On June 21, the Stanley Acropolis family of casinos had an amazing promotion. They paid 2 to 1 on blackjacks for the entire day. There was no minimum or maximum bet size, other than the usual limits of $5 to $100, and no catch other than you had to make a deposit during the promotion.
The blackjack rules at the Acropolis casinos are six decks, dealer stands on soft 17, player may double on any two cards, player may double after splitting, player may resplit (including aces) to three hands, no surrender, and dealer always peeks for blackjack. The house edge under these rules is 0.36%.
The cards were also dealt about 35% of the way through the shoe before a shuffle, giving the card counter an even lower house edge.
The extra 0.5 units per blackjack adds 2.27% to the player’s expected return, for an overall player edge of 1.91%. Under the promotion rules, the extra 0.5 units would not be given immediately but within a day after the end of the promotion.
After the promotion was over, a lot of players found themselves with big losses, despite what they could expect to get back from the extra 0.5 units on blackjacks. I was one of them.
First I lost, then I almost came back to break even, then during about a three-hour sitting I had a downhill slide with no mercy. I used a Kelly method of betting proportional to my bankroll, to minimize the probability of ruin. Unfortunately, it is harder to dig out from a hole using this method and the probability of a partial loss is greater than flat betting over a limited period of time. I didn’t keep any records other than how much I bet with every winning blackjack. Anyway, it is not the intent for this article to moan about my losses but to discuss money management under this promotion.
First let me say that I believe the Acropolis software to be fair. Others have questioned it after this promotion, but every brand of software gets questioned by players who lose. I think many lost money on this promotion as a result of overbetting their bankroll, including myself.
About a month before this promotion, I added a section to my own web site on the risk of ruin for the basic strategy player called blackjack appendix 12.
Although the player can play two hands using Acropolis software, let’s assume they played one hand at a time at a rate of 250 hands per hour. Also assume the player was willing to play for 12 hours, for a total of 3000 hands played. Further assume that the player deposited $2000 for this promotion. My appendix shows that for 3000 hands played the following the following number of units the player needs according to the risk of ruin.
To make an example, suppose the flat betting Slot Joker123 player above is comfortable with a 5% risk of ruin. The table shows that the risk of ruin with 137 units before 3000 hands are played is 5%. Dividing the bankroll of $2000 by 137 units results in a unit size of $14.60. I would wager to say that most people, including myself, were betting more than 1/137th of their bankroll per hand during this promotion.
Personally I was greedy and wanted a high expected win rate per hour. I was initially betting about 1/60th of my bankroll per hour and quickly fell into a hole. The table shows that if I had bet 1/62nd of my bankroll per hand and was flat betting my risk of ruin was 40%. So in retrospect I overbet my bankroll, and wouldn’t be surprised of many others did as well.
To suggest a money management method for this promotion, assume the player was comfortable with a 10% risk of ruin. The table shows the player should bet 1/116th of their bankroll for a probability of ruin of 10% before 3000 hands are played. So with a $2500 bankroll the bet size should be $21.55. Of course you have to bet in increments of $1 so by dropping down to $20 per hand the risk of ruin drops marginally.
Regardless of the bankroll size, the player should not bet more than 1/116th of their bankroll if they want a risk of ruin of less than 10% and plan to play 3000 hands. My appendix shows statistics for many other number of hands besides 3000, allowing the player to determine their bet size according to their own situation.