ten dealers, four floor persons, maybe another four people at the registration, reentries, plus catering people (and the food). Then the work we don’t see, before and after, including accounting, reports, etc.. That could easily be $15K to $20K, or who knows how much.
The “space and time” in casino where the tournament is held, if there would be no tournament, would earn some income as well, and will be missed, so now it has to be considered as the cost.
The comped entry fees for some players are fully (and then some) paid by gambling loses. But for some players the free entry, at least partially, have to be consider as an expense. This is because one has to deduct from their theoretical loses other comps, like food and room, and GN is often sold out on weekends, so, if the tournament players were not there, the other people would bring some (though, not necessarily as good) business.
To make it sound, or at least acceptable, business casino has to withhold some of the total of tournament’s (super)/(re)/ entries.
There are no reasons for having tournaments where all entries are returned as prize money unless it is a mistake or part of a broader marketing plan, where it could be considered a loss leader.

I know that you asking about monetary expected value but let’s think for a moment what blackjack tournaments are. Everybody thinks how great it would be to win and cash $50K, or at least some money on the final table. This is a proverbial and obvious “carrot”. But for almost everybody it is enjoyable, though not necessary apparent, social event. Casino provides service of entertainment for which they (and all other businesses) have right to charge a fee. The better the service the higher the prize. From what I hear GN is probably the best tournament in town and beyond. All comments I encountered were that it is on time, with clear and well executed rules, friendly staff, dealers, and organizers. A few of my friends wouldn’t miss it for the world and praise it for environment that allows them to meet old friends and make new ones, chat, gossip, argue tournament strategies, eat, drink and be merry (unless they lose a bunch, lol).
These are difficult to put a hard dollar sign on, but nevertheless of great importance.

S. Yama

 

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.