Long-term result in the short term

I had a weird thing happen this weekend, sort of. Bought in for $100 at our local casino and played for an hour; at the end of which I had $97. Seemed weird, I never seem to come out even close to what the math 'predicts' the expected loss is, and this was just about right on, playing mostly craps passline bets with low or no odds. Maybe math really does work!

Quote: AndyGB

I had a weird thing happen this weekend, sort of. Bought in for $100 at our local casino and played for an hour; at the end of which I had $97. Seemed weird, I never seem to come out even close to what the math 'predicts' the expected loss is, and this was just about right on, playing mostly craps passline bets with low or no odds. Maybe math really does work!

The math always works, in the short run and the long run,
when you consider variance and the standard deviation.

Not just house edge and EV like everyone does.
maybe only 99.9999% does.

The EV just shows the average loss over many many many trials but not the range around itself for one or two trials.
You will be closer to the house edge before the EV.
For just a few sessions do this... It will NOT take years...
Take your $net and divide by the $total of all your resolved bets.
That number is what you should be looking at. it will be closer to the actual house edge than will the EV.

You and everyone else is less likely to be lose exactly X$ over any one session than to be at the EV
Way more likely to lose X$ + or - (plus or minus) 3 times Z$s (99.7%)
The EV may say, for example, you will lose ~$8.50 after 4 hours of play (120 bets * $5 * (-7/495))
at Craps with 2X odds making $5 bets and $10 odds bets
but the range around that is what standard deviation is all about.
Pass line with 2X odds = $156.53 SD

many just think because the EV says they could lose about $8.50
and are horrified when they lose $325 in a 4 hour session.
"How is that fuc*in possible!"
"The math is never right."
"The math must be wrong."
Only if you look at house edge and EV only.

Like looking at the world with blinders on.
narrows the range of the view

The Wizard has a few comments about these concepts (variance) at WoO.
but he too mainly pushes house edge and EV only as the only numbers a player needs to know about.
https://wizardofodds.com/gambling/house-edge/

https://wizardofodds.com/games/craps/appendix/1/
bottom of page
a nice example
No mention of variance or standard deviation. Maybe got lost in the translation.
a 100 trial session and the range of possible ending outcomes assumes enough bankroll to last that many bets.
(session EV = -$1.41 and session SD = $29.55 for Full 2x odds
meaning a $1 flat on 6&8 can take $2.50 for odds and the odds pay exactly $3)

learn about variance and set yourself free
and see that the math is always right in the short run and the long run

Quote: Beethoven9th

If you tracked all of your bets over the course of, say, 5 or 10 years, I'm sure the math would turn out to be quite accurate.

Only with regular play.

I played about 24 hours just since Friday. Some people only play a few hours a year.

I know this is sort of obvious, but it's the number of rolls not the length of time. I apologize for being pedantic.

During my 24 hours of play, I came out ahead. The table wasn't always empty, so it wasn't 2400 rolls, but if I had been on an empty table that long, it would have been that many or more.

Points being, for the last 24 hours the math wasn't accurate for me AND in 5 to 10 years it might not be accurate for someone else if they don't play that often.

Quote: Ahigh

Points being, for the last 24 hours the math wasn't accurate for me AND in 5 to 10 years it might not be accurate for someone else if they don't play that often.

yes, the math was still very accurate when you consider both EV and SD (standard deviation)

You just did not show the math for your session of play.

EV per rolls and standard deviation per roll for every bet you made and every roll you saw.

Now add them all up.
your result will be the EV +/- 3 times the SD
99.7% of all the sessions you play, no matter how many bets or rolls are made or seen.

The math is always right when you do the math. All the math. EV and variance and standard deviation.

You want to lose exactly or very close to the EV.
Good Luck trying.

The math says EV and
variance and standard deviation

One rarely sees the standard deviation values for every craps bets on a per roll basis.
wonder why

Quote: Ahigh

Only with regular play.

I played about 24 hours just since Friday. Some people only play a few hours a year.