Tourney A Structure Puzzle: Can You Solve It? (2 Viewers)

[TheLemursReturn]

I know perfection (hitting every request below) may be a tall order. But I also know PCF is collectively genius. I've come very close to a few structures that hit everything. But all of my variations have to fudge at least one of the rules below.

I have plenty of chips for base-1, base-5, base-25, or base-100, so I feel like there must be a way to do this.

1. 14 players (just using the average for 2 tables)
2. 100BB stacks with 1x prebuy, plus an estimated 4% in bonus chips
3. BB always 2x SB (players are squirrels, remember)
4. No BB ante (squirrels)
5. Blind increases ranging from 33-50% (the occasional 25% permitted) OR ranging from 50-67%. No doubling from level 1 to level 2
6. First color up, first break, and the rebuy cutoff all align. I'm using a substitute TD while I'm away and I want to keep things dead simple for him. This should occur after at least 1h 15m
7. We've been allowing rebuys while they're worth more than ~16 BBs, then cutting off. But I'd like to nudge that up a bit, to more like 20-30 BBs
8. Only 2 color-ups, to keep it simple for the substitute TD and to allow the color-ups to align with two breaks. No delaying color-ups just to avoid or merge them
9. Minimum 16m levels (my squirrels deal SLOW and talk A LOT)
10. 4 hours of play, breaks additional

Obviously I don't NEED all of this. Fudging is fine. But I'm curious if anyone can get it all.

 

[TheLemursReturn]

Meant to page @BGinGA of course.

 

[Nine_high]

I know perfection (hitting every request below) may be a tall order. But I also know PCF is collectively genius. I've come very close to a few structures that hit everything. But all of my variations have to fudge at least one of the rules below.

I have plenty of chips for base-1, base-5, base-25, or base-100, so I feel like there must be a way to do this.

1. 14 players (just using the average for 2 tables)
2. 100BB stacks with 1x prebuy, plus an estimated 4% in bonus chips
3. BB always 2x SB (players are squirrels, remember)
4. No BB ante (squirrels)
5. Blind increases ranging from 33-50% (the occasional 25% permitted) OR ranging from 50-67%. No doubling from level 1 to level 2
6. First color up, first break, and the rebuy cutoff all align. I'm using a substitute TD while I'm away and I want to keep things dead simple for him. This should occur after at least 1h 15m
7. We've been allowing rebuys while they're worth more than ~16 BBs, then cutting off. But I'd like to nudge that up a bit, to more like 20-30 BBs
8. Only 2 color-ups, to keep it simple for the substitute TD and to allow the color-ups to align with two breaks. No delaying color-ups just to avoid or merge them
9. Minimum 16m levels (my squirrels deal SLOW and talk A LOT)
10. 4 hours of play, breaks additional

Obviously I don't NEED all of this. Fudging is fine. But I'm curious if anyone can get it all.

I love puzzles.

40k starting - 20 min levels

1. 200/400
2. 300/600
3. 500/1000
4. 800/1600
5. 1200/2400
B. color up 100 & 500, end rebuys
6. 2000/4000
7. 3000/6000
8. 5000/10000
9. 8000/16000
10. 12000/24000
B. color up 1000
11. 20000/40000
12. 30000/60000
13. 50000/100000
14. 80000/160000
15. 120000/240000

A rebuy in lv 5 is 16.67 bb, so not much increase there but I think it meets everything else. All increases are 50%-67%. Game should not run over 4 hrs even with two full tables and 100% rebuys.

 

[Craig D]

Like this:

Starting Stack: 10000
Players: 14
Starting Chips: 8x25 13x100 5x500 6x1000
Duration: 4 hours

18 Minute Blinds:

50/100
75/150
100/200

150/300

END REBUYS Colour Up 25s

200/400
300/600

400/800
600/1200
800/1600

Colour Up 100s

1000/2000
1500/3000
2000/4000

3000/6000* Normal End 14 Players EDIT NO REBUYS

4000/8000
6000/12000
8000/16000* EDIT: NORMAL END 14 REBUYS

 

[BGinGA]

Below is my shorthand summary of your requirements (easier for me to reference).

First question I have is regarding prebuy vs rebuy -- because you mention both, but they are different format constructs that affect the total chips in play (and thus tournament length).

'Pre-buys' are pre-paid re-buys (also known as "re-loads") which are used when a player busts, and any remaining unused are eventually auto-added at a predetermined point. 'Re-buys' are only purchased as needed (typically when busted), and generally result in far fewer total chips in play (usually 125%-133% of the total starting chips, vs 200% with pre-buys).

It also affects the extra stacks value in BBs (re-buys are valued based on the BB during the last level they are available for purchase, while pre-buys are valued based on the BB of the level after the unused pre-buys are auto-added).

Which construct do you wish to implement?

chipset: base-1, base-5, base-25, or base-100

1. 14 players
2. 100BB stacks, 1x prebuy, 4% bonus chips
3. BB = 2x SB
4. No BB ante
5. Blind increases 33-50% OR 50-67%
6. First color up, first break, and rebuy cutoff all align & occur at >= 1:15 into event
7. rebuys worth >16 BBs up to 20-30 BBs
8. Only 2 color-ups that align with two breaks (no delaying color-ups just to avoid or merge them)
9. Minimum 16-minute levels
10. 4 hours of play (excluding breaks)

 

[TheLemursReturn]

Prebuys. So 200x total "level-1 BBs" per player plus bonus chips.

 

[BGinGA]

T100-base chip set
T40k starting stacks (10/4/11/5, 30 chips)
T40k pre-buy stacks (3xT5000 + 1xT25000)
200/400 opening blinds (100 starting bb)
20-minute blind levels
1,164,800 total chips in play @ L6 start

chip set:
140 x T100
56 x T500
154 x T1000
122 x T5000 (includes 10x for color-ups)
20 x T25000 (includes 6x for T1000 color-up)
---------
492 total chips (plus your undefined bonus chips), with 142(+) chips in play at event end

L1 200/400
L2 300/600
L3 500/1000
L4 800/1600
L5 1300/2600
remove T100/T500 chips
add unused 40k pre-buys
L6 2000/4000
L7 3000/6000
L8 5000/10000
L9 8000/16000
L10 13000/26000
remove T1000 chips
L11 20k/40k
L12 30k/60k **eot
L13 50k/100k

Event should finish by end of L12, which is exactly 4 hours of play with 20-minute levels.

All blind increases are either 50%, 54%, 60%, 62.5% or 67%. First break (of two) occurs at the 1:40 mark.

The only fail is the BB value of the pre-buy stack forced add-on at L6 (10bb). This can be raised to 25bb if forced after L3 (1 hour), but would require a quick extra break to distribute the chips. For ease of TD duties, go with 10bb. For improved player stack equity, go with 25bb and an extra break.

It's similar to @Nine_high 's structure, but smoother with four fewer increases at the two extremes (1600-2600-4000 and 16k-26k-40k increases are 62.5%/53.8% vs 50%/66.7% with 1600-2400-4000 and 16k-24k-40k).

Fyi, @Craig D 's T25-base 10k structure above could easily run up to 4:45 plus breaks (16 levels @18 minutes) since you're doing pre-buys. Using 15-minute levels gets it finished in 4 hours.

 

[Nine_high]

Nice use of Fibonacci @BGinGA

Another solution, going for milder increases uses narayana's cows. Due to the consecutive 5x jumps, it works best in T1:

800 starting - 20 min levels

1. 4/8
2. 6/12
3. 9/18
4. 13/26
B. color up 1, end rebuys
5. 20/40
6. 30/60
7. 45/90
8. 65/130
B. color up 5
9. 100/200
10. 150/300
11. 225/450
12. 325/650
13. 475/950
14. 700/1400
15. 1025/2050

Game should not exceed 4 hrs with 14 players. Two full tables should still end on time using 18 min levels. Lv 4 rebuy is 32.5 bb, cutoff after 1:20 of play. Blind increases are 44.44%-53.85%

Purely academic math nerd puzzle solution, I would for sure play one of the previous structures in real life

 

[JustinInMN]

So I deliberately have not read any other responses just because I want to take my whack at this. (I will circle back after my post to compare notes.)

1. 14 players (just using the average for 2 tables)
2. 100BB stacks with 1x prebuy, plus an estimated 4% in bonus chips

Ok, so roughly 2900 initial big blinds in play, meaning the 20bb rule will be in effect when the big blind is roughly 145x the initial big blind.

3. BB always 2x SB (players are squirrels, remember)
4. No BB ante (squirrels)
5. Blind increases ranging from 33-50% (the occasional 25% permitted) OR ranging from 50-67%. No doubling from level 1 to level 2

So I do tend to advocate for a 2-4, 3-6, 4-8, 6-12, 8-16 progression of every chip in play, which fits the requirements in points 3 and 5. (Side note, sometimes I recommend early 1-1, 1-2, and 1-3 levels of the first chip in play at the start, but in this case, that would be afoul of the requirement in point 3.)

6. First color up, first break, and the rebuy cutoff all align. I'm using a substitute TD while I'm away and I want to keep things dead simple for him. This should occur after at least 1h 15m

So I do personally like 18-20 minute levels, but I think we need to get as many levels as possible in before this mark so I think we have to accept five 16 min levels for 1h20 of play (yes I peeked ahead at point 10),

This means we have to pick a "base" where the first jump is 5x. This eliminates t25 and T500.

7. We've been allowing rebuys while they're worth more than ~16 BBs, then cutting off. But I'd like to nudge that up a bit, to more like 20-30 BBs

8. Only 2 color-ups, to keep it simple for the substitute TD and to allow the color-ups to align with two breaks. No delaying color-ups just to avoid or merge them
9. Minimum 16m levels (my squirrels deal SLOW and talk A LOT)
10. 4 hours of play, breaks additional

Point 8 means we probably eliminate T100 as a possible base because then we have the second color up would be T500 which doesn't do much for tournament management. So I think we settle on base T5 with 10-20 as level 1 and a T2k starting stack, and try to wrap up on the 800-1600 level.

Let's see how close we get.

10-20, 15-30, 20-40, 30-60, 40-80 (remove T5, close reentries)

(Note on point 7, this would be about 25bb at the cutoff, nailed it.)

50-100, 75-150, 100-200, 150-300 (remove T25)

200-400, 300-600, 400-800, 600-1200, 800-1600

So this is 14 levels at 16 minutes each or 224 minutes of play (3h44m plus breaks)

If we assume roughly 58k in play that means about 37 big blinds in play at this level, it will often end here. However, you could add one more level at 1200-2400 (to skirt the natural t500 color up here) and get close to the 20bb rule. One more level also means exactly 4 hours of play.

So I think this checks all the boxes with one twist at the end.

As for chips, I suggest starting stacks of 10/10/7/2 of T5/25/100/500. 406 chips for starting stacks (29*14), plus extra t500 or 1000 for color ups and redemption add ons. 140/140/100/40/30 of T5/25/100/500/1000 for a 450 chip set.

I think this would also work fine for a T1 base.

 

[TheLemursReturn]

Wow - thanks a ton for all the intense analysis everyone. Really appreciate the effort.

It seems that we're still missing a perfect solution. Maybe it does not exist.

The last one comes close, but even with its final 67% jump, it doesn't get us to the 3k BB required (~5% of ~58k) for 14 players, let alone more players.

I'll post my best effort when I get back to my PC. I used base-25, 19 or 20m levels, 50-67%, and chose to fudge with a 100% jump from level 1 to level 2.