Tourney Mathematics of Blind Schedules (1 Viewer)

Alex Lundstrum

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* Warning * - Ramblings of a bored math nerd below:

Everybody knows the pain of being in a tournament with a TERRIBLE blind schedule. Jumps of 2-3x followed by a 10% increase in blinds, etc. Everybody also knows the pain of a hand taking just a little bit too long, landing themselves with an increased big blind on the subsequent hand. Whilst pondering these two aspects of tournament poker, an idea occurred to me. What if the blinds continuously and smoothly increased throughout the duration of the tournament, with the cost of the blinds being determined by the exact amount of time that had elapsed in the tournament following an exponential curve, rather than step changes. This of course wouldn't be realistic in a live tournament, but could very easily be done with an online tournament.

Following the conclusion that infinitely small step changes in blinds is not realistic in a live tournament, I started to ponder whether the inverse of this idea could be utilized. Instead of steadily increasing blinds by infinitely small amounts, what if a typical blind schedule was followed, except for that the length of each level would be directly correlated to the size of the upcoming increase to the blind - large jumps in the blinds would be preceded by longer levels, while smaller jumps would be preceded by shorter levels. This, unlike the original thought, could very easily be managed using a tournament manager software. Some mathematical wizardry involving logarithms and the like plop out an equation for the generation of the "Mathematically Pleasing Blind Schedule."

Time..........Small Blind.........Big Blind.........Level Length
0:00..........................50...........................100..........................0:24:22
0:24..........................75...........................150..........................0:17:17
0:41.......................100...........................200..........................0:24:22
1:06.......................150...........................300..........................0:17:17
1:23.......................200...........................400..........................0:24:22
1:47.......................300...........................600..........................0:17:17
2:04.......................400...........................800..........................0:24:22
2:29.......................600........................1200..........................0:17:17
2:46.......................800........................1600..........................0:13:24
3:00....................1000........................2000..........................0:24:22
3:24....................1500........................3000..........................0:17:17
3:41....................2000........................4000..........................0:24:22
4:06....................3000........................6000..........................0:17:17
4:23....................4000........................8000..........................0:24:22
4:47....................6000.....................12000..........................0:17:17
5:04....................8000.....................16000..........................0:13:24
5:18..................10000....................20000..........................0:24:22
5:42..................15000....................30000..........................0:17:17
6:00..................20000....................40000..........................0:24:22
6:24..................30000....................60000..........................0:17:17
6:41..................40000....................80000..........................0:24:22
7:06..................60000.................120000..........................0:17:17
7:23..................80000.................160000..........................0:13:24
7:36................100000................200000..........................0:24:22
8:01................150000................300000..........................0:17:17
8:18................200000................400000..........................0:24:22
8:42................300000................600000..........................0:17:17
9:00................400000................800000

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Thoughts, comments, concerns? I think it would be really interesting to see what effect the first idea would have on online poker tournaments - would eliminating the step-change in blinds greatly affect how people play? Also extremely tempted to try the second idea with a home-game tournament. Other than being needlessly confusing and pedantic, I don't think it would really affect gameplay. Anyone brave enough to introduce this to their group?
 
A theory of mine - for your average T10000 tournament, I think people play about the same for the first three or four blind levels, up to about a BB of 300, no matter how long or short the blind levels are.
Then they get concerned when they have to start shelling out 500+ for the big blind, and play with about the same level of concern and decisions until the BB gets to about 2000.
Above 2000 it starts to take significant chunks of your stack just to play, and they play about the same until they go out or they amass a large stack.
From there it’s about stack size:blinds that determines play.
So in my experience, ymmv, there’s four “phases” of play, and how fast the blinds go or how big the jumps are really doesn’t affect average peoples play within those phases.
So it doesn’t matter if you go from 25/50 to 75/150 or from 25/50 to 50/100 or even 25/50 to 100/200 people still play the same. They bitch a lot about it maybe, but they still play K9 off suit or A(rag) under the gun no matter the blinds within those levels. Then when blinds get above 500 they lose some of that behavior, and by the time they up to 2000 they no longer play those hands.

I’d consider a structure that had play 100/200 for an hour, then go to 500/1000 for an hour, then 5000/10000 for an hour, then 10,000/20,000 till the end and just skip those 15 minute increases of 50 or 100.
These kinds of structure are not popular, as you will soon see, but what they do is force you to make better starting hand selections, practice smart pot management, and with the exception of the short stacks shoving (which happens in ANY blind structure ever used) generally promotes better poker play I think.

But I digress from your specific point, just throwing some other stuff out there to think upon.
 
I run various blind structures in my league. It varies depending on the chipset in play. Not that the chips dictate the need, but why have different sets if you are just going to use the same structure every time?

On one end of the spectrum I have slow progression (20-33% jumps) every 12 minutes. On the other end I have low-end casino structures that take 2x jumps nearly every level with 30 minute levels. Either way, the tournaments are designed to last 4.5-5 hours.

Players do not perceptibly vary their play based on the structure.

In our 2-deck self-dealt group, posting the blind by either player counts as the start of the hand. At most, in "big jump" tournaments, you might get more scramble to "get the blinds out". Also, the last level in big jump games has been demonstrated to be less likely to induce a chop than slow-progression games, despite the so-called "luck-fest" that can ensue.

A well run tournament has predictable blind increases. The amount of time that the tournament is expected to run will vary tournament strategy, as do rules regarding rebuys, and tournament entry fees relative to the player's disposable income.

On a related note, good players do well regardless of the structure, poor players do poorly. Players that tend to finish around the bubble continue to do the same.
 
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So as a math guy, what value do you put on the stat “average chip count” in a tournament?
In my opinion, average chip stack doesn't really mean much other than when acting early preflop. Other than this, my play is going to be determined by the number of BBs held by the opponents that are playing - i.e. I don't care if I'm under average stack and Bill is over average if Bill folded. Early preflop, average chipstack gives a 10,000 ft view of what I'll be up against, but I'd still put more stock in each player's left to act stack vs. my own rather than my own vs. average.
 
Interesting idea. This would further smooth out the structure. Only problem is that players have to get used to this, as it is the case with every change. In normally spaced levels a plot of log (blinds) vs time also gives almost a straight line, but with your approach it´s perfectly linear. Nice idea

Cheers
 
A theory of mine - for your average T10000 tournament, I think people play about the same for the first three or four blind levels, up to about a BB of 300, no matter how long or short the blind levels are.
Then they get concerned when they have to start shelling out 500+ for the big blind, and play with about the same level of concern and decisions until the BB gets to about 2000.
Above 2000 it starts to take significant chunks of your stack just to play, and they play about the same until they go out or they amass a large stack.
Tell these people they have an open invite to any games I may have. :)
 
We have a relatively aggressive blind schedule -- 50-67% increases every time. We also start with 400 BB and our planned target time is about 4 hours for 20 players (2 tables). I've used a lot of blinds schedules, and the reason I use the current one is I have some players that think 20-33% increase are too slow. They think it should double every time. The reality is things are only slow or fast in relation to other things.

We use 20 minute blinds and tables of 10. I do that because with our pace of just under 2 minutes a hand, it gives every player the chance to be in every position about 1x/orbit. I have some that think we need to shorten the blinds, but they play in a bar league with 11 minute blinds more aggressive than mine. Others would like to see our blinds be 30 minutes; 20 is a decent compromise.

There are some players who have a good understanding of the interplay between starting stacks, blinds, blind increases, length of rounds, how long a tournament lasts, and how much luck is involved in the tournament structure. In my experience, they are the minority -- a SMALL minority! A lot of players have some of that, but few understand all of those factors.

Some think we should start fast and slow down, others think we should start slow and finish fast. We keep the pace steady throughout. That too is a compromise, though I personally prefer a steady increase throughout.
 
Love the theory and the thought experiment.

Does the "mathematically pleasing blind schedule" result in a more equitable payment of blinds than a standard schedule? @TexRex makes a good point:
We use 20 minute blinds and tables of 10. I do that because with our pace of just under 2 minutes a hand, it gives every player the chance to be in every position about 1x/orbit.
 
Love the theory and the thought experiment.

Does the "mathematically pleasing blind schedule" result in a more equitable payment of blinds than a standard schedule? @TexRex makes a good point:
I don't think it necessarily spreads the blinds out more equitably, I'd say the only way to do that would be to lengthen the level duration. With 20 min levels (also what I use), you might have each person hit that blind 0-2 times, whereas with 2 h levels, they'd hit it anywhere between 4 and 8 times. Even on slow end, the difference between 4 and 5 times is far less crushing than the difference between 0 and 1 time.

* Edit: If you wanted to use the equation above to lengthen the levels, change 3:00 to some longer time frame.
 
I've long been a proponent of three things regarding tournament blind structures: a) relatively consistent increases in total blinds from level to level across the entire structure, b) a relatively equal number of hands played at each blind level, and c) having every player post an identical value in total blinds during every level. The last two objectives are sometimes in conflict with one another.

Designing a structure that meets the first criteria is relatively easy, regardless if all 100% increases or 20% averages (or somewhere in-between), and can be done with most tournament sets no matter what base chip value is used.

The second objective is harder to manage (particularly when multiple tables are invoved), but can still be accomplished with variable-length blind levels based on the number of players at the table (along with the average amount of time spent per hand).

The third objective is easy to control if the structure increases blind values soley based on the number of hands played (vs time duration), but it's inclusion will often be at odds with the objective of maintaining an equal number if hands for each blind level value.

I'd be interested in seeing how the OP's approach affects those three objectives, either positively or negatively.
 
... a) relatively consistent increases in total blinds from level to level across the entire structure, b) a relatively equal number of hands played at each blind level, and c) having every player post an identical value in total blinds during every level...

I'd be interested in seeing how the OP's approach affects those three objectives, either positively or negatively.

My thoughts on @BGinGA 's objectives:

a) I feel that the theory of the proposed structure (not necessarily exactly what is posted) addresses this point most strongly. The blind levels are laid out such that the increases are relatively consistent. The modulating level durations allows for the fine tuning of the consistency in increasing.

b) The theory of the proposed structure deliberately works against this objective. By changing the level duration, the structure moves past blind levels that represent small increases more quickly than levels representing a more significant increase. This will certainly change the number of hands per level. If it were realistic to do so, the original thought (blinds constantly increasing per an exponential relationship to time) would eliminate levels altogether, making b) and c) moot.

We have a relatively aggressive blind schedule -- 50-67% increases every time. We also start with 400 BB and our planned target time is about 4 hours for 20 players (2 tables). I've used a lot of blinds schedules, and the reason I use the current one is I have some players that think 20-33% increase are too slow. They think it should double every time. The reality is things are only slow or fast in relation to other things.

We use 20 minute blinds and tables of 10. I do that because with our pace of just under 2 minutes a hand, it gives every player the chance to be in every position about 1x/orbit. I have some that think we need to shorten the blinds, but they play in a bar league with 11 minute blinds more aggressive than mine. Others would like to see our blinds be 30 minutes; 20 is a decent compromise.

There are some players who have a good understanding of the interplay between starting stacks, blinds, blind increases, length of rounds, how long a tournament lasts, and how much luck is involved in the tournament structure. In my experience, they are the minority -- a SMALL minority! A lot of players have some of that, but few understand all of those factors.

Some think we should start fast and slow down, others think we should start slow and finish fast. We keep the pace steady throughout. That too is a compromise, though I personally prefer a steady increase throughout.

I don't think it necessarily spreads the blinds out more equitably, I'd say the only way to do that would be to lengthen the level duration. With 20 min levels (also what I use), you might have each person hit that blind 0-2 times, whereas with 2 h levels, they'd hit it anywhere between 4 and 8 times. Even on slow end, the difference between 4 and 5 times is far less crushing than the difference between 0 and 1 time.

* Edit: If you wanted to use the equation above to lengthen the levels, change 3:00 to some longer time frame.

c) This point is tackled in the posts above by @TexRex and myself. Even if you can assume an average hand length (2 min/hand, etc.) the margin of uncertainty is still going to be such that there is a high chance that players do not get equitably affected by the blinds. The only way to do this is to extend the duration of blind levels. Consider the following examples:
1) 20 minute blind levels, 10-handed, 9 hands are played at 100/200 followed by 1 hand at 150/300 due to some of the hands taking longer than the estimated 2 minutes. One player has had to post 50% more in big blinds than any of the other players in the last orbit.
2) 2 hour blind levels, 10-handed, 55 hands are played at 100/200 followed by 5 hands at 150/300. Now 5 players have paid more in blinds over the past 6 orbits than the other 5, however, they have only paid 8.33% more in big blinds.
 
c) This point is tackled in the posts above by @TexRex and myself. Even if you can assume an average hand length (2 min/hand, etc.) the margin of uncertainty is still going to be such that there is a high chance that players do not get equitably affected by the blinds. The only way to do this is to extend the duration of blind levels.
Actually, the only way to do it is to increase the blinds after some multiple of orbits, vs a fixed amount of time. This approach ensures that all players nearly always pay the exact same amount (some minor discrepancies may occur as players bust out).

Of course, this approach also flies in the face of having an equal time spent at each blind level, which I think is the least important of all the objectives under consideration. The number of hands per level is much more important, even if some hands take significantly longer than others.
 
Alex, I don't disagree with you, but I think that complicates things unnecessarily. There is one easy way to make sure everyone gets the same number of hands in each position per round. Instead of going by time, go by the number of hands. Then in terms of "fair" it is the same for everyone every round. I agree with BG that the number of hands per level is more important than the time. However, that will only work for a STT. Once you get 2 or more tables, the pace will vary based on a ton of factors.

It is impossible with multi-table tournaments to equalize stuff like that. Unless you play hand for hand all the way through, then it works just fine, but that really shows the game down. It becomes even more problematic when you move players.

Random seating creates inequities too, though I think that's the best way to do it. Sometimes one table has a bunch of strong players while another is relatively poor players.

Finally, we all know cards can be streaky. Over time they even out within a very small margin, but it may take a really long time.

I think those factors are just how tournament poker works. To compensate, you need a good structure that allows players to overcome these things over time, but in any given tournament, it can be quite unfair to a particular player.

The things one can do to help control that is allow enough time at every level, have reasonably steady blind increases, and enough starting chips to allow skilled players to overcome the variations discussed here. There will never be a perfect structure once you get past one table, but have a good structure helps a lot.
 
It is impossible with multi-table tournaments to equalize stuff like that. Unless you play hand for hand all the way through, then it works just fine, but that really shows the game down. It becomes even more problematic when you move players.
Actually, there are ways to accomplish this that don't necessarily require slowing down the game by playing hand-for-hand. There is no hard fundamental law that says both tables need to be simultaneously playing at the blind level amounts, so long as the parameters of each table are the same (blinds increase per orbit or every two orbits, etc.). Balancing tables is pretty easy, too -- same general principles apply, although a player may get moved to a table where blinds are further along (or not yet to his/her current level). In the overall scheme of things, it is actually a pretty minor issue. Most times multiple tables will be pretty close to being synchronized in terms of orbits played, and very rarely will they be very far apart. Another approach is to have each table (in a two-table event) play down to five players and then combine the two.
 
BG, help me understand the last part. Isn't playing down to 5 players and then combining what you would always do? I'm not sure I see how that fits with the rest.

I think what you said actually verifies the comment you quoted, though i do understand that the same number of hands could be more beneficial than keeping the tables on the same schedule.

There is always the chance of the person getting moved getting a good or bad deal in the move. Only in hand for hand could you elimate that. I've run STTs where we went # of orbits before increasing. While I think it works, it also seems like those games are slower when I've clocked it. I think it is unrelated to that, though I have no evidence to support it.
 
Isn't playing down to 5 players and then combining what you would always do?
In this case, each table would play down to five players independently -- and those 10 players make the final table. No table balancing. It's similar to the format where 10 tables would play down to 1 player each, and those 10 players make up the final table. Can also be down with five tables (top two each), or three tables (top three each), etc.

Only downside is that all tables don't necessarily "play down" and end at the exact same time, so some players get a longer break than others before the final table starts. But its a LOT faster than hand-for-hand.
 
Ah -- that makes sense. I've never tried a tournament that way, but I have thought of it. The first tournament we hosted, when dinosaurs roamed the earth and we had no real idea what we were doing, we had two preliminary games. When we got to the final number (no switching of tables), we started a fresh game for final. We did that because I got outvoted on taking chip stacks to the final. Others wanted everyone at the final table to start even. It worked, but led to some odd situations. But if they kept their chip stacks, and the tables started with the same number, the final table would be made of two groups where total stacks were equal.

Oh, almost forgot ~ The first table finished much sooner the first year. They had time to go to dinner 10 minutes away, got back, and still had to wait!

Have you every actually tried that? If so, how did it go?
 
lol, I think I've tried just about everything at one point or another.

I ran a three-table event like that once (top three from each advanced), two tables finished about the same time while the first table had to wait about 1/2 hour for the other two. Biggest problems (besides potential wait) were a) not everybody's at the same blind level when they get down to 3 three (or whatever number) players, and b) it's possible for five of the strongest players to be seated at one table, yet only three of them can make the final table (which isn't necessarily the case when tables are balanced). Playing blinds per-orbit vs time sorta lessens the first problem, but unless you are seeding players and seating them based on strength (which does have some merits on it's own), limiting the number of players at a given table that can advance is arguably unfair to the stronger players.
 
I honestly think you (well, someone) could find something "unfair" about any tournament structure. The wait our first time was over 1.5 hours. Those guys were going crazy. One never came back because of that. It was an annual tournament. That wait left a really bad taste in his mouth.
 
Just need to plan for those contingencies -- shot clocks, extra activities, etc. No need for players to just sit around with thumbs-up-wahzoo if you plan for potential downtime. Never lose sight of the fun factor, and don't let them lose it, either.
 
It was our first time (1983) -- we had NO idea that could happen! We did plan better for it the next year. We never thought of moving one player to another table. We did it with antes -- didn't really even know what blinds were. We planned the first game for 2.5 hours, and then then top 3 at each table went to the championship game. We started with 4 and 5. Tables would only hold 8 -- never thought of just squeezing everyone in. Thought we needed at least 1 eliminated from each table. The other table had 4 and lost a player in less than an hour. My table had 5 and we couldn't KO anyone. I suggested we could just stop there and go to the championship game, but everyone else said we needed to stick with 6 and eliminate some from each table. It's comical now. Some were really upset we got down to 7 and the other table voted to play with 7 in the championship game instead of the planned 6. It saved us about 30 minutes. But dealing with that was a huge discussion in the group later. The guy who was the first KO'd was the only one who didn't see a problem with the remaining 8 playing in the championship game. I eventually agreed with him, but I was the only one. He and I were outnumber 5-2 on that. The discussion revolved around the "need" to eliminate at least one player from every table. We limited attendance to 16.

The next year we had 13. Players were more cooperative -- each table took turns eliminating players until we got to 8, then combined. We were just lucky we never had a bunch eliminated from 1 table and none from the others. We also didn't really know how to raise the antes, so we did it when someone was eliminated. The last 3 hours was the same 3 guys. We had a lot of fun, and it seemed to work. It sure does seem pretty crude now.

We couldn't find info on how the WSOP handled that back then, and that's where we got the idea of doing a tournament from. If only we'd ever even thought of moving a player from another table to keep the tables relatively even, but I don't remember that idea ever being broached.

A repeat of the first year would discourage me from trying having 2 tables play to 5. However, with the same number of chips on both tables, on combining you could easily go backwards on blinds for the second table and pick up where the first table stopped. And now, the way our blinds increase, it's hard to imagine a group sitting for almost 2 hours, at least with 2 tables. It's easier to imagine with 3 tables though.

We had a game earlier this year where the main table didn't have a single elimination. All of them took place at the second table. It got to be a joke. Being the guy sent to the second table as a replacement ("where players go to die") was like being sent to the Russian front! When we combined, of those who started at the main table, only one actually had been eliminated.
 

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