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Risk of Ruin is:

The probability that you will lose your entire bankroll

In the earlier post on Blackjack Bankroll Requirements you learned how to calculate win per hand when including comps.

• Reminder: net win per hand in units of 0.0029 was calculated in the earlier post
• If your total bankroll is $1,000 and you bet $5 per hand then your bankroll size is 200 units ($1,000 / $5)

Looking at the chart below your risk of ruin for this scenario is approximately 39.8%.

Here is another example of calculating risk of ruin based on receiving Free Rooms in Vegas.

• Betting unit size is $25 / hand
• Net Win per Hand is ( $85 in comps / 4 hours of play / 70 hands per hour / $25 betting unit size ) – 0.0060 loss from playing blackjack = 0.0061

If your bankroll is $5000 (200 units) then your risk of ruin is approximately 15.9%

If your bankroll is $7500 (300 units) then your risk of ruin is approximately 6.3%

It is critical to understand bankroll requirements when playing blackjack so that you understand the risk of losing your entire bankroll and you can size your bankroll appropriately.

One last reminder, you need to follow my 4 Rules of Blackjack Money Management for this strategy to work.

You have learned how to play blackjack with basic strategy and how to receive casino comps.

How big of a bankroll do you need to take advantage of these strategies?

The term for this is Risk of Ruin.  Risk of Ruin is the probability that you will lose your entire bankroll.

To calculate your needed bankroll size you need the following information:

• Net Win per Hand
• Standard Deviation per Hand
• Risk of Ruin desired (percent)

Net Win per Hand is the sum of:

1. Loss from playing blackjack
2. Amount received from comps = (comps received per hour) / hands per hour / betting unit size

Example:

• 2D H17 DAS game loss = -0.0046 units (decimal form of expected value %)
• Comps received = $2 / 53 hands per hour / $5 = .0075 units
• Net win per hand = -.0046 + .0075 = .0029

You need to follow my second rule of blackjack money management for these bankroll requirements to work.

Every time you receive a comp you need to add to your bankroll the cash value of the comp to replenish your bankroll. Remember you would have spent this money if you didn’t receive comps.

Standard Deviation per Hand is approximately 1.1418:

• In the post on bankroll probability fluctuation you learned that standard deviation per hand is approximately 1.1418.

My next post will finish the calculation for risk of ruin and give you an idea of the blackjack bankroll size you will need to use these comp strategies.

When playing blackjack, your bankroll will fluctuate throughout the course of a session. Another word for this is risk and is expressed by a statistical term called standard deviation (SD). Standard deviation is variation from the “average” (mean, or expected value).

In blackjack the standard deviation is about 1.1418 when you do not vary your bet size (flat betting).

The following charts lists the expected range of results for a given number of hand played:

You can interpret the standard deviation ranges as follows:

• 1SD will occur 68.3% of the time. As a result 68.3% of the time your results will be between the low and high-end of the range given.
• 2SD will occur 95.4% of the time.
• 3SD will occur 99.7% of the time. So in 1 of every 333 playing sessions your results will be outside this range.

To interpret the above chart, if you are playing a blackjack game for $25/hand and play 1000 hands, your result will be between -77 units and 67 units 95.4% of the time.  So your bankroll could be down as much as $1,925 over those 1000 hands.  These ranges assume you are using basic strategy.

For the mathematically inclined here are the formulas:

• EV (units) = EV (%) * Number of Hands
• SD (units) = ( Square Root of the Number of Hands ) * 1.1418
• 2SD Range Low = EV – ( 2 * SD (units) )

I hope that this post gives you some idea of the amount your bankroll will fluctuate over the course of a trip.  It is important to have enough money in your bankroll to get through these inevitable fluctuations.

Money management is as important as playing correct basic strategy.

When playing blackjack using basic strategy you will lose money over time. As you have seen, you will receive more back in the form of comps. These comps are what turn a losing game into a winning one.

4 Rules of Blackjack Money Management:

1. You need to set aside money specifically for your blackjack bankroll. I use the term 401(g) for this gambling bankroll. It is named after the 401(k) retirement plan.
2. Every time you receive a comp you need to add to your bankroll the cash value of the comp to replenish your bankroll. Remember you would have spent this money if you didn’t receive comps.
3. You should never take money out of your blackjack bankroll. If you can’t afford to lose this money you should not play blackjack.
4. Even if you win, you can’t take money out of your bankroll.

Here is a chart of a hypothetical bankroll fluctuation:

So as you can see, you lost $600 by playing blackjack, but you received $1,000 in comps so your blackjack bankroll increased by a net of $400. Another way to look at this is that you received $1,000 in comps for only $600. Where else can you take 5 vacations for $600?

Discussions of bankroll requirements and when to increase your level of play will be in future posts.