The relationship between variance and risk of Ruin

[JohnCrover]

Hello,
I was wondering if anyone here could help explain to me the relationship between variance and Risk of Ruin.
While digging for an old post I made about playing multiple hands of blackjack I found a comment made by D Schlesinger (or an imposter) saying that playing two hands of $75 will have the same RoR as playing one hand of $100 but will lower variance, and increase EV. I understand why EV will be increased, there's simply more money out there, and I understand why the variance would be lower, but I don't understand how variance can be lower while RoR remains the same. One would think of variance and risk coincide.

I should also note that in the above example of playing two hands vs 1 there is one other player at the table.

 

[Winneratlosing]

hows your bankroll doin john? did the casino joint your frequently catch on yet? you have to be in the mid west or west coast to be playing a double deck game they dont have those in the east coast, did you watch inside the edge yet? the man has 1/3 mil win/loss statements yet his college friend goes on to say he works at starbuck! you blackjack AP's are the strangest *head skewed and right eye widen alittle*

and you never said you have to pay back your investor? whats his contact? i could use some bankroll =)

 

[gronbog]

Hello,
I was wondering if anyone here could help explain to me the relationship between variance and Risk of Ruin.

Variance and RoR are positively correlated. That is, all else being equal, higher variance leads to higher RoR. Higher EV has the opposite effect. It leads to lower RoR.

While digging for an old post I made about playing multiple hands of blackjack I found a comment made by D Schlesinger (or an imposter) saying that playing two hands of $75 will have the same RoR as playing one hand of $100 but will lower variance, and increase EV. I understand why EV will be increased, there's simply more money out there, and I understand why the variance would be lower, but I don't understand how variance can be lower while RoR remains the same. One would think of variance and risk coincide.

The underlined phrase above is incorrect. You either misread it, misunderstood it or it was quoted from Don incorrectly. RoR is a function of variance and EV. By playing approximately 75% of the single spot bet on each of two spots, both EV and variance increase by about the same amount leading to approximately the same RoR as the single spot bet. The increase in EV is balanced by the increase in variance.

I should also note that in the above example of playing two hands vs 1 there is one other player at the table.

This detail does not matter in the context of this discussion.

 

[Winneratlosing]

RoR with unlimted money is a lie simply not true. After 4000 hours you should show a profit all ror means how far the deep end you go if 1 has 1% edge and 1000 max bets 100$ being max and 10being min you will never go broke john

 

[DSchles]

Variance and RoR are positively correlated. That is, all else being equal, higher variance leads to higher RoR. Higher EV has the opposite effect. It leads to lower RoR.

The underlined phrase above is incorrect. You either misread it, misunderstood it or it was quoted from Don incorrectly. RoR is a function of variance and EV. By playing approximately 75% of the single spot bet on each of two spots, both EV and variance increase by about the same amount leading to approximately the same RoR as the single spot bet. The increase in EV is balanced by the increase in variance.

This detail does not matter in the context of this discussion.

To John: forget about all the other nonsense in this thread and just read the above, which is 100% correct in every respect.

Don

 

[xengrifter]

To John: forget about all the other nonsense in this thread and just read the above, which is 100% correct in every respect.

I thought there was a counter argument, to the now conventional understanding of stabilized RoR vis-a-vis two hands at full value / 75% each, that actually indicates a higher risk of ruin?

Something perhaps that you and KJ discussed several threads / months ago? The sense of higher risk that the discussion bore had a nice intuitive ring for me, but it left me incomplete with not having any final resolution for further RoR assessment, though I note that you did concur with KJ.

 

[DSchles]

I thought there was a counter argument, to the now conventional understanding of stabilized RoR vis-a-vis two hands at full value / 75% each, that actually indicates a higher risk of ruin?

Something perhaps that you and KJ discussed several threads / months ago? The sense of higher risk that the discussion bore had a nice intuitive ring for me, but it left me incomplete with not having any final resolution for further RoR assessment, though I note that you did concur with KJ.

I'm not understanding your comment. If you bet one hand at, say, $100 and calculate the e.v., s.d., and ROR, you will obtain that same ROR from betting two hands of $75 (actually $73). For two hands, BOTH the e.v. and s.d. will be higher than for the one hand, but they will increase by the same percentage, leaving the ROR, which is a function of their ratio, the same.

I am simply repeating what Gronbog already said, correctly, above.

If, on the other hand (no pun intended), you decide to bet two hands of $100, which I don't think anyone was discussing, then all three variables increase: e.v., s.d., AND ROR will all be higher than for the one hand, which should be obvious.

Don

 

[kcchiefsfan1982]

I think the increase is the likelihood of getting black jack (paying 3:2) while having two hands out instead of one hand out. Maybe. Just a guess.

 

[DSchles]

I think the increase is the likelihood of getting black jack (paying 3:2) while having two hands out instead of one hand out. Maybe. Just a guess.

Nothing at all to do with it.

Don

 

[Backbayal]

Variance is not a bad thing if it's in your favor. With no varience you always lose exactly the house edge. Thus, varience is a fickle friend, but sometimes it's the only friend you have.

 

[Backbayal]

Poker players in a cash game sometimes want to "run it twice (or more) to reduce varience. How is this different than playing two smaller bet as in the example above?

 

[Backbayal]

OK VARIANCE. The above was just a varience.