Several weeks ago, a reader sent me a question about Blackjack betting schemes, asking which one is the best.
I essentially knew the answer before I finished reading the e-mail, but I figured I had to set out to provide some data to prove my point. I enlisted the help of an acquaintance to simulate the three different betting patterns that the reader had suggested.
The first was just a straight $5 wager on each hand. The second was to increase the wager about 40-50 percent when the player wins the previous hand. The third was to double the wager each time the player won. Starting with a $5 wager, the wager was capped at $100 in case of successive wins. If the player tied, the wager stayed where it was in the prior hand.
The simulations ran 100 hands per session and ran 10,000 sessions for each betting pattern. The player started with $100 and if all the money was lost, the session ended right there.
Let’s start with the piece of information that I knew before I saw any of the data. The overall payback of each session was essentially the same. As we only ran about 1 million hands, there will be some margin of error, but the sessions were all within about 1/10 of a percent.
How did I know this would be the case? Because the amount you wager does not impact the payback. It does not matter if you are wagering $5 on every hand or $100 on every hand. It does not matter if you pick random amounts to wager on each hand or if you some sort of pattern as described earlier. The payback is the total number of units returned divided by the total number of units wagered and the actual amount wagered does not impact this calculation.
So, we’ve already eliminated determining which one of these is best based on the most important criteria — payback. Beyond that, I guess it is a matter of what are your goals for playing?
Let’s look at ‘playing.’ That is, what is the likelihood that you get to complete your 100 hands. I was a little surprised to find that just over 11 percent of our sessions while betting a fixed $5 would wind up ending in bankruptcy. I have always joked that I could probably play Blackjack for a week on $100.
Perhaps not! This number jumps up to just under 25 percent with our second betting scheme. With our third scheme, it goes all the way to 66 percent. So, if your goal is to play for the full 100 hands, sticking to the $5 wager or greatly increasing your bankroll is your best bet.
What if your goal is to have the best chance of winning over the 100 hands? With our fixed $5 wager, you’re going to end up a net winner 49 percent of the time. This is not a huge surprise as the game is a bit like a coin toss with a slight edge to the house. With our second scheme, this drops to a just under 44 percent. With our final scheme, it goes to 28 percent.
This is not much of a surprise. Part of the reason it is so low is because of the bankruptcy rate. Once you go bankrupt, there is no coming back. If we’re to increase our bankroll size, the win frequency would bounce back, but we’d also still run the risk of losing even more money.
What’s left to measure? I guess that would be how much we can win or lose. If the third scheme has the player losing $100 about 2/3 of the time, then something must balance this out to get us back to the just under 100 percent payback.
We have a 22 percent chance of winning more than $100 over our session. Below $100, we tracked each $10 band (i.e. winning $1-10, $11-20, etc.). The probabilities of winning $20 were pretty similar to losing $20. But, with our losses capped at $100 our winnings did not have this cap. So the chance for a significant win is much higher using this third betting pattern. The probability of winning more than $100 with a flat $5 wager was only 6+ percent. With our second scheme, just below 14 percent.
So, which of these betting schemes is the best? I can’t give you an answer. Payback is the most important figure and this is the same for all of them. Beyond that, the only thing you are actually changing is the volatility. This impacts the bankroll you should brink with you and the size of the wins and losses you can expect.
This is a personal choice of how big of a bankroll you’re prepared to bring to the table and how well you can tolerate the ups and downs of the larger wagers.
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