Blackjack Odds (3 to 2 opposed to 6 to 5)

Hi guys. This is Mike.

In this edition of the Wizard of Odds Academy, we will discuss why it is crucial to understand blackjack the difference between 3 to 2 odds in blackjack and the 6 to 5 variation frequently found in casinos today.

Here in Las Vegas

Many players opt for 6 to 5 blackjack even with substantial wagers, which is perplexing. It's likely due to a lack of understanding of the math involved.

It's unfortunate that I have to point this out , but the math is clear: 3 / 2 equals 1.5, while 6 / 5 equals 1.2. This means players win 30% more on every winning blackjack with 3 to 2 odds compared to 6 to 5.

How significant is this disparity in mathematical terms?

Let"s see:

Let's assume we're dealing with six decks, which is standard. If the player has no prior knowledge about the deck composition, the chances of drawing a 10-point card first is calculated as 96 out of 312 cards, since there are 96 ten-point cards available (16 times 6 equals 96), in a total deck of 312 cards (52 times 6). If the player's first card is a 10-point card,

it gives them a chance for a blackjack. They will need to draw an ace as their second card. In total, there are 24 aces available among the remaining 311 cards.

However..

..the player may draw an ace right away. The odds of drawing an ace first versus achieving a blackjack starting with a 10-point card are equal. This consideration multiplies the possibilities by two. The overall probability of the player getting a blackjack is 4.75%. However, to truly benefit from this payout, it has to be a winning blackjack, as it holds no value if the dealer scores a blackjack as well.

Once the player has achieved a blackjack, what are the odds that the dealer will also get one? The dealer could draw either the ace and then the 10 or the 10 first before the ace. From the deck, there will still be 95 ten-point cards remaining out of 310 total cards left. By the time it becomes the dealer's turn, only 23 aces will remain after accounting for the player's two cards.

If the player has a blackjack, the dealer's chances of achieving their own blackjack drop to 4.56%. This decrease is due to the player already holding an ace and a ten from the deck. Consequently, the odds slightly diminish because of the removal effect. The likelihood of the player possessing a winning blackjack is calculated by 4.75% multiplied by (1 - 4.56%).

In summary, we find the probability of the player having a blackjack multiplied by the probability that the dealer does not have one, resulting in a probability of 4.53%.

The math of this is really quite easy

The The chance of the player obtaining a winning blackjack stands at 4.53%, which nicely translates to one in 21, which is memorable considering the game is known as 21. Each time the player secures a winning blackjack while playing at the 3 to 2 odds instead of 6 to 5, they earn 0.3 times more than their initial bet, as evidenced by (3 / 2) - (6 / 5) = 0.3. Thus, 4.53% multiplied by 0.3 equals 1.36%.

That means..

..if a player chooses the 6 to 5 option over the more favorable 3 to 2, they're effectively giving the casino an additional 1.36% of their bet for no better value, assuming all other game rules remain constant.

Alright, I hope I've managed to persuade you all to steer clear of 6 to 5 blackjack whenever possible. But if you're still uncertain, allow me to present you with more statistics.

These figures are based on standard Las Vegas Strip rules that you can generally find in most MGM/Mirage casinos. properties Dealers hit on a soft 17 , players can double down after splitting, doubling is allowed on any two cards, surrendering is an option, and players are permitted to resplit aces. When employing the correct basic strategy, and when blackjack pays 3 to 2, the house edge under these conditions is a low 0.46%.

This means the casino has an advantage of less than one in 200 hands.

It's a relatively affordable way to gamble. However, if we change the payout structure for blackjack from 3 to 2 to 6 to 5, as previously illustrated, the house edge rises by 1.36% to a total of 1.82%. This shift from 0.46% to 1.82% means the risk is nearly four times greater. Effectively, you're paying four times more for the exact same gambling experience.

Here’s what that translates to in terms of your anticipated losses each hour:

For a player wagering $5, playing for an hour would typically result in an average loss of $1.66 at a 3 to 2 table, versus $6.55 at a 6 to 5 table. A $10 player expects to lose $3.31 per hour at a 3 to 2 table, while they would face a loss of $13.10 at the 6 to 5 table. For someone betting $25, the expected loss would be $8.28 at a 3 to 2 table compared to $32.76 at a 6 to 5 table.

Lastly, a player with a $50 wager can anticipate a loss of $16.56 at a 3 to 2 table, soaring to $65.52 hourly at a 6 to 5 table.

I hope I've successfully encouraged you to avoid the 6 to 5 blackjack option whenever feasible. Now, I understand many of you might be thinking, "Mike, I'm a casual player. I'm not comfortable with the stakes at 3 to 2 tables.\" If that's the case, I completely understand.

In some scenarios, you may find yourself limited to the 6 to 5 table options, as your choices may be restricted. Unfortunately, the situation is trending in a less favorable direction.

The casinos in Las Vegas and, in fact, across the United States are gradually attempting to eliminate 3 to 2 blackjack as it is not particularly advantageous for them. everywhere I believe I've covered most of what needs to be said on this subject. Thank you for tuning in, and I look forward to seeing you in my next installment of the Wizard of Odds Academy. Take care, everyone.

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Written by: Michael Shackleford