Tourney Does the math of giant tourneys add up? (1 Viewer)

[Taghkanic]

Question: Do giant tournaments really make any sense to enter?

I am just OK at math, including basic probability. But my math education essentially ended the day I got accepted to college, at which point I was just starting to grasp the rudiments of calculus.

So I feel I’m out of my depth in trying to assess the questions below. I’d love to have some true math whizzes address this topic, and knock down some of the flawed assumptions/calculations I’m making below. I am posting this understanding that I’ve probably posited some pretty stupid stuff.

So:

Let’s say—very optimistically—that in a 9-handed live sit-and-go (one table tourney) which pays 2 places (22%), that I get in the money 50% of the time. That would represent a colossal edge, I’d say. It means I am outlasting at 87.5% of opponents half the time.

I should play as many SNGs as humanly possible, right?

Now say the field is 900 players, and the same percentage (22%) cash.

If the player pool is the same as the SNG, my edge is the same at each table I sit at. But to get in the money, I need to last until 699 players have been eliminated.

Put another way: My edge (cashing 50% of the time against 9 players) is going to have to hold up across multiple tables.

Each table is in theory the same challenge: I’m up against 7-9 opponents, and I’m a big favorite to outlast them. But once we get down to 5-6 players, I’m either going to have to pick up my chips and go to another full table, or we’re going to have the empty seats filled.

Every 3 times that another 2-3 players get knocked out and replaced, I’m effectively starting a new table. Some of these new arrivals will have smaller “starting” stacks than me, but some will have way more chips than me.

And for my 50% SNG cash rate to survive until the bubble, I have to have that hold up *over and over* again to get in the money. Maybe (in a 900-person field) it might be equivalent to surviving 6-8 SNGs in a row. Or more.

That seems like a massive parlay: 50% * 50% * 50% * 50% * 50% * 50% = 1.56%.

Now try that for a massive tourney like the WSOP, which may attract 8,000-9,000 players this year. How many “tables” of 9 will my 50% cash rate in a 9-person SNG have to hold up? Is that even a useful way to look at it?

- - - - - - -​

OK, try another way of looking at it:

In any given tournament, you’re going to see a limited number of hands. The fewer hands you see, the greater the variance in the quality of starting cards you are dealt.

If you’re dealt one hand, it might be 72o, or AA, or Q7o, or 45s, or T3o, or KQs, or 99, or J8o, or any number of other random combinations.

If you’re dealt only one hand, your rungood/runbad is going vary enormously. You might even bust out on that one hand with a premium starting hand (AA/KK/QQ/AKs).

In a one-table sit-and-go, if you outlast half your opponents 75% of the time, and are in the top two 50% of the time, you might see 150-200 hands over the course of the tourney, depending on how long you play shorthanded.

In a deepstacked large-field tourney, over the course of several days you might see 1,000 or more hands — thus in theory reducing the variance in your starting cards. Still, if you get “unlucky” and are knocked out early, you might see fewer hands than in a one-table SNG.

In any case, there is going to be a bell curve of rungood/runbad starting hands spread out across the field. The more hands dealt, the flatter that bell curve.

How these hands are distributed is independent of your skill. Your edge will derive from how you play what you’re dealt, and how they coordinate with board textures, player tendencies/experience at the table, and all the other things that keep us coming back to poker.

But it seems certain that even in a large-field, multiday tournament, that there will be a small percentage of people (let’s say 5%) who run much, much better than the field, and another 10-20% who are running merely better than average — balanced by 5%/10/20% who are running much, much worse.

My question then becomes: If you’re in the middle of the bell curve in terms of preflop holdings, how big a skill edge do you need to have to overcome the portion of the field who are running like gods?

My general hunch (based on both small and large tourney experience) is that the bigger the field, the more one’s skill edge gets whittled down. If you played in a billion-person tourney, what are the chances that the very best players survive to the money? I would suggest that it would be a lot lower percentage than in a 100-person tourney.

Yes, if we play enough, sooner or later each of us eventually should have a big score which makes up for most or all of the other variance, and restores our one-table SNG cashing rates.

But it seems to me likely to even out that variance in big tourneys is going to require both a huge investment of time and buy-ins to get results to smooth up/down toward your true skill level.

- - - - - - -

Part of this thinking-out-loud exercise is (a) to convince (or unconvince) myself to travel for the WSOP this year; and more importantly, (b) to try to figure out the sweet spot of smaller casino/social hall/private tournaments, so that I choose the most profitable option.

For me, that sweet spot for now seems to be 2-5 table tourneys, or roughly 15-35 players, with $100-$250 buy-ins. The time investment is manageable (3-7 hours to get in the money), and the payouts are decent in relation to my bankroll (typically between $700-$2,500 for 1st place).

As fields grow larger, it becomes necessary to set aside a lot more time, and also float a lot more losses until the rarer wins occur.

So… Maybe no WSOP visit for me. Or, if I do go, I’d rather select ten smaller $1,000 tourneys, increasing the number of tourney hands I see over the course of the visit, and maybe then play the Main Even if I bink one of those 10.

Did any of that make sense, or is it just a statistical mess?

 

[Taghkanic]

Reply #8 on this old 2+2 thread seems useful:

https://forumserver.twoplustwo.com/...-field-size-affect-tournament-ev-roi-1712279/

 

[toynoob]

#1 troll posts goes to.... Happy Easter @Taghkanic I quit reading on page 1 of your 25 page book

 

[ekricket]

Question: Do giant tournaments really make any sense to enter?

I am just OK at math, including basic probability. But my math education essentially ended the day I got accepted to college, at which point I was just starting to grasp the rudiments of calculus.

So I feel I’m out of my depth in trying to assess the questions below. I’d love to have some true math whizzes address this topic, and knock down some of the flawed assumptions/calculations I’m making below. I am posting this understanding that I’ve probably posited some pretty stupid stuff.

So:

Let’s say—very optimistically—that in a 9-handed live sit-and-go (one table tourney) which pays 2 places (22%), that I get in the money 50% of the time. That would represent a colossal edge, I’d say. It means I am outlasting at 87.5% of opponents half the time.

I should play as many SNGs as humanly possible, right?

Now say the field is 900 players, and the same percentage (22%) cash.

If the player pool is the same as the SNG, my edge is the same at each table I sit at. But to get in the money, I need to last until 699 players have been eliminated.

Put another way: My edge (cashing 50% of the time against 9 players) is going to have to hold up across multiple tables.

Each table is in theory the same challenge: I’m up against 7-9 opponents, and I’m a big favorite to outlast them. But once we get down to 5-6 players, I’m either going to have to pick up my chips and go to another full table, or we’re going to have the empty seats filled.

Every 3 times that another 2-3 players get knocked out and replaced, I’m effectively starting a new table. Some of these new arrivals will have smaller “starting” stacks than me, but some will have way more chips than me.

And for my 50% SNG cash rate to survive until the bubble, I have to have that hold up *over and over* again to get in the money. Maybe (in a 900-person field) it might be equivalent to surviving 6-8 SNGs in a row. Or more.

That seems like a massive parlay: 50% * 50% * 50% * 50% * 50% * 50% = 1.56%.

Now try that for a massive tourney like the WSOP, which may attract 8,000-9,000 players this year. How many “tables” of 9 will my 50% cash rate in a 9-person SNG have to hold up? Is that even a useful way to look at it?

- - - - - - -​

OK, try another way of looking at it:

In any given tournament, you’re going to see a limited number of hands. The fewer hands you see, the greater the variance in the quality of starting cards you are dealt.

If you’re dealt one hand, it might be 72o, or AA, or Q7o, or 45s, or T3o, or KQs, or 99, or J8o, or any number of other random combinations.

If you’re dealt only one hand, your rungood/runbad is going vary enormously. You might even bust out on that one hand with a premium starting hand (AA/KK/QQ/AKs).

In a one-table sit-and-go, if you outlast half your opponents 75% of the time, and are in the top two 50% of the time, you might see 150-200 hands over the course of the tourney, depending on how long you play shorthanded.

In a deepstacked large-field tourney, over the course of several days you might see 1,000 or more hands — thus in theory reducing the variance in your starting cards. Still, if you get “unlucky” and are knocked out early, you might see fewer hands than in a one-table SNG.

In any case, there is going to be a bell curve of rungood/runbad starting hands spread out across the field. The more hands dealt, the flatter that bell curve.

How these hands are distributed is independent of your skill. Your edge will derive from how you play what you’re dealt, and how they coordinate with board textures, player tendencies/experience at the table, and all the other things that keep us coming back to poker.

But it seems certain that even in a large-field, multiday tournament, that there will be a small percentage of people (let’s say 5%) who run much, much better than the field, and another 10-20% who are running merely better than average — balanced by 5%/10/20% who are running much, much worse.

My question then becomes: If you’re in the middle of the bell curve in terms of preflop holdings, how big a skill edge do you need to have to overcome the portion of the field who are running like gods?

My general hunch (based on both small and large tourney experience) is that the bigger the field, the more one’s skill edge gets whittled down. If you played in a billion-person tourney, what are the chances that the very best players survive to the money? I would suggest that it would be a lot lower percentage than in a 100-person tourney.

Yes, if we play enough, sooner or later each of us eventually should have a big score which makes up for most or all of the other variance, and restores our one-table SNG cashing rates.

But it seems to me likely to even out that variance in big tourneys is going to require both a huge investment of time and buy-ins to get results to smooth up/down toward your true skill level.

- - - - - - -

Part of this thinking-out-loud exercise is (a) to convince (or unconvince) myself to travel for the WSOP this year; and more importantly, (b) to try to figure out the sweet spot of smaller casino/social hall/private tournaments, so that I choose the most profitable option.

For me, that sweet spot for now seems to be 2-5 table tourneys, or roughly 15-35 players, with $100-$250 buy-ins. The time investment is manageable (3-7 hours to get in the money), and the payouts are decent in relation to my bankroll (typically between $700-$2,500 for 1st place).

As fields grow larger, it becomes necessary to set aside a lot more time, and also float a lot more losses until the rarer wins occur.

So… Maybe no WSOP visit for me. Or, if I do go, I’d rather select ten smaller $1,000 tourneys, increasing the number of tourney hands I see over the course of the visit, and maybe then play the Main Even if I bink one of those 10.

Did any of that make sense, or is it just a statistical mess?

I go to the WSOP almost every year, and my strategy has changed. I avoid the 4000+ entry fields and instead concentrate on the daily deep stacks to make a profit there. I may have to change it up this year now that all the starting stacks have increased.

I do play some events to be social, everyone in the group wants to play the seniors for example, but I don’t count on that making any money for me. I stick to the daily’s, $1000-$1500 buying for others, and some tourney play at downtown for grins.

 

[BGinGA]

Question: Do giant tournaments really make any sense to enter?

I am just OK at math, including basic probability. But my math education essentially ended the day I got accepted to college, at which point I was just starting to grasp the rudiments of calculus.

So I feel I’m out of my depth in trying to assess the questions below. I’d love to have some true math whizzes address this topic, and knock down some of the flawed assumptions/calculations I’m making below. I am posting this understanding that I’ve probably posited some pretty stupid stuff.

So:

Let’s say—very optimistically—that in a 9-handed live sit-and-go (one table tourney) which pays 2 places (22%), that I get in the money 50% of the time. That would represent a colossal edge, I’d say. It means I am outlasting at 87.5% of opponents half the time.

I should play as many SNGs as humanly possible, right?

Now say the field is 900 players, and the same percentage (22%) cash.

If the player pool is the same as the SNG, my edge is the same at each table I sit at. But to get in the money, I need to last until 699 players have been eliminated.

Put another way: My edge (cashing 50% of the time against 9 players) is going to have to hold up across multiple tables.

Each table is in theory the same challenge: I’m up against 7-9 opponents, and I’m a big favorite to outlast them. But once we get down to 5-6 players, I’m either going to have to pick up my chips and go to another full table, or we’re going to have the empty seats filled.

Every 3 times that another 2-3 players get knocked out and replaced, I’m effectively starting a new table. Some of these new arrivals will have smaller “starting” stacks than me, but some will have way more chips than me.

And for my 50% SNG cash rate to survive until the bubble, I have to have that hold up *over and over* again to get in the money. Maybe (in a 900-person field) it might be equivalent to surviving 6-8 SNGs in a row. Or more.

That seems like a massive parlay: 50% * 50% * 50% * 50% * 50% * 50% = 1.56%.

Now try that for a massive tourney like the WSOP, which may attract 8,000-9,000 players this year. How many “tables” of 9 will my 50% cash rate in a 9-person SNG have to hold up? Is that even a useful way to look at it?

- - - - - - -​

OK, try another way of looking at it:

In any given tournament, you’re going to see a limited number of hands. The fewer hands you see, the greater the variance in the quality of starting cards you are dealt.

If you’re dealt one hand, it might be 72o, or AA, or Q7o, or 45s, or T3o, or KQs, or 99, or J8o, or any number of other random combinations.

If you’re dealt only one hand, your rungood/runbad is going vary enormously. You might even bust out on that one hand with a premium starting hand (AA/KK/QQ/AKs).

In a one-table sit-and-go, if you outlast half your opponents 75% of the time, and are in the top two 50% of the time, you might see 150-200 hands over the course of the tourney, depending on how long you play shorthanded.

In a deepstacked large-field tourney, over the course of several days you might see 1,000 or more hands — thus in theory reducing the variance in your starting cards. Still, if you get “unlucky” and are knocked out early, you might see fewer hands than in a one-table SNG.

In any case, there is going to be a bell curve of rungood/runbad starting hands spread out across the field. The more hands dealt, the flatter that bell curve.

How these hands are distributed is independent of your skill. Your edge will derive from how you play what you’re dealt, and how they coordinate with board textures, player tendencies/experience at the table, and all the other things that keep us coming back to poker.

But it seems certain that even in a large-field, multiday tournament, that there will be a small percentage of people (let’s say 5%) who run much, much better than the field, and another 10-20% who are running merely better than average — balanced by 5%/10/20% who are running much, much worse.

My question then becomes: If you’re in the middle of the bell curve in terms of preflop holdings, how big a skill edge do you need to have to overcome the portion of the field who are running like gods?

My general hunch (based on both small and large tourney experience) is that the bigger the field, the more one’s skill edge gets whittled down. If you played in a billion-person tourney, what are the chances that the very best players survive to the money? I would suggest that it would be a lot lower percentage than in a 100-person tourney.

Yes, if we play enough, sooner or later each of us eventually should have a big score which makes up for most or all of the other variance, and restores our one-table SNG cashing rates.

But it seems to me likely to even out that variance in big tourneys is going to require both a huge investment of time and buy-ins to get results to smooth up/down toward your true skill level.

- - - - - - -

Part of this thinking-out-loud exercise is (a) to convince (or unconvince) myself to travel for the WSOP this year; and more importantly, (b) to try to figure out the sweet spot of smaller casino/social hall/private tournaments, so that I choose the most profitable option.

For me, that sweet spot for now seems to be 2-5 table tourneys, or roughly 15-35 players, with $100-$250 buy-ins. The time investment is manageable (3-7 hours to get in the money), and the payouts are decent in relation to my bankroll (typically between $700-$2,500 for 1st place).

As fields grow larger, it becomes necessary to set aside a lot more time, and also float a lot more losses until the rarer wins occur.

So… Maybe no WSOP visit for me. Or, if I do go, I’d rather select ten smaller $1,000 tourneys, increasing the number of tourney hands I see over the course of the visit, and maybe then play the Main Even if I bink one of those 10.

Did any of that make sense, or is it just a statistical mess?

If you're using non-denominated chips, I don't think it matters.

 

[Taghkanic]

Certainly, if you’re unable to remember the value of a color chip without it bearing a denomination, you probably should not play higher than .01/.02 cash

 

[Mr Winberg]

Now say the field is 900 players, and the same percentage (22%) cash.

A random player will cash 22% of the time. If you are better than average (which you ought to be if you cash 50% of each SNG) you should be cashing more than 22% of the time.

And for my 50% SNG cash rate to survive until the bubble, I have to have that hold up *over and over* again to get in the money. Maybe (in a 900-person field) it might be equivalent to surviving 6-8 SNGs in a row. Or more.

I don't think this is equivalent. One big difference is that a different skill set is required to play at a full table, which you will be doing most of the time, than to play the ever shrinking table size of a SNG.

Another reason that it isn't equivalent is that a random player will cash 22% of the time, but according to your calculations:

That seems like a massive parlay: 50% * 50% * 50% * 50% * 50% * 50% = 1.56%.

a highly skilled player only cashes 1.56% of the time. That doesn't make sense to me.

Each time you add a factor of 50%, you are adding a number representing the probability of outlasting 78% of the field, derived from playing a bunch of SNGs. If you want to apply this, I would say you only have one factor, i.e., 50%, but as I said, the skill sets are different.

Imagine if the numbers where correct, and if everyone was this skilled. Then everyone would cash 1.56% of the time in a tournament where 22% cash...

 

[Frogzilla]

I don’t think any of that SNG parlay math is relevant. If you’re actually evaluating single table tourney vs multi table, relevant ROI differences will come from three big differences

1) MTT are played almost entirely 8-9 handed. SNG have many more situations 3-6 handed.

2) Differences in field competition

3) Differences in time commitment

2 and 3 are venue dependent. And likely offset each other to some extent. #1 is player dependent. If a SNG crusher primarily dominates because he’s got a much better handle on short handed play, he is rarely going to be in that very profitable situation in a MTT and so SNG is the way to go. If he’s better at the early SNG stages, he might have even more success in a MTT.

Personally, I have more fun in MTT. I like watching people come and go, the tables breaking, etc. I’m close to break even after rake, so ROI isn’t what I’m going for

 

[Taghkanic]

I have more fun in MTT. I like watching people come and go, the tables breaking, etc.

Me, too. But the question I’m trying to get at is *how* multi-tabled is really worth it.

Still trying to get my head around the parlay concept here. Maybe it’s off point, but let me try another analogy:

Say I have a weighted coin which comes up tails 55% of the time.

Betting tails on every flip (even money bet) is guaranteed to be profitable long term.

But betting that it will come up tails *seven times in a row* is not going to pay off very often, even with the weighted coin.

At some level of payoff, the bet makes sense, if we flip the coin enough times. But the way most massive tourneys are structured, not sure most of them do, except as entertainment. (IIRC last year’s WSOP paid only about 15% of entrants.)

Quantifying this seems tricky.

 

[witlessdiviner]

Make sure you calculate ev. With the weighted coin scenario it’s the same +ev. you will just get a large payout infrequently on the seven coin in a row flip.

So the question becomes what’s the ev of playing a sng x# times vs playing the big tournament once you make your rough estimations of probability of success in each.

 

[Huck]

I remember seeing Dan Harrington asked at the WSOP main event what he thought his chances of winning were. He said whatever percentage of the total chips were sitting in front of him was roughly what his percentage chance of winning would be, maybe a bit more because he's Dan Harrington. (probably an understatement)

 

[Cackalacka Slim]

If you're thinking about poker tournaments along the lines of expected value and probability, here's a fun diversion that you may already know: the St Petersburg Paradox.

https://en.m.wikipedia.org/wiki/St._Petersburg_paradox

Here's the abridged version: I offer you a game in which I flip a coin repeatedly until it comes up tails, at which point the game ends, but if we keep flipping heads the game continues. Your winnings start at $2 and double each time the flip is heads. So if it comes up tails on the first flip, the game ends and I pay you $2. If it comes up tails on 2nd flip, I pay you $4. 3rd flip, $8. etc. So your winnings double each time heads comes up in a row. What would you pay for the opportunity to play this game?

The paradox is that the expected value of such a game is infinite, and yet, nobody would be be willing to pay very much to play it because of the overwhelming likelihood that a tails will appear within the first handful of throws.

A resolution to the paradox is found through the concept of utility instead of expected value. And in a happy coincidence, some of the above replies have already hit on this idea of utility. Even if your long run expected value is equal in smaller SNGs and larger MTTs, you may personally find more utility in SNGs because of lower time commitment and better cash flow because of more frequent, but smaller wins.

 

[Mr Winberg]

Meh... that game is sooo easy to beat. All I need to do is convince you to accept infinity minus 5 dollars for me to play. With an infinite EV, I stand to win $5! Easy peasy!

 

[Taghkanic]

Make sure you calculate ev. With the weighted coin scenario it’s the same +ev. you will just get a large payout infrequently on the seven coin in a row flip.

That’s why I added “At some level of payoff, the bet makes sense...” Yes, in hundreds of flips, there is at some point going to be a seven-tails run, and if it pays off huge (200-to-1, maybe?) it might be worth it.

But I’m not convinced that the payouts in most large-field tourneys really get me to +EV after rake/fees.

One casino where I’ve played in large, multiday re-entry tourneys with $250-$500 buyins pays about 12-15% of entrants. But a ton of those 12% are really quite small cashes. I can typically make more money in a 2-5 table 4-6 hour knockout tourney in a social hall or firehouse than spending two 8-12 hour days getting past 400-700 entrants.

Maybe that’s a leak in my game; one big large field tourney score would pay for countless swings and misses. But I think it is more of a problem with casino payout structures.

 

[waddadonk]

I remember seeing Dan Harrington asked at the WSOP main event what he thought his chances of winning were. He said whatever percentage of the total chips were sitting in front of him was roughly what his percentage chance of winning would be, maybe a bit more because he's Dan Harrington. (probably an understatement)

WSOP interview segment - "I got 8% of the chips, my chances of finishing first are 8%. (If) I think I'm better than the field, alright so make that double. If you wanna be real generous, thats what my chances are"

 

[Darson]

I'm no mathematician so I'm not going to attempt to calculate but here are my thoughts:
1, The final tables in large MTTs are mostly full of big name pros
2, There are also many big name pros that bust out without any return
3, If you're cashing STT 50% of the time it may be profitable to you but what are the caliber of the people you're playing with? Any big name pros there?
4, If 50% STT cash is guaranteed money, why aren't big name pros at those tables? Probably because although the ROI in percentage is high, the absolute values are low

So I think that winning players in large MTTs are likely a lot better that cashing 50% of STT - probably more like cashing 80% or 90% but they reason they don't play STTs is because the sums involved aren't worth the time they spend playing them.

But then again, what do I know, I'm just a home poker player who watches a lot of MTTs on TV

 

[kmccormick100]

Theoretically the larger tournaments should be more profitable than the smaller buy-in ones as their percentage rake is usually lower. Most $100-400 tournaments are marginally profitable (if it all) when you consider the percentage of rake taken out. Figure a decently skilled player cashes in 20% of tournaments, in these smaller buy ins the rake may be a full 10+% of that, so you're potential ROI is immediately cut in half.

For example in this year's WSOP, the $600 buy in deepstack has a total of 12% rake, where a $10k buy in has 6% rake and the 50k high roller has 4% total.

That said, if the skill level at higher buy ins goes up, your edge may go down...

 

[Huck]

WSOP interview segment - "I got 8% of the chips, my chances of finishing first are 8%. (If) I think I'm better than the field, alright so make that double. If you wanna be real generous, thats what my chances are"

Great find! I guess my memory is holding up better than my wife would have me believe.

 

[Anthony Martino]

This is why the vast majority of long-term pros are focused on cash games. It's a steadier and more reliable source of income, without such a huge time sink and significant stretches between return on investment.

You also have to factor in that the lower buy-in events not only have a greater percentage of rake, but they're also going to have weaker structures, which lowers your skill edge than deeper-stacked and slower-structured events where an unlucky hand doesn't mean you're out.

Personally I'd prefer to see tournaments with flatter payout structures (20% of the field) and less top heavy. In Tampa I've got four poker rooms nearby but the vast majority of their events pay the top 10% of the field, and offer rebuys through 11 levels of play. So it gives the edge to deep-pocketed pros willing to fire fire fire and who can take more chances than someone with only one bullet into the $1,100 or $1,650 main event.

 

[Schmendr1ck]

If the Powerball jackpot is more than $604 million, buying a $2 ticket is +EV. Still, don't start counting your money.

Large MTTs are similar. They might have the same or better EV than a STT or small MTT, but the variance is much higher. The payoff, when you hit, is also higher.

I greatly prefer cash to tournaments. Someday I'd like to play in a big WSOP event just for the experience, but if I were a pro I'd stay far away from big field events and focus on cash play. My ROI is probably the same over the long term, but the variance is so much lower.

 

[ando5k]

Basically it's the time-sink that is the issue here. As a one off, the MTT is definitely the better investment for time because of the risk-reward. You have a one time chance for said prize, therefore there is no metric to measure profitability vs X event. Therefore, you have to look at the top prize as what your potential profit could be as opposed to what you could do at X hours at a sit and go. Now if you entered enough MTT's to sink alot of time into where there was a measurable metric, then you could say "I could be making this amount over this time as opposed to that over that". Bottom line, if you feel like you can play well enough to give yourself a chance and think you might get lucky enough to win, go for it. But to weigh the two out for profitability isn't a fair one.

 

[Taghkanic]

ICM models would suggest that Harrington on that final table had a better than 8% chance, even setting aside any skill edge, no?

 

[Taghkanic]

Another thing about the smaller, more local tourneys that I play in is that one tends to see many of the same opponents regularly. The player pool in these events is relatively small and static. If there are 50 players, I might recognize 35-40 of them, and have pretty good mental notes on at least half of them. Not so in tourneys with much larger fields.

Now, of course they also see *me* more regularly. But players at this level (with definite exceptions) tend to be much less attentive. They aren’t usually making mental notes about their adversaries' c-betting frequencies, bet sizing tells, etc., and mainly play their own cards. These tourneys often offer a fairly soft field, in which you can ID a sizable portion of your opponents, putting them on fairly predictable ranges—and steering clear of the known sharps until it becomes unavoidable at the final table.

But the chance of a massive score isn’t there, obv.

 

[fieldsy]

ICM models would suggest that Harrington on that final table had a better than 8% chance, even setting aside any skill edge, no?

Not really. The basic assumption of ICM is that it assigns chances of winning based on stack size relative to the number of chips in play. Then calculates real-money equity associated with that player's chances of winning or reaching other payouts. And ICM does not account for skill edge.
http://www.pokerology.com/lessons/icm/

 

[fieldsy]

This may be even more long-winded than the OP. My overarching reaction is that you're comparing apples to oranges by trying to translate EV in SnG's to MTTs, but you're also not assessing oranges very realistically. First things first, they're just very different games and have very different paths to profitability. It would be a wild mistake to assume a SnG player with excellent results will necessarily do well in large-field MTTs. Much of the time in SnG's is played short-handed, while MTT's are usually full-ring well past the money bubble (and in live tournaments often 10-handed for many levels). There's also the issue of stack sizes, which you mention. No one at a STT will ever have a stack more than 8-9x the starting stack, while Day 1 chip leaders in big tourneys might have 20-30x starting stacks. Min-cashes in SnG's are often higher than min-cashes in large tournaments as a return on investment. For example, the 10-handed single-table-satellites at the WSOP are generally winner-take-all. Online 9-player SnG's often pay 3 spots at 50%-30%-20% of the prize pool (which means even third place gets a near double-up, ignoring rake). Live MTTs usually pay between 10-15% of the field, with a top-heavy payout structure and a min-cash that is sometimes barely more than the buyin. And this is important: profitable live tournament players do not play for min-cashes. Because of the variance and the low ROI for a min-cash, tournament players have to make deep runs, final tables, wins, to be successful over the long run.

Each table is in theory the same challenge: I’m up against 7-9 opponents, and I’m a big favorite to outlast them. But once we get down to 5-6 players, I’m either going to have to pick up my chips and go to another full table, or we’re going to have the empty seats filled.

Every 3 times that another 2-3 players get knocked out and replaced, I’m effectively starting a new table. Some of these new arrivals will have smaller “starting” stacks than me, but some will have way more chips than me.

And for my 50% SNG cash rate to survive until the bubble, I have to have that hold up *over and over* again to get in the money. Maybe (in a 900-person field) it might be equivalent to surviving 6-8 SNGs in a row. Or more.

That seems like a massive parlay: 50% * 50% * 50% * 50% * 50% * 50% = 1.56%.

You're making this too complicated. Even if you could analogize MTT play to surviving a series of single tables, you know at the outset how many players on average you need to outlast. The WSOP pays 15% of the field, or just over 1 in 7 players. So to min-cash, on average you're just going to have to outlast 6. I don't know where you're getting 0.50^6 in assigning that probability, and you know it can't hold up because you already know 15% of the field cashes (not 1.5%).

Here's an anecdotal perspective. Last year I played the Millionaire Maker, and everyone who made Day 2 cashed. I happened to be seated at a table that did not break all day on Day 1. One other guy and I survived at the (10-handed) table the whole day, while every other seat turned over at least once. Since that guy and I each had to outlast 6 other players in the tournament (on average) to cash, one would expect that 12 other players sat and busted at our table over the course of Day 1. And while I can't give you an exact number, I think that's probably about right. I am guessing that around 12 people busted from those 8 other seats at our table over the day.

My general hunch (based on both small and large tourney experience) is that the bigger the field, the more one’s skill edge gets whittled down. If you played in a billion-person tourney, what are the chances that the very best players survive to the money? I would suggest that it would be a lot lower percentage than in a 100-person tourney.

That doesn't sound right. Increasing the sample size reduces variance and increases the importance of edge. Tournaments are rarely going to allow the absolute "best" players to come out on top because of variance and the fact that when you're eliminated you can't keep playing hands. But over the course of that many hands, and over many tournaments, better players will prevail on average. I don't think it's coincidence that WSOP Main Event final table has been dominated by professional players for many years, despite the relatively huge number of amateurs in that tournament's field.

I guess the main point is this is not really a fruitful exercise, so get out of your head. Small tournaments play out differently than larger tournaments. And if you're like most rec players and are only looking at a handful of really large-field tourneys every year, your sample size isn't going to be large enough to really bear out your EV with any accuracy anyway. If you go and play three WSOP tournaments and bust all three, does that mean you were right? No. If you really feel like your skills are best suited to the single-table format, just play the WSOP single-tables and sell the lammers that you win. Or play the $1500 or $3k Shootout tourneys. But don't (1) assume the same skills apply in MTTs as in STTs, or (2) talk yourself out of playing MTTs by trying to model an entire tournament into a series of STTs.