Short On Bankroll

I get questions from members on different forums about all kinds of things. One that is ever reoccurring is something along the lines of "I only have $500 to use for a bankroll, what are my AP options?" I received a similar question recently and thought it would be beneficial to put the answer here for others with similar thoughts/questions to see... and for others to weigh in with their opinions/etc.

Question for the pole: If you had a $500 bankroll, what AP move would you do with it?

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Well in any aspect of AP there exists concepts such as kelly betting and bankroll management. Kelly betting is a mathematical formula that tells you how much you should be betting of a given bankroll given a specific advantage and variance of the game. Thus, it makes sure you'll never go broke with an advantage.

One AP play you can definitely do while being underfunded is study. I don't mean to say this as a joke either. Before I was funded I spent my days reading, learning, and practicing. When it came down to just having the bankroll, that was a problem that was easily solved by saving up, etc, etc. It didn't require more learning or practicing, just time and money. I would definitely recommend you find the areas that interest you and study up on how to AP them, whether it be counting cards, must hits, progressives, promotions, etc.

On a $500 bankroll there isn't much you could do that wouldn't be putting your Risk of Ruin (RoR) way higher than most would find acceptable... but that's another thing. Your level of risk and loss tolerance is up to you. Some pro's only play with < 1% RoR. Some part timers play with upwards of 5-10% RoR. And still others play on "replenish-able bankrolls." This is where you dedicate $500 now, because that's all you have, and "if" you get unlucky and go broke then you'll dedicate more money later down the road. This is actually what my partner and I did when we first started playing together. We only had about $4k between us, but we calculated our bets/etc off of a theoretical $32k bankroll that we both were willing to commit over time if necessary. This is certainly something you could do, but you MUST understand that just because you don't have to have the money now doesn't mean you won't one day possibly need it. By doing this you're fully understanding that $500 isn't your real bankroll nor your real dedicated amount and that you must provide more funds to your bankroll to meet your theoretical amount you're comfortable with. If you do this, then you can pick a number you're comfortable with (say $5k over the next year) and start calculating a spread/etc that will work for now.

I'll be honest with you though, with only $500 that will limit your options greatly. Most of the more lucrative plays come with a LOT of variance, which will shoot your small bankroll right in the foot. You'll need something that has low variance, such as blackjack (1.15). With that amount you should be able to AP $5 blackjack tables. I just jumped out to my 3rd article to leverage the standard deviation chart, as well as found an average bet for a $5-$50 spread with the spread sheets I've posted in my A-Z thread. The average bet for a $5-$50 spread (wong out after TC -1 and max bet out by TC +3) is $12.25 and will yield about $7.70/hour. Given this average bet, and an average 1% advantage, we can figure your standard deviations in the short run to see just how your $500 bankroll stacks up.

OriginalSD = 1.1*AvgBet = 13.50

NumHands = 1,000
Expected Value = (numhands*avgbet)*advantage = (1,000 * 12.25) * (.01) = $122.50
Standard Deviation (SD) = Sqrt(NumHands) * OriginalSD = Sqrt(1,000) * 13.50 = $426.91

So what does this mean? This means after 1,000 hands, which at 80 hands per hour is 12.5 hours of play, you could expect to be UP $122 +/- $427. One standard deviation comes with 68% confidence, but anyone taking the game seriously does at least 2 SD which is 95% confidence. 2SD is literally just 2 * SD = $854. So with 95% confidence you will be up $122 +/- $854... I hope you see how the "most" you could be down (122 - 854 = -732) is more than your $500 bankroll, which tells you that you are under funded. There is a chance though that the best you could do after 12.5 hours is 122 + 854 = 976, which you could put right back in to your bankroll and triple your bankroll to $1500.

I could go on and on. My favorite quote from my college stats professor was: Figures never lie, but liars sometimes figure. I can make the numbers work for you. I can make them not work for you. Given the above you "could" play on your $500 bankroll and have a 1SD (68%) confidence that you wouldn't go broke after the first run of about 10-15 hours. It would be absolutely essential and crucial though that you take any winnings you have an re-invest them in to your bankroll as I hope you can tell a "total bankroll" of $500 will NOT work. This is why I talked about the replenish-able bankroll to give you your options at this point.

At the end of the day you need to understand what your risk tolerance and total loss can be. Are you comfortable losing up to $5k by the end of the year? What about $1k? The example above shows that you could play for a short time on a $1k bankroll, but what about for 100 hours? All the math is there, so I implore you to re-run some of the numbers for 50 hours of play, 100 hours of play, 500 hours of play. Then the picture of just how much bankroll you'll need will really come in to focus. Again, not that you'll ever NEED that amount at 1 time, but there must be a number that you're willing to commit to your bankroll over time if you're going to go the replenish-able route. Find that number and re-do the numbers I've given you above to find out if that's enough. If it's not, then continue to study and practice while saving up longer until you have an amount you're both comfortable with and will mathematically work for you.

So many (including myself) are entirely too eager to start playing. Those that study and practice more than they need before playing are "usually" the successful players.

What do you other guys think?

Find a flashing dealer. Or stick with vulturing UX, Multi-Streak, etc.

Quote: Ibeatyouraces

Find a flashing dealer. Or stick with vulturing UX, Multi-Streak, etc.

Even games with a good dealer come with a very high level of variance. Sure, your edge is higher which will up your Expected Value, but your SD will also shoot up through the roof from your OriginalSD, which is the variance times your avg bet.

Video poker alone (9/6 jacks or better) has a variance of 19.51, as opposed to the 1.15 variance of blackjack. Think about that standard deviation window now...

I think Vulturing UltimateX is a fantastic idea for a low bankroll, because with just a couple multipliers you can easily be over 100%. This might be geographically limited though, if you don't have very much available around you or have a ton of competition...

Quote: Romes

Even games with a good dealer come with a very high level of variance. Sure, your edge is higher which will up your Expected Value, but your SD will also shoot up through the roof from your OriginalSD, which is the variance times your avg bet.

Video poker alone (9/6 jacks or better) has a variance of 19.51, as opposed to the 1.15 variance of blackjack. Think about that standard deviation window now...

Certainly. The problem with counting though, is that bets don't remain constant, unless wonging. That would be last on the list if I were to play off the $500 only. Personally, I'd stick with the vulturing until I built up big enough to withstand the swings.

And just for the record, I recently lost $500 on a first card MS game playing only $5 a hand in less than 2 hours. So I know where you're coming from.

A Flashing Experience

A year ago we found a good MS table (3rd card) and my buddy and I were down $1200 after 5 hours just betting $5 and $10 - even with 95% accuracy. With an hour left in the dealer shift my buddy says let's go for higher bets to try and get even. I should have agreed because each hand was very +EV regardless of how we were running but we only had $800 combined cash left in our wallets. Of course this last hour is where we go on our heater and end up leaving with $1800 (+$600) on all $5 bets. But, had we done higher bets the whole time we would have ran out of money before hitting an upswing.

Moral: Have (or have access to) way more money than you think you need.

Don't you also have to consider whether or not you can play rated ? If you can play rated and use that $500 towards playing less than optimal games at least you will be compensated for your future travel expenses (plus access to various other promotions) while the unrated player would not be able to invest like this.

Quote: BTLWI

...Moral: Have (or have access to) way more money than you think you need.

This. So much this. I will ALWAYS rather have more money than I need than come across a great game and have not enough!

Quote: DiscreteMaths2

Don't you also have to consider whether or not you can play rated ? If you can play rated and use that $500 towards playing less than optimal games at least you will be compensated for your future travel expenses (plus access to various other promotions) while the unrated player would not be able to invest like this.

Anyone playing low stakes it should be almost a given to play rated. When you're playing for low stakes you need every dollar of EV you can get, such as the free play that comes in for playing, free buffets, drawing entries, etc, etc.

With only $500 do not play casino games. Some places might offer you $5 to $10 just for signing up for a players card. That's about the limits of what is both profitable and sensible. If all you can do is look for Ultimate X multipliers and back count a six deck game until you can jump in with $15 bets, you're struggling to make half of what a minimum wage job would pay. When collecting cans or working at McDonald's for a week is a better way to double your bank roll than an entire month at the casino, you shouldn't be playing casino games.

When playing casino games, expected value = income. If you have to give up EV due to variance, your low bankroll is stopping you from earning money.

A 21-year-old college student will be fine if he ends up completely broke (most have negative money). I know there are exceptions, but for most of us, if we can't figure out a way to earn money outside of a casino, we'll have almost no chance of being able to earn money inside of one.

Maybe the best way is to find a job that gives you paycheck and earn $600 per year cashing it in every other week (maybe even $1200 if it's one of the rare places that pays weekly; or just find two part time jobs)

Quote: TomG

...Maybe the best way is to find a job that gives you paycheck and earn $600 per year cashing it in every other week (maybe even $1200 if it's one of the rare places that pays weekly; or just find two part time jobs)

Good advice... I'm going to go ahead and put this under the "keep studying/practicing and saving!" =)

Assuming the person has a regular job, I would prefer playing on a replenishable bank. If no regular job, don't play. Get a job and read/practice at their own pace. Is the player looking to supplement their income significantly or more for the pleasure of the Casino enviornment. Making less than minimum wage can become a brutal experience depending on the individual and what they want to get out of it. Sometimes it's not worth it to be too careful. Just my opinion.