re the variance thread blowup NL

[TNixon]

Sorry, I'm trying *really* hard not to be confrontational.

I'd *really* like to get over this issue, so that there can be some rational discussion about the original question, because as long as there's disagreement on this point, we're not even existing in the same universe.

I would love for somebody from the math forum to come over here, but I can guarantee 100% that they're going to agree with me.

In fact...we're both gamblers. Care to place a bet on it? If so, lets settle the details on the bet before we get somebody over here to check the thread out. I'd be willing to put $100 on them agreeing with me, with the condition that we manage to attract a regular poster who appears to have a pretty good idea of what they're talking about.

[TNixon]

[ QUOTE ]
as such, once you find the std dev in $/hand you should account for how much that money that represents with respect to the table stakes

[/ QUOTE ]
You know, I really think this sentence represents the key to the entire disagreement.

Why should we account for how much that money represents with respect to the table stakes?

Table stakes are arbitrary. I can play any level I want. The real effect I want to see is how my bankroll is affected.

To be able to make any sort of valid comparison between HUSNG and cash, you *have* to be able to compare different stakes directly, because late in a $100 sng, your $100 stack is no longer worth 75BB. It's worth 10BB. You've said that this situation is exactly the same as a situation comparing a 100BB $100 stack against a 10BB $10 stack. I vehemently disagree, and have given all the mathematical proof that I possibly can.

You know what?

I'm talking in circles again. I cannot possibly restate this in any way that is more clear than the ways I have already stated it.

So, do you accept the bet or not?

[TNixon]

Whether there's a bet or not, when picking an appropriate judge, would it be best to query the probability forum, or the science, math, and philosophy forum?

I'm thinking probability.

[HokieGreg]

[ QUOTE ]
Can someone summarize?

[/ QUOTE ]

Honestly, no, I can't.

[TNixon]

I can't either. This thread is an attempt to convince the only really active poster on the topic that he's making a mathematical mistake in his comparisons, so we can actually move on and discuss the original topic, which was comparing HUCASH and HUSNG variance.

In other words, about three million posts on a fairly small (but very important) detail.

So far, it's been a resounding failure.

[checktheriver]

What I understand :
omgwtfnoway says that playing $10 stacks at NL100 is lower variance than $10 stacks at NL10, because the st dev in big blinds will be higher at NL10. It really doesn't make any sense imo and I agree with TNixon you have to think in $ here, that's what is relevant.

Also I'm not sure I understand the point in your calculations where you push at 60% equity different stack sizes, since the deeper the stacks the less often these situations will happen and you have to take this into account.

[LordMushroom2]

I am a little interested in what we are actually looking for here, finding out which HU gametype has the higher standard deviation per hour when the SnG buy-in is 100 times greater than the big blind in the cash-game.

But I wasn´t too interested and was hoping the guys would find this out for me. This seems far away at the moment, so I will try and help (read: make it worse [img]/images/graemlins/laugh.gif[/img]).

First I wish to dispute that a shortstack will have smaller variance than a big stack if the blinds are the same.

I can understand how one may think it is so (I did it myself not long ago). One would think that a 10 big blind stack would have a smaller variance than a 100 big blind stack because it is limited how big pots it can create. With a 10BB stack the pot can maximum be 20BBs, but if you had 100BBs you could have made the pot bigger because you have more to throw into the pot.

But the thing is there are situations where a small stack would create a bigger pot than a big stack would. When stacks are smaller than 10BBs, for example, it is common to open-raise all-in. If your stack is 9BBs, you are effectively making a 9BB raise! And the opponent is not more scared of calling than he would have been if stacks had been 100BBs and the raise only 3BBs!

Such a huge open-raise would never take place with a big stack. With a big stack you would have bet 3BBs and if the opponent calls one of you will often take it down by making a 4BB bet on the flop winning a 6BB pot instead of the 18BB pot in the shortstack-case.

There are of course situations where a big stack would create a larger pot too, and this roughly cancels out the larger pots of the shortstacks, making both stacks creating roughly the same average pot.

Just look at the 30BB Cap-games on Full Tilt, they have about the same average pot as non-cap-games.

Obviously when stacks get tiny, the average pot must go down as the stacks are getting so small at some point that even if both players were all-in in all hands, the average pot would be smaller than the average pot of a normal game. I don´t know exactly where the stacks start decreasing the average pot, but I would guess around 7BB stacks.

Then here is how I think we should approach our problem:

1) We simplify and assume there is no rake and no fees.

2) We simplify further and assume all players are equally skilled.

3) We assume you can play the same number of hands per minute in an SnG as in a cash-game.

4) Since stacks don´t influence the standard deviation in cash-games as long as stacks are greater than 7BBs, we make it easy for ourselves and assume the cash-game stacks are always 9BBs and either go all-in or fold (easy to relate too and not too unrealistic).

5) Let´s say both players will go all-in in the SB with their 70% best hands and call all-in in the BB with their 40% best hands.

This means the BB will win the SB 100% - 70% = 30% of the time. The SB will win the BB 0,7 * (1-0,4) = 0,42 = 42% of the time. And they will compete for an 18BB pot 0,7 * 0,4 = 0,28 = 28% of the time.

Pokerstove says the SB has a 44,6% chance of winning the 18BB pots and the BB thus has a 55,4% chance of winning. I am ignoring the small chance of a draw because it is so rare.

6) Let´s set a specific monetary size on the games. It is NL100 and a $100+0 SnG.

7) We know that in a $100+0 SnG, you will either win $100 or lose $100 after having played a number of hands. So the "variance" (used very unmathematically here) of it is $100.

8) Run a simulation of a hand in a cash-game where the possible outcomes of a hand are according to the probabilities pointed out in step 5. Note the amount player A (just choose one of them) won/lost.

Then do the same for the next hand and add/subtract what player A won/lost to/from his gain/loss from the last hand.

Then do the same for next hand a summarize the gain/loss from all three hands.

Keep doing this until player A has either won or lost a total of $100, then note the number of hands it took.

9) Repeat step 8 (note the number of hands it took). Do it again and again until you feel you have done it enough to get a fair sample. Then calculate the average number of hands it took.

10) If a particular type of HU SnG lasts more number of hands on average than the number found in step 9, it has less variance.

[TNixon]

Ok, I came up with one more way of stating the problem that isn't saying something exactly the same way that I already have.

In fact, this is how I'd want to frame the question for anybody coming over from the probability forum to settle a bet.

The following question is asked:

"I have a $1000 bankroll, that I don't mind replacing if I go broke, so I want to play it very agressively, but I'd still prefer *not* to go broke if I can avoid it, while keeping in mind that I want to maximize value by playing agressively.

I've narrowed my choices down to two:

Choice A: Playing full buyins at 100NL.
Choice B: Buying in short at 1000NL, for $100 or 10 big blinds.

Which of these 2 choices is going to be lower variance? (and please don't try to talk me out of playing above my bankroll. I've already stated that I want to play agressively. Just tell me which of these two choices is lower variance)"

What is your answer, and why?

My answer is Choice A is obviously lower variance, with a smaller chance of going broke, as long as you don't play a supper-aggresive style where you're playing "optimal" push-or-fold.

Your answer, if you're going to be consistent with everything you've already said, should be that choice B is lower variance. You even "proved" mathematically that choice B would be lower variance, despite the fact that you would be getting the chips all-in more often as the 10BB stack, because the average pot size in choice A would have to be less than around 9BB for choice A to be the lower-variance choice.

Is that your final answer?

If so, do we have a bet? I'm even willing to give you 2 to 1 odds. Your $50 to my $100, or your $100 to my $200.

[tautomer]

It's unfortunate that the original topic was locked. I am wondering what affect the game structure has on the HUCG vs HUSNG variance question. A tourney has an obvious endpoint, it is over when someone loses all of their chips or 1 buyin. However a cash game has no defined endpoint. Say HUSNGs average 50 hands per match (just guessing), the most each player can win or lose is one buyin at the end of the match. In theory a cash game player can win or lose 50 buyins in the same 50 hands. More to the point, a cash game player can have multiple buyin swings within those 50 hands and still win or lose just one buyin as the end result. Does this affect variance?

[jay_shark]

Tnixon , I'm actually from the math forum and I agree with Omg .

Nothing you're saying is really adding up . Perhaps I still don't understand what you're trying to convey .