Mathematics In Sngs

[Jam-Fly 8]

I've noticed some recurring themes this summer in the SNG department. Things like, what odds do you need to call an ai when holding Ace-rag on the BB, shud i push ai with 9xBB with J9 on the cutoff etc.Heres some specific hands i recorded:How do I upload pics that i have saved ? ill show the hands when i know how to do this, ty

[copernicus 0]

I've noticed some recurring themes this summer in the SNG department. Things like, what odds do you need to call an ai when holding Ace-rag on the BB, shud i push ai with 9xBB with J9 on the cutoff etc.Heres some specific hands i recorded:How do I upload pics that i have saved ? ill show the hands when i know how to do this, ty

the best answer is going to be to buy sitngo power tools and play with different scenarios....at least until Actuary figures out what ive forgotten about probabilities and fixes an ICM formula and spreadsheet that will answer a lot more questions than SitnGo power tools, albeit using ICM, and not eastbay's (the author of SNGPT) proprietary and supposedly more advanced tournament model than ICM.

[Jam-Fly 8]

too many big words and abbreviations

[copernicus 0]

too many big words and abbreviations

and a horrible run on sentence! Translation:1. SitnGo Power Tools (abbreviated SnGPT) is the best program available to get comfortable with the impact of changes in scenario on tournament payoff equity.2. SNGPT was written by a mathematician and 2+2 poster named Eastbay, and is based on some sort of tournament simulations that he did, which he believes are more accurate (though modestly so) than the Independent Chip Model (abreviated ICM). which is the standard method of estimating tournament winning probabilities. ICM is just based on ratios of chip stacks, and was described by Sklansky in Tournament Poker for Advanced Players (TPFAP) ...if I remember the name correctly.3. I am writing a spreadsheet that will be more general than SNGPT, but using ICM.4. I am old, and 30 years away from Part II of the Actuarial Exams, and therefore screwing up a basic ICM formula, which is preventing me from moving on in creating the spreadsheet. I have sought help from Actuary to correct my faulty memory.You didnt get all that out of the above post? sheesh.

[Actuary 3]

Done!I never get to actually use math here, so that was cool.I"m in the criticism camp though on ICM.Essentially thinking it leaves too much out.But assuming no impact of other forces and some ability to "adjust stacks for impactful criteria" it probably does as decent job.I tend to diagree with the intial overriding premise that your likelihood of finishing in the highest unclaimed spot is proportional to your chip stack compared to those gunnig for the same spot.For example, let's just take 1st place with 3 left and stacks as such:A: 6000B: 4000C: 2000I don't think player A finishes in 1st 1/2 the timeI think it's less.How do I know.I don't.

[copernicus 0]

Done!I never get to actually use math here, so that was cool.I"m in the criticism camp though on ICM.Essentially thinking it leaves too much out.But assuming no impact of other forces and some ability to "adjust stacks for impactful criteria" it probably does as decent job.I tend to diagree with the intial overriding premise that your likelihood of finishing in the highest unclaimed spot is proportional to your chip stack compared to those gunnig for the same spot.For example, let's just take 1st place with 3 left and stacks as such:A: 6000B: 4000C: 2000I don't think player A finishes in 1st 1/2 the timeI think it's less.How do I know.I don't.

actually im attempting another project that might support or refute ICM but if it refutes it my guess is it will go in the other direction...bigger stacks have more than a proportional chanceCertainly ICM has to be close enough for translation of uncertain tEV calcs to $EV

[mjd 0]

I tend to disagree with the intial overriding premise that your likelihood of finishing in the highest unclaimed spot is proportional to your chip stack compared to those gunning for the same spot.

Me too. I've been thinking of a possible logarithmic derivative of this premise instead of a straight proportion. But, I haven't collaborated with Sklansky on a book yet, so clearly don't have anything firm. :-)

[iggymcfly 0]

Done!I never get to actually use math here, so that was cool.I"m in the criticism camp though on ICM.Essentially thinking it leaves too much out.But assuming no impact of other forces and some ability to "adjust stacks for impactful criteria" it probably does as decent job.I tend to diagree with the intial overriding premise that your likelihood of finishing in the highest unclaimed spot is proportional to your chip stack compared to those gunnig for the same spot.For example, let's just take 1st place with 3 left and stacks as such:A: 6000B: 4000C: 2000I don't think player A finishes in 1st 1/2 the timeI think it's less.How do I know.I don't.

I'm almost positive it's more. Being the big stack has to be an advantage. I mean, if there's no ante and B eliminates C in a blind battle, do you really think that A's chances of winning the tournament go up? His prize equity might go up, since he's now assured second, but I can't imagine his chances of winning the tournament do. It's just too easy to get free blinds when the other players are worried about moving up position. Let's take another example:A: 9000B: 6000C: 4500D: 2500What do you think A's chances of winning are here? I'd guess they're at least 50%. B, C, and D are all going to have to sacrifice chip equity to make sure they don't bubble, and where do you think that equity's going to go? To A of course! The assumption only holds true if A, B, C, and D all understand these concepts, and B, C, and D focus on maximizing their value while A exploits the situation, but I think the big stack has a net equity gain the vast majority of the time.

[copernicus 0]

"I'm almost positive it's more. Being the big stack has to be an advantage. I mean, if there's no ante and B eliminates C in a blind battle, do you really think that A's chances of winning the tournament go up? His prize equity might go up, since he's now assured second, but I can't imagine his chances of winning the tournament do. "Under ICM As chances of winning dont go up, they stay the same, since his proportion of the total chips is unchanged.I do agree with where I think you were headed, though, which is that they probably actually go down somewhat. the concentration of chips in one hand instead of two gives that player more leverage than there was in the two separate hands.(This of course is in direct contrast to the "additional chips lose value" paradox (or fallacy, if you prefer). But Ive posted about that before)

[Actuary 3]

I'm almost positive it's more. Being the big stack has to be an advantage. I mean, if there's no ante and B eliminates C in a blind battle, do you really think that A's chances of winning the tournament go up?

yes, a tad

Let's take another example:A: 9000B: 6000C: 4500D: 2500What do you think A's chances of winning are here? I'd guess they're at least 50%. B, C, and D are all going to have to sacrifice chip equity to make sure they don't bubble, and where do you think that equity's going to go? To A of course! The assumption only holds true if A, B, C, and D all understand these concepts, and B, C, and D focus on maximizing their value while A exploits the situation, but I think the big stack has a net equity gain the vast majority of the time.

I'll agree a good aggressive big stack player at the bubble could have a better chance to win than his stack would indicate proportionally. I think pre-bubble and post bublble, it's slightly less. I picture you see this as a "rich get richer" view. I see more of the luck/randomness being an equalizer and negating some chip advantage as the smaller stacks have to push.furthermore, this highlights another style differenceI'm realively better with ShrtStack. Of course I want big stack, but prorportionally, I don't cash more with it. So, that bias enters my ********************************************************Coper,what about considering this from th perspective of next one out?A 1000B 2000C 3000D 4000Say A is 9/30 to go out next?Say A is 8/30 to go out next?Say A is 7/30 to go out next?Say A is 6/30 to go out next?

[copernicus 0]

Coper,what about considering this from th perspective of next one out?A 1000B 2000C 3000D 4000Say A is 9/30 to go out next?Say A is 8/30 to go out next?Say A is 7/30 to go out next?Say A is 6/30 to go out next?

viewed from chip proportions and ignoring blinds I would have gotten A=12/25, B=6/25, C=4/25 and D= 3/25 (eg D should be 1/4 as likely to go out next as A).However, i think looking at it from that perspective is much more dodgy than ultimately finishing in the nth spot, because proximity to paying the next blind impacts similar stacks, and low stack to blind ratios would be much more likely to go out than their ratio to other chips would indicate.While the converse (contrapositive?) is also true..a low stack to blind ratio will have a smaller than proportional chance to finish first, that probability is low enough to start with that it wouldnt affect the other conditional probabilities as greatly...I think!

[Actuary 3]

viewed from chip proportions and ignoring blinds I would have gotten A=12/25, B=6/25, C=4/25 and D= 3/25 (eg D should be 1/4 as likely to go out next as A).

yeah, I didn't like my numbers; but not sure I'd agree with yours; although, I realize it follows ICM logic. But 2x more like to go out first with 1000 than 2000?and the rest of that, I'm too tired to comprehend.. lol

[copernicus 0]

yeah, I didn't like my numbers; but not sure I'd agree with yours; although, I realize it follows ICM logic. But 2x more like to go out first with 4000 than 2000?and the rest of that, I'm too tired to comprehend.. lol

You are tired 1/2 as likely to go out next with 4000 as 2000

[delasoul 0]

Just keep pushing until you can figure out what you can and can't go all-in with and at what times. I read but I like to play and make mistakes and learn from them. It gets expensive sometimes but when you make a donk move and know it there's a chance you won't do it again

[Actuary 3]

Just keep pushing until you can figure out what you can and can't go all-in with and at what times. I read but I like to play and make mistakes and learn from them. It gets expensive sometimes but when you make a donk move and know it there's a chance you won't do it again

yeah because results from one individual should overide all math and experience from millions of other trials.***************Coper,I editted, later.I saw that before your post but not in time, apparently.

[copernicus 0]

yeah because results from one individual should overide all math and experience from millions of other trials.***************Coper,I editted, later.I saw that before your post but not in time, apparently.

I think i'll have an Excel ICM function coded by Sunday that will handle up to 10 players, and the rest of a spreadsheet to do call/raise/fold comparisons for flexible payout structures sometime next week. You can have the honor of trying to break it!My brain was becoming too fried to code 9 place conditional probabilities myself, so I farmed it out!