To calculate the craps payouts and odds for this number, we multiply the three by two (the two dice that players use in the game), and the result we get is six. Thus, the odds are 1:6 and seven is the most frequent number that comes up in craps games. How to convert the chance to roll a particular number into odds?

1. Craps Odds Calculator
2. Payouts For Craps
3. Craps Odds Payout Calculator

Below you will find a general craps Payouts table. This may vary between some casinos so always check with the casino to get their payout tables. Don't Pass Odds. True Odds: These are the calculated odds that you will win or lose based on the bet you make. The amount of money you place doesn’t figure into the odds, but it does figure into the Craps payout. Craps Payout: For a 1/1 payout, if you bet $5 and win, you only get $5 on top of the $5 you bet. 90 + 45 = 135 add the zero 1350 - 45 payoff is 1305. There are to many keys to list I have one or more for just about every wager on a craps table but not the time to post them. If you want to know any of the keys post it here on the thread and I will see if I can help you #6.

... the house payoffs for bets made with the house odds and then paid for true odds. ....

I had some difficulty understanding this part of your question, so what I offer here may not be what you are asking for. I'll limit myself to the topic of how many chips to include in your bet and leave the rest to someone else. With the exception of those few craps tables with minimums of less than $5, this should work for you. All of the following must be adjusted to comply with minimums greater than $5.
Pass, come, don't pass, don't come, and field bets in increments of $5. Place bets in increments of $5 except in increments of $6 for bets on 6 and 8. I've never made a lay bet, so I will leave that and buy bets for someone else to discuss.
Pass line and come bet odds bets (usually) in increments of $5, always an even number for pass/come odds bets on points of 5 and 9, and a maximum odds bet as specified for the particular table/casino, usually a multiple of the pass/come bet you made. Don't pass and don't come odds bets work out easiest if they are six times the don't pass/come bet.
Most proposition bets can be any amount from $1 to the maximum allowed. Horn bets in multiples of $4 and horn-high bets in multiples of $5.
I probably left something out, and I apologize if this response is trivial and not what you meant.
Edit: as for forumulae, payouts for place bets are 7 to 6 on six and eight, 7 to 5 on five and nine, and 9 to 5 on four and ten. Payouts for pass/come odds bets are 6 to 5 on six and eight, 3 to 2 on five and nine, and 2 to 1 on four and ten. Invert those for payouts on don't odds bets. Again, sorry if this is not what you were asking for.

Craps Odds Calculator

your question in a bit confusing (house odds????) but if you are asking about putting odds behind your passline bet, this might help/
6&8..........units of 5 because every 5 wins 6
5&9.........units of 2 because every 2 wins 3
4&10........units of 1 because every 1 wins 2

House odds are also known as house payoffs. Pretty much there are house odds and true odds (it's how house edge is calculated).
And flip it for lay odds.
Increments of 6 for 6/8.
Increments of 3 for 5/9.
Increments of 2 for 4/10.
House odds on lay bets (opposite of place bets) are weird and must be in high increments. This is posted on the wizards site, although I have no idea off the top of my head.

Payouts For Craps

Craps Odds Payout Calculator