New tournament format, what do you think?

Toolman, I didn't really take in the above quote the first time I read it. I think it strikes at the heart of the fallacy in your argument.

In order to have the same EV as every other of the 144 initial players, you must be equally prepared to rebuy. If you rebuy less than the average, you will advance less than average and your EV will be reduced proportionately. You cannot start factoring additional money from other players rebuys into your potential winnings, without also factoring in the cost of your own rebuys into your outgoings.

We are attempting to analyse the situation as it stands before the first card has been dealt, before any rebuys have been bought, before anyone has been eliminated. At this point the average EV for each player in the tournament must (by definition) be zero, since all the prize pool is to be shared among all the players, and all of it is being contributed by the players. If at that point we know that the round-2 and round-3 direct buyins will have positive EV, this can only mean that those entering in round 1 have negative EV. It is the proverbial zero-sum game.

I think you've misunderstood. My first method derived the figure -$60.50. This method derived the figure -$53.15. The difference is $7.35, and I've explained where I think it comes from. [**Wrongly, it turns out. See next post for more details.**]

That's not the case. All I've done is replace the $250 cost of entry which you used, with $380.21. I explained why this has to be done. So to put it in percentage terms, whereas you had -

Round 1 buy-in for $250 with an EV of $327.06 is + $77.06 or 31% (77.06 / 250)

I effectively have-
Round 1 buy-in for $380.21 with an EV of $327.06 is -$53.15 or -14% (53.15 / 380)

If you repeatedly attend tournaments and rebuy as often as the average player, $380.21 is the average amount you will spend to play, and $327.06 is the average prize money you will win.

While we often apply the term EV to the expected payout, the interesting figure comes when we subtract the entry fee from this value and see whether the result is positve or negative, and this too may be called EV. We can also, as you did, then do a division, to convert this into a percentage. I don't know of any alternative terms to EV to explicitly distinguish the latter versions. (One might simply say, 'expectation', or 'value', but they can both be applied to the first version too.)

In fact, you've used the same definition as me in the very first paragraph I quoted above, when you talk of negative EV. There really is no specific TBJ definition of the term.

But it is worthwhile to note that if you never rebuy in this tournament, then your EV from round 1 will be exactly 1/9 of your EV from round 3.
1/9 * 1402.78 = 155.86
155.86 - 250 = -$94.14 ( -37.8% )

And in any 'normal' tournament which offers rebuys at a discount, you have the same consideration - the more you are able and willing to rebuy, the better is your overall EV [in the '(winnings - cost) /cost' sense of EV].

 

Wildcard

I think we may be in danger of overdosing on mathematics, but just to finish this point -

I went back to my original calculation and updated it with this new round-1 method.

i.e.

EV of a round-3 seat is $1402.78
Probability of reaching round 3 from round 1 is 98/144 * 1/3
Average cost is $380.21
Therefore, round 1 EV =
98/144 * 1/3 * 1402.78 = $318.22 (compared to Toolman's figure of $327.06)
318.22 - 380.21 = -$61.99 (-16%)

So then I wondered where the discrepancy came from. Eventually, I remembered that one of the round-3 places is a wildcard, and I hadn't included that in the probability of reaching round 3.

I think this accounts for the small amount of missing EV. If players knocked out in both round 1 and round 2 are eligible for the wildcard (which may not actually be the case), then the additional EV for a player buying into round 1, gained from the wildcard route to round 3, can be calculated as follows -

[144+10-36=118 players having been knocked out, there is a 1/118 chance of having your name drawn, if you did not qualify. This is assuming that the 10 'businness class' players are eligible for the wildcard.]

Knocked out in round 1:
(144-98/144) * 1/118 * 1402.78 = +$3.80
Knocked out in round 2:
(98/144)*(2/3) * 1/118 * 1402.78 = +$5.39
----------
+$9.19
----------

Which makes my revised total 318.22 + 9.19 = $327.41.
(Close enough to Toolman's $327.06)

 

EV - Let's define it

The discussion on this thread related to EV is of no value because we are comparing apples and oranges. We are using different definitions of EV so our conclusions must be, of course, different. So let's each define and present a mathematical formula to arrive at EV as it applies to BJTs. I'll start.

Definition as understood by toolman1:
EV, as it applies to Blackjack Tournaments, means the value of a seat in a given round. Or to put it another way, if John Doe (who is an average player) plays a trillion tournaments with the same rules, same number of players and the same prize pool, EV is the the average amount will he collect from the prize pool.

Formula as understood by toolman1:
Let EV = Expected Value
Let PP = Prize Pool
Let NP = Number of players
FORMULA: EV = PP / NP


So that's the basic definition/formula, as I understand it, which I reserve the right to "tweak" if I missed a minor point. This is not my definition/formula but rather my understanding of the way BJTers have come to accept the term "EV" as it relates to BJTs. I would like to have one or several persons of recognized authority confirm or dispute this definition and/or formula. Yes, Ken Smith comes to mind among others. Are you out there Ken?

 

Common, unambiguous terminology would certainly be useful. But, in terms of the discussion so far, we actually both got to the same value ($327) for the EV, as you have just defined it, for a tournament with the maximum number of entries (including rebuys) at every level. (I just used a different method to get there.)

Where we then differ is that I maintain that you have made an error in your next step, the calculation of the 'thing-for-which-we-cannot-agree-a-name'.
You cannot say (327-250)/250 = +31%.

If you include the assumed maximum number of rebuys in your calculation of the prize pool, from which you derive the $327 EV, you cannot then assert that you (i.e. the player for whom you are performing this calculation) are exempt from this frenzy of rebuying, and have only contributed $250 to the pot.

If your calculation includes the profit gained from potentially winning a portion of the additional rebuy money (the $18,750 that you mentioned), then it must also include the cost of your own contribution to that money. And the average total contribution (entry + rebuys) is $380.


And the problem with not including the rebuys in our calculations, in some way, is that we are seeking to compare the value-for-money of the $1000 and $400 entries, which do not permit rebuys, with the $250 entries, which do. To treat them as equivalent would not give meaningful results.

 

Rooting for you....

Count me in when you get this thing up and running Tex! Good to hear from you....

I know that you'll dot the "I"s and cross the "T's! When you do so, and you solicit input from others on this Board, as you are now doing, it'll pay some huge future dividends for all of us who decide to participate.

Skipper

 

good discussion

Count me in as well, we can turn this thing upside down. But I think the concept has real potential for skilled players to cowboy up and make some money.

 

good try

Rick, there are some interesting elements in this concept.
My approach would be to recognize unique points and systemize them applying some structured math. Continue very good analysis offered in the previous posts in this thread by finding mathematically “fair” ratio of original and higher round entry fees and then somwhat change it to meet the objectives.

I like the idea of some people getting a chance to play in a “high prizes” tourney with a lower entry fee. Those who are fortunate enough to be able to “risk” higher entry fee should be rewarded by just slightly better return at specific higher fee tournament entry points. With good marketing it should be completely filled up, assuring players of desired casino’s guaranteed total prize pool. Let’s give a fixed percent of total players at each level to players willing to pay higher entry fees, better yet, I think it should offer a higher ratios of paid entries at lower stages. Everybody playing first round is guaranteed at least one reentry and other good rules we all know should be there. It could be easily set up for different numbers of entrants with convenient for casino numbers of tables per round.

Sounds like a sure shot, right? Now, the reality kicks in.
On technical side, the system can be tweaked to look better by lowering entry fees compared to paid entry fees you originally proposed. It would work even better if the tourney offered paid entry fees that look so attractive (only double the cost when chance of advancing is 1/3) only to people playing in the previous round, and more pricy, but close to the real value, to players wanting to just jump in at a higher level. I am afraid that this creates a system that would look too complicated to both players and facilitators. As stated before it is a zero sum game (entries and prizes) or even negative if casino wishes to keep some profits. It is possible to make value of prizes look more attractive to some of entrants but only at a cost to others. There is a thin line that differentiates between good marketing and gimmicks. A good thing for this format is that it looks that for entry fee at any level, especially in the first round, it offers very good SV – it is not obvious at the first look that as we insert more players at higher rounds the value gets “diluted”. Also, we know that there would be a few thickheaded people who for personal reasons would like to hamper it, regardless the merit and value it could bring to blackjack community. And the biggest problem is with the casinos, as we know how reluctant they are to try anything new.
I commend you for trying and actually finding an interesting format.

S. Yama

 

I've put together a spreadsheet that allows the number of entrants and size of entry fees to be entered for each class, and then uses Toolman's excellent method to generate a nice overview. It also hopefully makes clear the whole zero-sum game issue, showing the redistribution of wealth between the different classes, so to speak.

Further to what S. Yama just said, my own experiments with varying the entry fees made me think that reducing coach class to $200, with $100 rebuys, might make all the difference. Coach class would still be the poor relation, offering negative equity, but it would be at a level not too disimilar to the sort of thing we are used to when paying a rake in online games.

If you are interested, I can upload the actual spreadsheet, so that you can play with it, but in the meantime I'll post the results for the numbers we've been discussing.

I'm not sure if what follows will align nicely on everbody's screens. In essence what it shows is that for the few big spenders to average 40% and 20% returns on their investments, everyone else has to average a 14% loss.

The last part also shows how vital it is to rebuy whenever you have the opportunity!

Hope this is useful.

Code:

	         No.	Cost	Prize Pool		
					
Coach Entries	144	250	36000		
Coach Rebuys	150	125	18750		
Bus. Entries	10	400	4000		
1st. Entries	17	1000	17000		
					
			        75750		
					
		        Results per Class:			
		        Cost	Diff	%	Total Won
[B]Round 3[/B]					
Players:	54				
Seat Value	1402.78	1000	402.78	40.28	6847.22
Tot Non-1st EV	51902.78	
			
[B]Round 2[/B]					
Players:	108				
Seat Value	480.58	400	80.58	20.15	805.81
Tot Non-bus EV	47096.97				

[B]Round 1[/B]					
Players:	144				
Seat Value	327.06	380.21	-53.15	-13.98	-7653.03
					
			Zero-sum sanity check:		0
					
If a specific coach-class player rebuys -					
	       EV  	Cost 	Diff	%	
Never:          160.19	250	-89.81	-35.92	
Up to once:	266.99	333.33	-66.34	-19.9	
Up to twice:	338.19	388.89	-50.7	-13.04				

 

This concept seems overly wordy and for me seems to reinvent the wheel. What's wrong with just following the tried and true formats of the poker satellite system. For Example:

Day 1: Satellite Day

Step 1 Entries: For $125, you play in a 6-person SNG with 2 people winning a $350 tournament entry chip.
Step 2 Entries: For $350 (or a $350 entry chip), you play in a 6-person SNG with 2 people winning an entry into the Main Event.

Day 2: Main Event

Main Event starts with $1000 entry fee.

Even if only 30 people win or buy in seats, the Main Event already has decent sized prize pool. The advantage of this is that people can rebuy to the original event to their heart's content, or even win multiple entries and sell them back. The casino can award complementary entries to step 1, step 2 or the Main Event, based on what is appropriate to their play.

The main thing this seems to lose is the rigor of a tournament and the randomness of opponents on Satellite Day. This can be solved by instead having fixed "super-satellite" times, where all of the step 1 and step 2 entries are taken at once and grouped into mini tournaments (for example, made up of randomly-assigned brackets of 12 Step-1s and 2 Step-2s).

 

Both I guess

It will be a guarantee starting out, after that call it what you will. All entries and re-buys will be added to the prize pool along with the casinos $20,000. Now out of this $20,000 they will have seats to give to their local players by winning weekly qualifiers or just comps for their bigger players.

All open players entries and re-buys will be added to the $20.000 to build the prize pool for both the monthly and Championship events.

 

Thank you for the kind words my friend, it players like you (and all the others who have offered feedback on this thread) and my love for tournament play that make me want to continue trying to build better tournaments.

I'd love to get a Vegas casino to host these events and currently talking with a couple about just that, (8 qualifiers held every 7 weeks with the Championship event at the end). But if Vegas falls through maybe we could start out in one of the Indian casinos, there's several in Oklahoma that might be interested and they have to give away so much players money anyway. It might be an easier sell to them.

 

Hey Rick, I guess I'll throw my 2 cents in on this one. It's been awhile and I'll come out of my shell for a bit anyway. I think this new format is very interesting but very confusing for us average folks. Your TBJPA rules are the best out there. Multiple re-buys and at least 2 advance every round are what make your tourneys the best. If I fly cross country for a tourney there is nothing worse then bombing out in the first round, getting no-rebuy, ie. stardust and others, and going home. At your tourneys you always stood a good chance of advancing.

I feel the reason turn out was low at your tournaments was because there was not a guarantee or contribution if you will. Your new format is using a $20,000 guarnatee as an example. If you were to get that type of guarantee for your old style tourneys they would have been a success, IMHO. I appreciate your hard work on this and trying to keep the dream alive. Thanks, thrasht

 

Tx has been after me to add my thoughts here, so........

First of all, I like this general idea very, very much. An affordable entry fee at the bottom, with the opportunity for rebuys - an attraction for those of us who'd have to travel many miles. The TBJPA rules are excellent, too, as they tend to reward skilled play much better than some of the one-advance donkfests that I've already seen. Then there is the magic word - guaranteed - that will help those on-the-fence players decide to make the trip (that's where UBT really screwed up). If these can get going, we might actually have a real BJT Tour some day!

What worries me the most is the host casinos getting their meathooks into it, mostly by trying to have their say in who can and cannot play, as well as monopolizing the high level entry points by comping their favored players (thereby making those entries unavailable to those of us who are willing to pay for it). Figuring out a way to negate such a monopoly would be desireable.

Toonces has a very good point. In the fashion that the rules and etc. are stated now, it's easily confusing even to those who are highly familiar with TBJ. Those who might be interested but can't figure it out are likely to stay away. However, running those two lower-level entry points as "satellites" and "super-satellites" are understandable to almost any card player due to poker's influence and popularity. Merely semantics, a change of terms. Something to seriously consider.

I'll stay out of the previous mathematical discussions re: EV. You guys have already covered that ground pretty well.

 

I'll try to simplify the format

Airline format example:

Round 1 total 144 players, 2 advance from each table
*Note: should round 1 not be filled re-buys will be offered to fill any empty seats.

Re-buys total up to 144, 2 advance from each table (max 24 tables)

Wild cards - 2

Round 2 total 108 players, 2 advance from each table

Wild card - 1

Round 3 total 54 players, top 2 adavnce from each table

Round 4 total 18 players, top 2 advance from each table

Round 5 total 6 player

You can see the rounds and session will be played like a normal event. the twist is that we will offer enries into multiple rounds with the entries adjusted acordingly to where the players enter.

Don't sweat who bought in where just play the tournament as you normally would. Only differance is some may risk more money to start deeper into the tournament than others. Everyone will have the same chance to buy in which ever round they like, based on avliblity.

I hope that simpified the working of the airline format for you.

The days of 500 - 600 player tournaments with paid entry fees are long gone, even 150 - 200 player events are becoming harder to find. But with this new concept just a small turnout can produce a big prize pool.

Entries will be limited to 64 - 96 players for round 1 (based on how many players the host casino allows in, $20,000 @ $250 = 80 players). Only 10 players for round 2. And 17 players for round 3. Total of 123 total entries (max).

Now that seems to be more in line with the size turnouts most events have been getting anyway, so why not juice up the price pool and make the events more inviting and at the same time make them something that you sign up for faster and not wait until the week of the event.

By offering limited seating and real limited seating in the 2nd and 3rd rounds, this will make players "**** or get off the pot" pardon my French.

If players know for sure what the prize pool will be before going to an event is a hugh help in deciding which events to play. If I can get a $20,000 guarantee sell out the 17 First class seats 3 - 4 weeks before the event, players will know that the pool is worth a mimimum of $37,000 should no one else enter.

I hate it when I would go to a $50,000 event and then told when sitting down for the 1st round the prize pool has been cut to $32,000. I'd rather offer a 100% guarantee at $20,000 and then hopefully tell players sitting down in round 1 that the current prize pool in the 30's or $40,000's with re-buys still to be added in.

 

After some additional consideration, I'm revising my thoughts on the price structure. I think a price structure of $250, $500, $1,000 would be better:

1) This gives a wider difference between levels 1 and 2 which I think will encourage more ploppies to enter at the $250 level.

2) This structure looks more logical to the average player - each level is double the previous, just sounds nice.

3) With the 2nd level raised by $100 more prize money is added to the prize pool.

 

That would also mean that -

4) The 2nd level now, like the first, has a negative player advantage (though only marginally). i.e. the seat value is less than the $500 cost.

It's negative if you have the maximum number of $1000 entries, at any rate; only 10 or 11 $1000 entries, together with the maximum $250 entries + rebuys would make it a roughly break-even proposition.

My vote would be to lower the first-level entry to at most $200, rather than raise the second-level entry, even though that may mean a slightly smaller prize pool.

 

Why I came up with the fees I did.

The $250 entry was as low as I wanted to make the entry fee for the following reasons:
Make it affordable for the players and still have a big enough prize pool to make it worth players traveling in for.

I like the simple double the entry fee every round math, but does that really work?

Now as a player I wouldn't enter the 2nd round for $500 when I could enter round 1 and play two re-buys at the same $500. As a season tournament player, I'd take my chances to advance once out of three chances.

Now at $400, I would stop in think about it and the time and stress I could save myself by entering round 2 instead.

We all know there are players who if they play will jump on the $1,000 entry level everytime, but there is a lot more that will only be able to play if we offer the $250 entries. And to have a successful tournament you need a range of all level of players.

Are the number right? Guess I'll find out after we host an event or two, if there not I'll twick them at that time and if it isn't broken then I won't have to fix it...lol.

 

That assumes you will get two opportunities to rebuy.

There's a curious paradox about the first level: If it isn't popular, then it can potentially be a good deal for the few who do play, because they effectively have unlimited rebuys.

But if it becomes popular (which is, after all, the intention), then the limit on the number of rebuys becomes a factor.

 

Re-buys