The straightforward answer to the question is 4.76%. The more complicated answer depends on two things. How much you can push the house and how much you bet. Some casinos will allow you to buy the 4/10 for more than $20 and still only charge a $1 commission until you get to $40. If you can buy it for $25 the house advantage (HA) is 3.85%. It you can buy it for $35 the HA is 2.78% and if the house lets you buy it for $39 the HA gets reduced to 2.5%.
The rules for placing or buying the 4 and/or 10 are as follows: If one places the 4/10 the payoff is 9 to 5. When the commission is paid up front, if you bet at least $20 you can buy the number for a 5% commission that is paid to the house at the time you make the bet. Thus the commission is paid regardless of whether you win the bet or not. A buy bet on the 4/10 pays 2 to 1 odds on the base bet. The commission paid is locked up by the dealer and is not part of your bet.
Let’s say you place $10 on the 4. You cannot buy this bet because it is less than $20. If it hits you get paid $18 plus your original bet for a total of $28. At this point you could tell the dealer to buy the 4 and he would keep $11 from the $18 win and hand off $7 to you. He would put $10 on top of your $10 for a total of $20 and set a button on top of your bet that says, “buy”. This indicates you bought that bet and it is paid at “true” odds of 2 to 1. If this bet hits you get paid $40 in addition to your bet of $20 for a total of $60.
It makes sense to buy the 4/10 whenever you bet $20 or more because it is better than the place bet that has a 6.67% HA. In the example I just gave you, notice you are paid a total of $60 for the buy bet that cost you $21 to make. Your net win is $39. If you placed the bet for $20 instead of buying it you would be paid 9 to 5 for a total of $56 if it wins. Your net win is only $36. Thus the $1 commission you pay to buy the bet will win you a net of $3 more when the bet wins.
As I said initially some casinos allow you to push the house on the buy bet of the 4/10. This means when they calculate the 5% commission on your bet, they drop the cents and round the commission down to the nearest dollar amount. All bets in increments of $20, round to an even dollar amount. 5% of: $20 is $1, $40 is $2, $60 is $3 and so forth. If you bet $25 the 5% commission would be $1.25. Many casinos will allow you to buy the 4 or 10 for $25 and only charge you a $1 commission. They do not take coins for the commission so you do not pay the additional 25 cents. This gives you an additional benefit by dropping the HA further to 3.85% on a $25 buy of the 4/10. Many casinos will also allow you to put an additional $15 on any increment of $20 and not charge any additional commission on the $15. Thus you can buy the 4 or 10 for $35 and pay only $1 commission, reducing the HA even further to 2.78%. Some casinos will even allow you to buy the 4 or 10 for $39 and still only pay a $1 commission. This would reduce the HA to 2.5%.
If it fits within your bankroll and risk tolerance you should always bet the additional amount allowed on your buy of the 4/10. This bet is paid off at true odds of 2 to 1 and there is no commission charged on it.
One thing to note when you make a buy bet on both the 4 and 10 at the same time. The commission is collected on the total amount bet on both bets together, not on each one separately if you make both bets at the same time. If you were to bet $35 on the 4 and $35 on the 10 at the same time, this would be treated as a $70 bet rather than two separate $35 bets. The dealer would charge $3 commission on the $70 because 5% of $70 is $3.50. But if you made the bets separately you would only be charge $1 on each $35 bet because the $1.75 commission gets rounded down to $1. There has to be at least one roll made between both bets in order for them to be treated as separate bets. If you want to make this bet just after a come out roll a good way to do it is to make one bet on the come out and one bet after the come out. On the come out put $36 on the layout and say, “Buy the 4 for $35, off on the come out”. After the next roll hand in another $36 and buy the 10. This way you can get both bets made for only $2 rather than $3 and the first bet was not working during the come out. If you want to make the bet after the come out you will have to put the bets up one at a time with at least one roll in between each bet to avoid paying the extra $1 commission.
If the house allows the extra $15 without any extra commission you can do this on every increment of $20. You could buy the 4 or 10 for $35, $55, $75, $95 and $115 for commissions of $1, $2, $3, $4 and $5 respectively. The HA will still be lowered but not as much on the higher amounts because of the way the math works out. It is still a good idea to push the house as much as they will allow on the buy bets because it still lowers the HA for the bet. The following table shows the HA for different amounts bet on the 4 or 10 when the commission is rounded to the lowest even dollar amount.
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