If you have to pay the vig up front, in other words on every bet then it is a bad idea to buy the 5 or 9. What you would be missing is you are only calculating the vig on a win. You are not taking into account the vig you pay when the bet loses.

Let us look at what happens if you have to pay the vig on every bet.

You bet $21 five times. For random you can expect to lose the bet three times and win it two times.

You wager a total of $105 and collect a total of $100 losing $5 out of $105 wagered (5/105=.0476). The house advantage is negative 4.76%.

If you place the bet for $20 five times. For random you can expect to lose the bet three times and win it two times.

You wager a total of $100 and collect a total of $96 losing $4 out of $100 wagered (4/100=.0400). The house advantage is negative 4.00%.

So not only is a HA of 4.00% better than 4.76%, clearly it is better to lose $4 out of $100 than $5 out of $105.

If they only charge you a $1 vig up front on wagers over $20 up to $38, you can do better with a buy bet than a place bet for wagers over $24. But the HA is still pretty high even then. It becomes break even at $24.

When you wager $24 + $1 five times, you wager a total of $125 and collect a total of $120 losing $5 out of $125 wagered (5/125=.0400). The HA is negative 4.00% which is the same as a place bet.

At $30 the HA drops below that of a place bet but it is still a high HA.

When you wager $30 + $1 five times, you wager a total of $155 and collect a total of $150 losing $5 out of $155 wagered (5/155=.0323). The HA is negative 3.23%, a fairly high HA.

Once you get to $38 it drops even more.

When you wager $38 + $1 five times, you wager a total of $195 and collect a total of $190 losing $5 out of $195 wagered (5/195=.0256). The HA is negative 2.56%.

So if you are going to make a place bet anyhow, it makes sense to make a buy bet once you want to wager from $26 to $38.

If you only pay the vig when the bet wins, then it is a good idea to buy the 5 or 9.

Let us look at what happens when you only pay the vig when the bet wins.

You bet $20 five times. For random you can expect to lose the bet three times and win it two times.

You wager a total of $100 and collect $98. They take the $1 vig from your winnings the two times you win the wager.

You wager a total of $100 and collect $98 losing $2 out of $100 wagered (2/100=.0200). The house advantage is negative 2.00%.

You can reduce the HA even more if they let you wager $30 or better yet, $38 and still only collect $1 for the vig.

For $30, you wager a total of $150 and collect $148 (2/150=.0133). The house advantage is negative 1.33%.

For $38, you wager a total of $190 and collect $188 (2/190=.0105). The house advantage is negative 1.05%

Skinny, what a thorough well written analysis. Thank you for taking the time on this on everybody on the board can understand.

Doc

OK, so don’t buy it at < $24 otherwise it’s better than placing it. I can live with that.

Thanks Skinny.

Cool. Happy to help.

Just thought of another way to look at it.

If you place it for $35, it pays $49 and you get a total of $84 ($35+$49).

If you buy it instead, you buy it for $34 + $1 vig for the same $35 bet each time. But the buy pays $51 and you get a total of $85 ($34+$51).

That might be an easier way for you to figure out which is the better bet. I am only looking at the win. But I am looking at it by betting the same amount as a place or buy. Thus I have the same amount at risk for all my bets. That is why I can look at just the win here. When you looked at only the win wager you were looking at betting different amounts. The bet can not be compared that way.

The reason I tell you this is because at higher amounts the buy bet may not be the better bet.

For example, $115 place bet pays $161 for a total of $276. You could buy it for $110 + $5 vig for the same $115. The buy would pay $165 giving you a total of $275.

At this level a buy bet is always worse than a place bet.

Figure which pays more, the place or buy for the same amount to figure which way to go.

You can do it using dollars and cents even though that is not the way they would pay you to see theoretically which is the better bet.

Say you wanted to buy it for $46 + $2 vig. It would pay $69 for a total of $115. A $48 place bet would pay $67.20 for a total of $115.20. Here a place bet is better. You need to get to $50 – $58 to make the buy bet the better bet. That is because the buy at $48 + $2 vig pays $72 for a total of $120. The place bet of $50 pays $70 for a total of $120. At a $2 vig you need to bet $50 to make the buy bet the same or better bet.

Thus for a $1 vig you can buy it between $24 and $38. But for a $2 vig the range is only $48 to $58. The range narrows as you get to the higher amounts. For a $5 vig the place bet is always better.