Gambler's Fallacy #2?

Low Variance in BJ is Bad, Right?

There are plenty of posters and threads that indicate that it is practically a given that the one thing that players want is lower variance in non-AP, -EV BJ. Game designers are evidently seeing success by raising HE and lowering variance!

Now is certainly the time to explain to me why less variance is desired in -EV play, as that makes no sense to me.

Is it the 'other' Gambler's Fallacy? Or is it my skull that is filled with a fallacy?

It depends on what you're talking about... If I could take variance out of the equation and always win my sessions by a margin of about 52% then I would love that! No variance and always EV! There'd be no risk of ever going broke, etc, and my bankroll would slowly (very slowly) just creep up. However, since this isn't possible, and it would show just how slow of a grind it is, the swings in variance can be a good and bad thing pending which side of the coin you're on. If you have good variance, then you'll see wins much higher than your EV. Likewise, poor variance will swing you losses not expected. We use averages, playing hours (long run), etc, to calculate that these swings in variance, or luck, are expected and that they will level out over time. Thus, as counters/AP's we know if we play long enough, we are in fact eliminating the variance to get to our true EV!

From a non-AP perspective, I can see why they'd want less variance. People are there to play and have fun, and most of the time even expect to lose their money. So, if they can order 'free' drinks, crack jokes, win some and lose some over a few hours, this is a LOT more fun than if they were to sit down, hit some really bad variance, and be broke in 10 minutes. There's nothing fun about buying in and just losing it all quickly without much 'play' or back and forth.

Take Pai Gow Poker for example. My brother and friend love playing this 'for fun' because there's a ton of pushes... i.e. a lot less variance. Your chips stack won't shoot up, but it also won't shoot down. They enjoy this because they can play for hours without losing a ton of money (nor winning a ton of money). For the non-AP, this is where they get their entertainment, and thus why I could understand them enjoying less variance, even at a cost of a higher house edge (which most non-AP's don't even know/care about).

I think most casino patrons want MORE variance, not just in BJ sidebets either. Why else would they prefer Double Double Bonus over Jacks or Better.

The side with the advantage desires lower variance.
The side with the disadvantage desires higher variance.

Hows this for variance ? Watching Price Is Right. Young lady gets picked from audience. wins chance to play for a car, then picks the number 18 and BINGO wins the car. Oh, why did she pick 18. Because it is her birthday. she is 18 !

Quote: JB

The side with the advantage desires lower variance.
The side with the disadvantage desires higher variance.

Disagree on the 2nd point. Some people accept an entertainment value for gambling. PGP and even simple DW/JoB are games where you can make money last for awhile because variance is fairly low.

And I think there is a curve for an acceptance of higher variance by time spent at a casino. That is, people who are there for shorter amounts of time play higher variance games.

I think most non AP -EV players want higher Variance but with the following skew.
Win High amounts with low frequency
Lose Smaller amounts with higher frequency.
ie a distribution with a tail on the right side that extends much further than the tail on the left.

The entairtnemnt 'value' of the occasional high win and most of the all the anticipation to repeat that high win when playing is the 'entairtenment value' or 'high' that the player gets by paying the cost of -EV.

Quote: JB

The side with the disadvantage desires higher variance.

Only if they're playing to win by getting lucky and quitting while ahead.

If they're buying the entertainment value of the play, I expect a lower variance is desired.

Quote: Dieter

Only if they're playing to win by getting lucky and quitting while ahead.

If they're buying the entertainment value of the play, I expect a lower variance is desired.

I concede that that is correct. I was erroneously assuming that the opposite of "the side with the advantage wants lower variance" was true, which is not necessarily the case. I should have said, "the side with the disadvantage likely wants a variance greater than zero."

OK, I guess my view will have to moderate. I certainly don't want the kind of variance where you lose all the time with a remote chance of a spectacular win. That's why I won't play the megawhatever lotteries, even if someone claims the EV turned positive.

I still say, though, that the variance in BJ is too low. Too low for me, anyway.

Quote: odiousgambit

If that's the case just start spreading 1-30 instead of 1-15. You should see a lot more swings from variance =P.

Quote: Romes

If that's the case just start spreading 1-30 instead of 1-15. You should see a lot more swings and variance =P.

I guess betting more [at whatever prompt] is supposed to increase variance, but I can't quite get my mind wrapped around that.

Quote: odiousgambit

I guess betting more [at whatever prompt] is supposed to increase variance, but I can't quite get my mind wrapped around that.

It doesn't increase the variance, it amplifies it. For example, in a "generic" game of blackjack where the HE is .5%, you will wait until a TC +2 to raise your bet because at TC +2 you are then the .5% advantage. Again, generically speaking, for each positive TC you gain approximately .5% advantage towards the player.

Thus, when the TC = +2, you're ~.5% favorite, so let's bet more! This is where the "variance" can shine. Even if you're a .5% advantage, that still means you're only 50.5% to the house advantage of 49.5%. Basically, in the short run, you 'probably' won't see these numbers exactly though, and the difference you do is is the "variance." In fact, you might win 60% or you might lose 60%. You only see that true .5% advantage in the long run when the law of large numbers averages them out to your true Expected Value... 50.5%.

So, with that understanding... It should be easy to see how raising your spread even more will not cause more variance, but it will AMPLIFY your variance. Say in a session you're "lucky", or you have 'good variance', and you're winning 60% of the time when your advantage is only 50.5%. Normally you're betting 2 units at TC +2... so out of 10 hands, you'd win 6, and you'd win 12 units, and lose 8 from the other 4 hands... for a net win of 4 units.

Now let's UP that spread and say at TC +2 you bet 10 units instead of 2... In the same scenario of 10 hands you'd now win 60 units, and lose 40, for a net win of 20 units! This is obviously a big difference and a much larger "swing." Notice that upping your spread 5x amplified your winnings 5x from 4 to 20.

The same goes the other way though! Take the example I just gave and pretend you lose 60% of the time because you're having bad "luck" or 'bad variance.' Now instead of losing 4 units, you lose 20 with the bigger spread.

Thus, I should hope it's a bit more clear to see now in both good and bad scenario's above your "variance" was the 60% number...and did not change. Upping your betting spread AMPLIFIED your variance and will create much wilder swings both up and down...

Coming from the world of coin-operated arcade games, it should be apparent that if you completely eliminate variance from a negative expectation gambling device, you have a, what we call in arcade game business, "rental model." You are renting the machine and paying for units of time on the machine.

Older style arcade games were actually more like gambling experiences because as you became a good enough player, your cost per unit time became negligible, and your payoff for risking quarters to play the game was to master the game. Games like Asteroids, Defender, Pac-Man, and Donkey Kong all employed more of a gambling element where your goal was to reduce the cost per unit time to play. Nobody ever got quarters to come out of the machine, but you were gambling that you could increase your skill and have a longer game time through repeated plays and learning how the game works.

In my opinion, the "rental model" as it was majorly kicked off with the earnings from "Gauntlet" slowly took the gambling elements out of arcade games.



I included Atari's patented "ghost car" to introduce gambling elements to San Francisco Rush 2049 coin-op (awarding free games) to try to get further away from a strict rental model in Rush 2049 coin-op. This was, in my opinion, a compelling portion missing from previous versions of San Francisco Rush and Rush/Rock for single player modes, and gave you a reason to play over and over (try to beat the free game ghost car).

https://www.google.com/patents/WO2001005475A1?cl=en&dq=aaron+hightower&hl=en&sa=X&ei=wtYJVPbUN9KzogTUnYGQCA&ved=0CB0Q6AEwAA

Without taking risks and without being rewarded, just renting a machine and watching it do it's thing is pretty boring in my opinion. Even if it's really pretty as many slot machines are. People like being rewarded for doing well.

We have lead Artist Adrian Ludley (from Rush 2049), Game Designer Steve Riesenberger (from Rush 2049), and cabinet designer Mark Gruber (from Rush 2049) all working on our pinball game we will be showing in a few weeks at booth #2712 at G2E. I hope to see folks there.