Magnolia's Theory Calculations

[Jman28]

Hey,

I was hoping that some of you guys could help with a calculation of this. I think this theory may have some merit, and I ran some quick numbers.

I'm unsure of a couple of assumptions I have made.

I made a hypothetical player with an ROI of 36%.

When the tourney starts, his equity is 15% of the prize pool. I got to this by taking the ~$4 profit per tourney he makes, which means he wins about $15 a pop in an $10+1 SNG (15-11=4). That $15 is 15% of the $100 prize pool.

So, he makes $4 in 45 min.

= $5.33/hr

Next, the same player plays a tourney looking for a coin flip early. We'll say it takes him 5 minutes on average to find this coinflip. 50% of the time, he is out in 5 minutes, and down $11.

The other half of the time, the ICM gives his equity as 18.44%. I took this number and increased it by 50%, because his equity was increased by 50% when he went from the average 10% of the prize pool to the 15% that a skilled player gets. This is the assumption I'm shaky on. It brings his equity when he doubles up to 27.66% (not the full double of his previous equity of 15%, but still uncomfotably close).

So, he plays twice. Half the time, he loses $11 in 5 minutes, and the other half, he makes $16.66 (27.66 - 11)in 45 minutes.

-11 + 16.66 = 5.66

This takes 50 minutes, which makes his new hourly rate $6.79/hr.

That's a 27% increase in hourly rate!

I think the assumption I mentioned in bold above is off. What would you consider the 36% ROI player's equity to be after doubling up? If I got my numbers about right, the minimum equity after doubling to make this a profitable move is 25.5%.

We also haven't taken into account the edge you get from having the big stack on the bubble, which I think is a HUGE edge.

It's intriguing. Thoughts?

-Jman28

[eastbay]

[ QUOTE ]

The other half of the time, the ICM gives his equity as 18.44%. I took this number and increased it by 50%, because his equity was increased by 50% when he went from the average 10% of the prize pool to the 15% that a skilled player gets. This is the assumption I'm shaky on.


[/ QUOTE ]

I don't think that's quite right. I think your model is like jcmxxx's (sorry I forget) in that it gives absurd results when taken to logical conclusion. So if the guy is HU with all but 1 chip, and ICM gives him 99.9% of the prize pool, you're going to give him credit for 149% of the prize pool? It's an extreme example, but I think it points to a flaw in the reasoning behind it.

No, I think the way to do it is to scale the stacks, not the prizes. An effective 1700 starting chips to everybody else's 1000 gives a player a 36% ROI.

[ QUOTE ]

I think the assumption I mentioned in bold above is off. What would you consider the 36% ROI player's equity to be after doubling up?

[/ QUOTE ]

The method I just proposed puts him at about 25% (double through to actual 2000 chips, worth about 3400 via skill factor.)

But these exercises are a little Heisenbergian, because maybe part of his skill factor in achieving 36% is avoiding such flips.

eastbay

[Jman28]

But these exercises are a little Heisenbergian, because maybe part of his skill factor in achieving 36% is avoiding such flips.

I'm not sure what you mean here.

The coin flips will hurt his ROI, of course. But once he has doubled up, he goes back to playing well, trying to maximize his ROI from that point on.

-Jman28

[eastbay]

[ QUOTE ]
But these exercises are a little Heisenbergian, because maybe part of his skill factor in achieving 36% is avoiding such flips.

I'm not sure what you mean here.

The coin flips will hurt his ROI, of course. But once he has doubled up, he goes back to playing well, trying to maximize his ROI from that point on.

-Jman28

[/ QUOTE ]

What I mean is that he achieved 36% by following a strategy X. Now you're going to give him strategy Y, and you want to hold his ROI fixed. This is a questionable assumption, as we're not sure strategy Y also achieves 36% ROI.

eastbay

[SuitedSixes]

[ QUOTE ]
[ QUOTE ]
But these exercises are a little Heisenbergian, because maybe part of his skill factor in achieving 36% is avoiding such flips.

I'm not sure what you mean here.

The coin flips will hurt his ROI, of course. But once he has doubled up, he goes back to playing well, trying to maximize his ROI from that point on.

-Jman28

[/ QUOTE ]

What I mean is that he achieved 36% by following a strategy X. Now you're going to give him strategy Y, and you want to hold his ROI fixed. This is a questionable assumption, as we're not sure strategy Y also achieves 36% ROI.

eastbay

[/ QUOTE ]

Bingo.

[The Yugoslavian]

[ QUOTE ]

The method I just proposed puts him at about 25% (double through to actual 2000 chips, worth about 3400 via skill factor.)

[/ QUOTE ]

Would this now give the quick doubler only $3/50 minutes or something like $3.60/hr instead of $6.79/hr??

Oh....he'd also have the higher variance.

Plus, your coinflip is never going to actually be a coinflip. Perhpas it'd be 47/53 than 50/50 for the quick doubler-upper who is 'forcing' action.

And to Eastbay's point, I'm not sure you can extrapolate a 36% ROI from the doubling point onwards. I guess you may think it's higher due to the 'huge' big stack advantage but I'm not so sure.

Yugoslav

[Jman28]

What I mean is that he achieved 36% by following a strategy X. Now you're going to give him strategy Y, and you want to hold his ROI fixed. This is a questionable assumption, as we're not sure strategy Y also achieves 36% ROI.

Let me try and understand you. Do you mean to include the early coinflip in strategy Y?

If so, this isn't a questionable assumption, it's dead wrong. I never said that he would have a 36% ROI now. I believe I said that his ROI would be lower, of course. We know that this is supposed to sacrifice ROI for hourly rate.

If you mean that he now has a different edge over the other players, even taking into account his bigger stack, than he had without doubling up, then I'm not really sure. This should factor into our assummption of his new equity.

If you're saying that he takes his coin flip on a hand that normally is a +EV hand when played correctly, then I think you have a point, but it shouldn't make an enourmous difference.

-Jman28

[Jman28]

I guess you may think it's higher due to the 'huge' big stack advantage but I'm not so sure.

Do you disagree that there is a very large advantage to having the big stack on the bubble?

-Jman28

[The Yugoslavian]

[ QUOTE ]
I guess you may think it's higher due to the 'huge' big stack advantage but I'm not so sure.

Do you disagree that there is a very large advantage to having the big stack on the bubble?

-Jman28

[/ QUOTE ]

No, I'm not disagreeing with that at all. My concern is with the degree it is advantageous, not whether having the big stack on the bubble is an advantage or not.

Yugoslav

[Bigwig]

One other point. Is it really possible for a player 'searching' for a coinflip will actually get one in the early 2 levels? Someone playing this aggressively is likely to get involved in dominated pots fairly often (his QQ vs KK, his AQ vs AK). I don't think a 50% chance of doubling is accurate.

[eastbay]

[ QUOTE ]
What I mean is that he achieved 36% by following a strategy X. Now you're going to give him strategy Y, and you want to hold his ROI fixed. This is a questionable assumption, as we're not sure strategy Y also achieves 36% ROI.

Let me try and understand you. Do you mean to include the early coinflip in strategy Y?

If so, this isn't a questionable assumption, it's dead wrong. I never said that he would have a 36% ROI now. I believe I said that his ROI would be lower, of course. We know that this is supposed to sacrifice ROI for hourly rate.

If you mean that he now has a different edge over the other players, even taking into account his bigger stack, than he had without doubling up, then I'm not really sure. This should factor into our assummption of his new equity.


[/ QUOTE ]

Right. Not that he has a 36% ROI literally, but that he has the same edge which generated the 36% ROI - I guess I misspoke there.

You can imagine lots of scenarios here that make the situation murky. If the player gets all his ROI from playing a mean short-stack on the bubble, then it's a fool's trade to want half the opportunities with twice the stack to get there, when he can get there 90% of the time by folding into it.

I don't know, these $/hr effects exercises are interesting to muse about, anyway.

eastbay

[Jman28]

[ QUOTE ]
One other point. Is it really possible for a player 'searching' for a coinflip will actually get one in the early 2 levels? Someone playing this aggressively is likely to get involved in dominated pots fairly often (his QQ vs KK, his AQ vs AK). I don't think a 50% chance of doubling is accurate.

[/ QUOTE ]

Yeah, I thought about this problem too.

I guess I wanted to talk about it hypothetically before taking all the other factors into consideration.

-Jman28

[Jman28]

[ QUOTE ]
If I got my numbers about right, the minimum equity after doubling to make this a profitable move is 25.5%.

[/ QUOTE ]

I got that wrong. I meant 26.5%.

[eastbay]

[ QUOTE ]
[ QUOTE ]
If I got my numbers about right, the minimum equity after doubling to make this a profitable move is 25.5%.

[/ QUOTE ]

I got that wrong. I meant 26.5%.

[/ QUOTE ]

Looks like a losing prop. according to the scaled chip heuristic then, eh?

eastbay

[Jman28]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
If I got my numbers about right, the minimum equity after doubling to make this a profitable move is 25.5%.

[/ QUOTE ]

I got that wrong. I meant 26.5%.

[/ QUOTE ]

Looks like a losing prop. according to the scaled chip heuristic then, eh?

eastbay

[/ QUOTE ]

It probably is yeah.

It all depends on the number we settle on, which probably is close to your 25%.

The 1-2% makes a huge difference since you have to subtract 22 from it to get the true earn for that 50 minutes.

Well, it's fun to look at. And we could probably figure out from this at what edge close gambles early become profitable, if we felt like checking that out.

-Jman28

[rybones]

the other problem with the strategy X and strategy Y theory is that Magnolia never claimed such a swith in strategy once he doubled up. He seemed to imply he used his stack to bully the table. I would give the quote, but I am too lazy to find it right now. Either way, we don't really know for sure how his strategy plays out once he has doubled.

That said, one could argue that he is quite right to bully the table once he has his stack just so long as he is good at such a game. Additionally, he seems to imply he is willing to take a second coinflip after he has alread doubled up. If he is then I think the system is dangerous but I am not sure how the math would play out. Perhaps he is still in good shape since a loss merely puts him back to the average stack? On the other hand, if you continue to take coinflips early you need only loose two in a row and you are done. Now he has wasted more of the time he did not want to waste and he is still not itm. Moreover, if he is taking multiple (what he thinks are) coin flips The advantage goes to the tight player who finally gets queens or better.

does this make sense?

Ryan

[eastbay]

[ QUOTE ]
the other problem with the strategy X and strategy Y theory is that Magnolia never claimed such a swith in strategy once he doubled up.

[/ QUOTE ]

I think you miss the point. Once you make a play specifically to double up, you're playing a different strategy.

Who is Magnolia?

eastbay

[The Yugoslavian]

[ QUOTE ]
[ QUOTE ]
I guess you may think it's higher due to the 'huge' big stack advantage but I'm not so sure.

Do you disagree that there is a very large advantage to having the big stack on the bubble?

-Jman28

[/ QUOTE ]

No, I'm not disagreeing with that at all. My concern is with the degree it is advantageous, not whether having the big stack on the bubble is an advantage or not.

Yugoslav

[/ QUOTE ]

Also, FWIW, you'll need to double up twice more or less to really be the big stack on the bubble. Once will certainly get you there with a higher chance of being the big stack...but unless you continue to push marginal edges, you're likely to just be a medium stack once there (at least not small I guess).

Yugoslav

[Jman28]

Who is Magnolia?

http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1838843&page=0&view=c ollapsed&sb=5&o=14&fpart=1

[MagnoliasFM]

Wow. I am amazed at all the responses this has gotten. Let me start off by saying that I'm not really a math-oriented person (I'm a business major) so more than half of what you guys are saying (the numbers part) looks like a foreign language to me. Nevertheless, I would like to answer some of your questions as best as I can.

[ QUOTE ]

Oh....he'd also have the higher variance.


[/ QUOTE ]

You're absolutely right that it produces higher variance. My standard deviation is close to 2 buy-ins instead of the normal 1 buy-in StdDev. This is because I have more 1st places than usual. However, increased variance isn't a negative factor unless you don't have an adequate bankroll or you're prone to go on tilt after losing 15 tourneys in a row.

[ QUOTE ]

Plus, your coinflip is never going to actually be a coinflip. Perhpas it'd be 47/53 than 50/50 for the quick doubler-upper who is 'forcing' action.


[/ QUOTE ]

[ QUOTE ]

One other point. Is it really possible for a player 'searching' for a coinflip will actually get one in the early 2 levels? Someone playing this aggressively is likely to get involved in dominated pots fairly often (his QQ vs KK, his AQ vs AK). I don't think a 50% chance of doubling is accurate.


[/ QUOTE ]


By coinflip I do not mean any specific hand vs. hand. For example, if you have QQ and you know your opponent is going to put all his chips in with AA, KK, QQ, JJ, TT, 99, 88, 77, AK, AQ, AJ (On average), you are actually a healthy favorite over that range. If you do that once and get called by KK and lose doesn't mean you suck and should've saved your chips for later. It just means you got unlucky on a coinflip where you were actually the favorite. This seems counter-intuitive to some but if you look beyond what's immediately in front of you, you will find that in this game not everything is what it seems to be.

[ QUOTE ]

the other problem with the strategy X and strategy Y theory is that Magnolia never claimed such a swith in strategy once he doubled up. He seemed to imply he used his stack to bully the table. I would give the quote, but I am too lazy to find it right now. Either way, we don't really know for sure how his strategy plays out once he has doubled.

That said, one could argue that he is quite right to bully the table once he has his stack just so long as he is good at such a game. Additionally, he seems to imply he is willing to take a second coinflip after he has alread doubled up. If he is then I think the system is dangerous but I am not sure how the math would play out. Perhaps he is still in good shape since a loss merely puts him back to the average stack? On the other hand, if you continue to take coinflips early you need only loose two in a row and you are done. Now he has wasted more of the time he did not want to waste and he is still not itm. Moreover, if he is taking multiple (what he thinks are) coin flips The advantage goes to the tight player who finally gets queens or better.


[/ QUOTE ]

Let me correct some misunderstandings. Once I double-up early in a tournament, I'm done gambling until the blinds increase to high enough where I can flip coins with much higher edges (Commonly with all-in moves once the blinds are 100-200+). The point of doubling up early is it affords you the luxury of not having to double-up later. You can focus on stealing high blinds which is much less risky. As for the player who waits for queens, first of all, rocks like that are very very rare in $22 and below tournaments, and second of all, if a tight player to my left manages to make it to level 5, it's a huge boost to me because all his chips are basically mine the 9 out of 10 times he doesn't get lucky and pick up QQ or better before his entire stack gets stolen by me.

Another thing is, I believe that in early rounds, it is pointless to play after the flop. A lot of people say to just raise to 150 or so with AK or maybe call a raise with it. What this will end up doing is you either win a medium pot or lose a medium pot (sometimes you will win a big pot when someone else hits their A or K along with you). However, if you are up against AQ, for example, and you just call his raise PF, you are only going to get money if an A hits. If you go all-in PF you are going to either lose all your money or win all of his. Early on, you do not want to win or lose medium pots. You want to either double-up, giving you a good chance of winning the tournament, or you want to bust-out, giving you a good chance of winning the next tournament you enter.

[rybones]

[ QUOTE ]


Quote:
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the other problem with the strategy X and strategy Y theory is that Magnolia never claimed such a swith in strategy once he doubled up.


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I think you miss the point. Once you make a play specifically to double up, you're playing a different strategy.

Who is Magnolia?

eastbay

[/ QUOTE ]

I am not sure I did miss the point. I get that if you double up you are automatically playing different because you now have the big stack (I think that is what you are saying?). However, Magnolia's original post does not make clear whether he continues to push in what he feels are coinflip situations once he has doubled. My read is that he does. If this is true, I wonder how the math works out? is this +ev?

Assuming you are really in a coinflips, what is the likelyhood you will get a second coinflip opportunity? If you get that second coinflip, what is the likelyhood you will win the second one? Now what are the odds of a third coinflip, etc.

Additionally, I am currious to see the range of hands and circumstances where he thinks he has a coin flip. This thread is titled "Magnolia's Theory calculations." How do you do these calculations without this information?

What I am really trying to say is that my sense is that he is willing to coinflip several times and that without know his range of push hands/situations you cannot really do the math. That said, I would love to know the answers and see the math.

Ryan

[rachelwxm]

[ QUOTE ]
The other half of the time, the ICM gives his equity as 18.44%. I took this number and increased it by 50%, because his equity was increased by 50% when he went from the average 10% of the prize pool to the 15% that a skilled player gets. This is the assumption I'm shaky on.

[/ QUOTE ]

This is why it breaks down. The extra chip worth less even without the added skill factor. In your example, let's say hero double up twice, so he has 4*initial chips and equity according to formula is 60%, more than first prize payout. /images/graemlins/tongue.gif