# Phoenician - Does this seem mathematically "wrong" to anyone else?

#### shandrakor

##### Dormant account
I just doubled up my sticky bonus on Phoenician casino, so I had \$500 in "free money" to play around with. I figured it was only fair to them that I actually wager that money for a little while, so I went to go play some Pontoon.

The game plays with about a 0.17% house edge, about a third the edge that Blackjack plays with, and considering their comp program pays out 0.2%, I was actually playing with a *tiny* edge over the casino.

Betting in \$5 increments, over the course of a few days, I wagered somewhere between 14,500 and 15,000 and lost \$400. That loss of more than 2.6% seems extreme enough, but more than \$250 of the loss was in a nearly continuous string of losses over the course of something less than 5000 in wagering. In other words, at least 5% loss, or 30 times the expected loss amount.

For anyone good at probability out there, does that sound like a very harsh, though realistic loss, or does it sound like Phoenician isn't playing entirely fair?

Or the game has a rather large standard deviation or equivalently variance!

\$400 over the given wagering is a walk in the park. I've had much, much worse.

Pontoon is video poker on valium.

sw2003 said:
Or the game has a rather large standard deviation or equivalently variance!

Well, according to wizardofodds, "The house edge following the basic strategy above is 0.17%. The average final bet size is 1.125 units so the element of risk is 0.15%. The standard deviation is 1.44"

I'm afraid it's been far too long since I took a class on statistics, and none of that means anything to me. Is there anybody who could figure the probability of the swing I took?

shandrakor said:
The game plays with about a 0.17% house edge, about a third the edge that Blackjack plays with, and considering their comp program pays out 0.2%, I was actually playing with a *tiny* edge over the casino.

Betting in \$5 increments, over the course of a few days, I wagered somewhere between 14,500 and 15,000 and lost \$400. That loss of more than 2.6% seems extreme enough, but more than \$250 of the loss was in a nearly continuous string of losses over the course of something less than 5000 in wagering. In other words, at least 5% loss, or 30 times the expected loss amount.

For anyone good at probability out there, does that sound like a very harsh, though realistic loss, or does it sound like Phoenician isn't playing entirely fair?
The odds of loosing 400 or more, betting \$5 per hand during 15000 wagered is 17.3%, or 1 in 5.8.
The odds of loosing 250 or more, betting \$5 per hand during 5000 wagered is 14.7%, or 1 in 6.8.
It's not harsh at all.

Oh, wow. That's quite a bit more likely than it seemed like it would be.

The thing I'm most surprised by is that the 250 over 5000 is so close %-wise to the 400 over 15000. Any chance you're willing to walk me through the math?

shandrakor said:
Any chance you're willing to walk me through the math?

"I played t hands of blackjack one at a time, flat betting and religiously following basic strategy. My final outcome was a gain of r (a negative r represents a loss). The house edge under the rules I played was h. What is the probability of losing this much or more in a fair game?

Using Excel type this into any cell, substituting the correct values for h, t, and r:

=normsdist((r+t*h+0.5)/(t^0.5*1.16)).

The 1.16 is the standard deviation per hand. This will vary slightly from one set of rule to another but I feel 1.16 is a good benchmark. Let's take an example. Suppose the number of hands is 1000, the house edge is 0.41%, and the player lost 100 units. The formula for the probability of losing this many units or more is =normsdist((-100+1000*0.0041+0.5)/(1000^0.5*1.16)) =
normsdist(-2.600700765) = 0.004651712."

The above is from, where else, the Wiz website. I never can find the link so my apologies for not posting it.

The only thing I would do slightly differently than freebie is assume the number of hands was \$15000 wagered divided by the average bet size of \$5* 1.125, rather than assuming you played 3000 hands @ \$5. Either way, going forward, you should keep track of the number of hands played rather than dollars wagered for this type of question. I'm sure you can see how things could easily get out of whack if you varied your bet size in any way which is why the formula above explicitly assumes flat-betting.

By creating a little spreadsheet with cell references, it's 2 seconds work to answer this question for any session since all you have to do is plug in the variables which, the second time around for any game will only be number of hands played and units lost because the standard deviation and house edge will be constants.

If you have any trouble applying the formula, let us know and we'll walk you thru it.

Clayman said:
The above is from, where else, the Wiz website. I never can find the link so my apologies for not posting it.

Clayman said:
The only thing I would do slightly differently than freebie is assume the number of hands was \$15000 wagered divided by the average bet size of \$5* 1.125, rather than assuming you played 3000 hands @ \$5.
Once again, you are right. I didn't pay attention to the final bet size.
This equation is good to "estimate" the odds, it's not an exact answer though.

hhcfreebie said:
This equation is good to "estimate" the odds, it's not an exact answer though.

I just wanted to say, it's also not a "risk-of-ruin" formula and shouldn't be used as such - I wasn't sure if maybe you thought it was. In fact, I think "risk-of-ruin" would be about twice what this formula gives you.

And thanks for the link (again)!