Risk of Ruin is:
The probability that you will lose your entire bankroll
To calculate the bankroll size you need for an acceptable risk of ruin, you need the following information:
- Net Win per Hand of Blackjack Played
- Standard Deviation per Hand of Blackjack
- 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
- 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
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 of Blackjack
When playing blackjack and flat betting (not varying your bets between rounds), the standard deviation per hand is approximately 1.1418.
Blackjack Risk of Ruin
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.