Category Archives: Blackjack
Blackjack
Blackjack Risk of Ruin
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.
Blackjack Bankroll Requirements
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:
- Loss from playing blackjack
- 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.
Las Vegas Trip Report – July 2011
Here are the actual results of my July 2011 Las Vegas Trip.
| Day | Blackjack | Room Comps | Food Comps | Drink Comps | Net Win |
|---|---|---|---|---|---|
| 1 | $170 | $60 | $14 | $10 | $254 |
| 2 | $368 | $60 | $20 | $10 | $458 |
| 3 | -$245 | $60 | $13 | $10 | -$162 |
| 4 | -$438 | $60 | $10 | $10 | -$358 |
| Total | -$145 | $240 | $57 | $40 | $192 |
The results of my blackjack play were very close to the expected amount. Note that I had 1 good day (won $368) and 1 bad day (lost $438). Both days were about equally likely due to fluctuation. Also, as expected, I received more in comp value than I lost playing blackjack.
Las Vegas Trip – July 2011
Here is my plan for a Blackjack Vacation in Las Vegas during July 2011.
On this trip I am going to use 2 offers from 2 different Las Vegas casinos:
- 2 Nights, $25 in Food, and $25 in Free Play
- 2 Nights and $40 in Food
Here is my expected loss from playing blackjack at an average of 70 hands per hour:
| Game | $/Hand | EV | Hours | Expectation |
|---|---|---|---|---|
| 2D H17 DAS | $25 | -0.46% | 10 | -$80.50 |
| Free Play | $25.00 | |||
| 2D H17 | $25 | -0.60% | 10 | -$105.00 |
| Total | -$160.50 |
Here is the value of casino comps I will receive:
| Comps | Days | Value | Total |
|---|---|---|---|
| Room Comps | 4 | $60.00 | $240.00 |
| Food Comps | $65.00 | ||
| Drink Comps | 4 | $12.50 | $50.00 |
| Total | $355.00 |
In total, my out-of-pocket costs are expected to be $160.50 (the blackjack playing loss) for this Las Vegas trip. Where else can you go on vacation for 4 nights this cheaply?
The blackjack expected loss is subject to fluctuation. Will I be lucky and actually walk away a winner from playing blackjack or will I lose much more than expected. Both are equally likely on any one trip.
I will post the actual results of this trip when I return.
Blackjack Probability Fluctuation
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:
| Hands | EV (%) | EV (units) | SD (units) | 1SD (units) | 2SD (units) | 3SD (units) |
|---|---|---|---|---|---|---|
| 100 | -0.50% | -0.50 | 11.42 | -12 / 11 | -23 / 22 | -35 / 34 |
| 200 | -0.50% | -1.00 | 16.15 | -17 / 15 | -33 / 31 | -49 / 47 |
| 300 | -0.50% | -1.50 | 19.78 | -21 / 18 | -41 / 38 | -61 / 58 |
| 400 | -0.50% | -2.00 | 22.84 | -25 / 21 | -48 / 44 | -71 / 67 |
| 500 | -0.50% | -2.50 | 25.53 | -28 / 23 | -54 / 49 | -79 / 74 |
| 600 | -0.50% | -3.00 | 27.97 | -31 / 25 | -59 / 53 | -87 / 81 |
| 700 | -0.50% | -3.50 | 30.21 | -34 / 27 | -64 / 57 | -94 / 87 |
| 800 | -0.50% | -4.00 | 32.29 | -36 / 28 | -69 / 61 | -101 / 93 |
| 900 | -0.50% | -4.50 | 34.25 | -39 / 30 | -73 / 64 | -107 / 98 |
| 1000 | -0.50% | -5.00 | 36.11 | -41 / 31 | -77 / 67 | -113 / 103 |
| 1100 | -0.50% | -5.50 | 37.87 | -43 / 32 | -81 / 70 | -119 / 108 |
| 1200 | -0.50% | -6.00 | 39.55 | -46 / 34 | -85 / 73 | -125 / 113 |
| 1300 | -0.50% | -6.50 | 41.17 | -48 / 35 | -89 / 76 | -130 / 117 |
| 1400 | -0.50% | -7.00 | 42.72 | -50 / 36 | -92 / 78 | -135 / 121 |
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.
