Risk of Ruin with tips (or something else)

I read this somewhere (although I couldn't find it again) and just wanted to verify that my thinking is right on this idea. Lets say that you have a WR in a game of $10/hr and a RoR of 5%. You also decide to give away $1/hr in tips consistently. So, because your BR is not growing as fast as it should be, it will take longer for the WR to overcome the variance, resulting in a lower RoR that can be estimated by .05^.9 to give a result of ~6.75%. Is this right?

PS: I suppose this can also be used if living off of a BR and calculating monthly expenses to estimate the RoR after said expenses.

So for your RoR calculations consider your WR to be $9/hr and your variance to be the same. Here's an interesting article that discusses this topic:

http://www.bj21.com/bj_reference/pages/overheadeffectonriskofruin.shtml

-Sonny-

Well, not sure, but the way I interpret that article I think that would be right assuming, like Sonny said, your variance would not change.

Except you say "resulting in a lower RoR that can be estimated by .05^.9 to give a result of ~6.75%" and your calc seems to yield a higher ROR of 6.75% vs orig 5%? I assume you meant "higher"?

Perhaps, since apparently you liked that 5% ROR to begin with, something to consider would be to increase the number of units in your roll by 11.1111% so that, after suffering a 10% decrease in WR, your ROR will still be the same 5% you liked in the first place.

I suppose it could be used for monthly expenses too except that those must be paid regardless of whether you are winning or losing. Tips are discretional.

I suppose if it costs you $10 in gas to get to a casino every time you go and you want to pay for that $10 out of your BJ roll every time you travel, I'd guess things could get more complicated if sometimes you only played 1 hour and sometimes 12.

Actually, all this is just one big guess in the first place but it's my best one lol.

I'd feel alot better about it if Sonny or someone who actually knows what they are doing would comment on what either me or you said lol.

Hmm interesting...

So the website is saying that having your costs = 1/2 your WR is optimal? Why would any costs on your WR be optimal?

errhh, i haven't read the article, but i'd guess some cost value has the potential of being optimal because essentially in reality there can be a range of costs, but some costs aren't optional, ie. some cost value is a fact of life.:cry::whip:

In theory, it would be optimal to have no expenses at all. In practice, this usually isn’t possible. Most games have some sort of opportunity cost that offsets the EV to some degree. As the article states:

“Under the assumptions made above, that there fixed expenses F which must be met and lower the counter’s expected earnings…We obtain a very simple result: The optimal betting scale is that for which hourly earnings equal to twice the Fixed Costs.”

Increasing the size of your unit in order to increase your EV will increase your RoR. We all know about that one. It’s the old “I can earn twice as much if I bet twice as much” approach. You need to choose a unit size that is appropriate for the size of your bankroll. Betting more money in order to make up for your expenses is obviously a dangerous plan.

In contrast, reducing the size of your unit in order to lower your RoR may decrease your EV to the point that your expenses are too high. The game may not bankrupt you but your expenses probably will. You need to be betting enough to make a decent net profit but not so much that your risk is unacceptable. According to the article, earning twice as much as you spend is the best compromise in that situation.

Obviously there are limitations to the practicality of this approach. If you can keep your expenses low, play with a very large bankroll or play with a large advantage then this is much less of an issue. If a player is serious enough to be factoring his expenses into his RoR then he should be doing at least one of those things already.

-Sonny-

Fixed Expense

The term fixed expense sounds to me like a misnomer. The nature of the expense sounds more like a *variable cost, and earning could have been more clear if the word profit was used. Also, I think we should consider the "Assuming the optimal betting: m = 2F" part. My best guess is that m = 2F only because the variable cost was half of the hourly rate. Maybe that blows away some fog.

Aside from a minor confuse-block, what MathProf asserts sounds correct if and only if Kelly betting that are used in BJ does assume all proceeds from the game is being used as increase in the initial capital just like compound interest. Assuming the variable cost is mandatory, and the unit of production being hour, it only makes sense to subtract the hourly expense right out of hourly revenue.

Conversely, a RoR calculated in this manner could be decreased once this variable cost can be decreased or eliminated altogether. Candide would be happy to hear this!

On the other hand, if this cost was a mandatory one, food for instance, the situation may become a little tricky. Hypothetically speaking, if a player knew exactly what amount of action grants a comped meal, and realized that he could raise his action by raising his betting unit by x%, he may be able to hit the g-spot that enables him to 1)increase win rate, 2)reduce expense, and therefore 3)reduce RoR. I haven't tried graphing or anything for that matter yet, so I don't know anything for sure. It would be lovely if someone more able than I could help me with this.

It would also be interesting to calculate expected value of # of hands that a back-counter gets to play in an hour along with the SD of # of hands played in an hour. This would provide a more clear insight into how much the variable cost can be expected on a per hand basis as well as variable cost per initial wager amount for that matter.

I've been looking into the original Kelly formula, and I haven't found my way out of the maze, so I won't know this for sure until I see a daylight. Maybe I should consult help from my math professor.

*variable cost - in total, variable cost varies directly proportional to changes in the level of activity. I just added this in case I was being unclear.

tipping

Oh, I forgot to mention this. I'm by no means an expert in either behavioral psychology or BJ - and for that I'm grateful - but one thing to consider is which dealer behaviors are being reinforced.

For instance, in terms of reinforcing a behavior, tipping regardless of what he/she does wouldn't be wise. All things being equal and assuming that no other factor interferes with the reinforcement schedule, a player should tip a dealer ASAP only when the dealer behaves in a satisfactory way to maximize the likelihood of these applaudable events like deeper penetrations. Any sensible mind would react to this in a way that is beneficial to the player provided that there is no restraint.

The difficulty, of course, would be implementing it; e.g., how much tip is considered as an incentive, how beneficial is it to you, how often should you tip in order to establish the behavior, etc. I have yet heard of any APs who have conducted a controlled experiment, but I realize that when justifying the satiation of curiosity via controlled experiment without external funding, R&D just doesn't cut it sometimes...