Traditionally, Vegas blackjack games offered 3-2 payouts for blackjacks, when a winning bet of $10 pays $15. Several years ago, however, casinos started offering 6-5 payouts, when a winning $10. And the payoff for a winning bet on the Banker side is 19 to 20 which is less due to the house deducting 5% house commission. Based on an eight-deck shoe, the House Edge (with ties considered) on both sides are: Banker = 1.06% Player = 1.24%. And the probabilities of winning (excluding ties) are: Banker = 50.68% Player = 49.32%.
Hi guys. This is Mike.
The topic of this Wizard of Odds Academy video will be on the importance of a blackjack paying 3 to 2 odds in blackjack as opposed to 6 to 5, which is a very common rule variation right now.
Here in Las Vegas
You see a lot of players playing 6 to 5 blackjack even at high amounts. Frankly, I have no idea why other than out of a ignorance of math.
I hate to have to insult your intelligence by even pointing this out, but 3 / 2 = 1.5, 6 / 5 is 1.2. The player will get 30% of a bet more with every winning blackjack if he's playing 3 to 2 blackjack as opposed to 6 to 5.
How important is that rule mathematically?
Let's see:
Let's assume six decks of cards, which is the norm, and that the player has no knowledge of any other cards in the deck. The probability that the first card the player gets is worth 10 points, is 96 / 312 because there are 96 10-point cards, 16 x 6 is 96, and 312 total cards in the shoe. 52 x 6 is 312. Assuming the player's first card is a 10-point card.
He at least has hope of a blackjack. He will need an ace or that second card. There are 24 aces in the shoe, and 311 cards left.
However...
...the player might get the ace first. It's just as likely to get the ace first in a blackjack as a blackjack, starting with a 10-point card. We multiply this by two. The probability the player gets a blackjack is equal to 4.75%. However, in order for this pay to make any difference, it must be a winning blackjack. If the dealer gets a blackjack too, then it doesn't make any difference.
Once the player has a blackjack, what is the probability that dealer will get one? Well, again, the dealer could get the ace and the 10 in either order thus the two. There will be 95 10-point cards left in the shoe out of 310 cards. After you take out the two player cards, there will be 23 aces left by the time it's the dealer's second card.
Assuming the player has a blackjack, the probability that the dealer gets one as well is 4.56%. It goes down because the player already has an ace and a 10 out of the shoe. The odds are a little bit down due to the effect of removal. The probability that the player has a winning blackjack equals 4.75% x (1 - 4.56%).
In other words, the probability of a player blackjack and times the probability that the dealer does not have a blackjack, so the probability that the player has a winning blackjack is equal to 4.53%.
The math of this is really quite easy
The probability the player has a winning blackjack is 4.53%, which is conveniently one in 21, and the game is called 21. That's easy to remember. Every time the player gets a winning blackjack, if he's playing 3 to 2 blackjack as opposed to 6 to 5, he will win 0.3 times his bet more because (3 / 2) - (6 / 5) = 0.3, as we showed before. 4.53% x 0.3 = 1.36%.
That means...
...f the player plays 6 to 5 blackjack as opposed to 3 to 2, he's giving the casino an extra 1.36% of his bet, probably for nothing. This assumes all other rules being equal.
Okay, I hope that I have convinced you guys not to play 6 to 5 blackjack when given the choice. However, if you're still on the fence, let me throw some more numbers at you.
These are all based on what are normally, otherwise, fairly standard Las Vegas Strip rules. You can find these at most of the MGM / Mirage properties. Dealer hits a soft 17, double after split allowed, player make double on any two cards, surrender is allowed, and resplitting aces is allowed. With correct basic strategy, and a blackjack paying 3 to 2, the house advantage under those rules is a nice low 0.46%.
That is giving the casino less than one in 200 hands.
It's a pretty cheap way to gamble. However, if we just change that blackjack pay from 3 to 2 to 6 to 5, then, as I just showed you, the house advantage goes up by 1.36% to 1.82%, so 0.46% to 1.82%, that is almost four times as high. That's paying four times as much for the same service and product.
Let me tell you what that looks like in terms of your expected losses per hour:
Odds Of Winning Video Blackjack Games
If you are a $5 player, an hour worth of play on average will cost you $1.66 at a 3 to 2 table, and $6.55 at a 6 to 5 table. A $10 player can expect to lose $3.31 per hour at a 3 to 2 table, and $13.10 at a 6 to 5 table. A $25 player can expect to lose $8.28 at a 3 to 2 table, and $32.76 at a 6 to 5 table.
Finally, a $50 player can expect to lose $16.56 at a 3 to 2 table, and $65.52 per hour at a 6 to 5 table.
I hope I've convinced you to stay away from 6 to 5 blackjack wherever you can. Now, I'm sure a lot of you are saying, 'Mike, I'm a low roller. I'm uncomfortable with the limits at the at the 3 to 2 tables.' If that's true, okay, I get it.
You may not really have the choice in that situation, and you may be stuck with 6 to 5, if you must play. Sometimes there's just nothing you can do about it and the situation is only getting worse.
The casinos here in Las Vegas as well as I think everywhere in the United States, are trying to phase out 3 to 2 blackjack slowly but surely as it's really not very profitable for them.
I don't think I have anything much more to say on this topic. Thanks for watching and I'll see you in my next Wizard of Odds Academy video. Thank you. Bye, guys.
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What Are Blackjack Odds Of Winning
If you want the video blackjack odds then take a look at the house edge and different strategies to help you win.
Odds Of Winning Blackjack Hand
We have frequently been asked about the house edge on Video Blackjack and how different rules and playing perfect strategy affect the odds against you. Many players like the smaller wager limits with the video version and the fact that they can play at my own slower pace. These visitors are right in that there are plenty of advantages to video blackjack with the low minimum bankroll required, with some machines taking as little as 5 cents a hand to play. The machines also spare the player the intimidation of playing in a live game, and can be used as a great way to practice working on the perfect basic strategy.
Blackjack House Odds
There are a few disadvantages though and one of them is how tough it is to find a machine that pays you the true value of a blackjack in which you get one and a half times your money back. Most video blackjack machines only pay out even money on natural 21’s. Since in a live blackjack game at the tables you can expect a blackjack every 21 hands or so, this disadvantage of losing the bonus money loses an additional 2.3 percent to the house edge. If you take into account that the normal house edge for blackjack is only less than half a percent for a perfect strategy player, this is quite a hit on the odds.
Blackjack Odds Card
Also note that some machines round down on blackjack payoffs. If you do happen to find a machine that pays the bonus for a blackjack but rounds down, make sure your wagers are for even amounts so that you can get the maximum value on your blackjack payouts and aren’t losing this small edge for no good reason.