using wins on bets to pay for other bets and figuring the odds

Howdy,

Suppose you made a bet and intended to take the winnings from that bet and make a different bet. How would you calculate the percentages involved?

just multiply the expectations together.

So if you placed the 6, hit it, then used the winnings to place, say, the 9. You multiply the 1.5% for the 6 and the 4% for the 9 n get 6% for the total wager?

Quote: nickdel

So if you placed the 6, hit it, then used the winnings to place, say, the 9. You multiply the 1.5% for the 6 and the 4% for the 9 n get 6% for the total wager?

I'm not 100% sure that this is the right way to do it, but if you come up with how much money you'd have if there were no edges, and how much money you have with an edge, then take the difference and divide that by the amount of money you have with no edge, you get the compounded edge.

The formula is as follows:
HA.total = 100% - (100%-HA.1)*(100%-HA.2)

E.g. 4%, 1.5%: 100%-(0.985*0.96)=5.44%

For small edges (<1%) it's actually close to and a bit below HA.1+HA.2. Don't multiply them, add instead. Or, better, use the formula above.

In the case of a different bet amount, though, there's not proper weighting with that formula.

Let's say you make a $6 eight, do a full press to $12 on the first hit, then move to a $25 buy on the four for the last hit.

$6 -> $12 -> $25 -> $74 and down

The edge per your forumula is:

100% - ( 100% - 1.51% ) * ( 100% - 1.51% ) * ( 100% - 1.33% ) = 1 - .9849 * .9849 * .9866 = 4.29%

If you look at the way I describe it with no edge:

$6 would pay $7.20 - put a dollar in the rack
$12.20 would pay $14.64 - put a dollar in the rack
$25.84 would pay $77.52
$77.52 + the two dollars in the rack would be $79.52

With an edge you get $74 + two = $76

$79.52 - $76 = $3.52 which is how much the house kept to pay you $76 for your sequence of bets.

3.52 / 82.52 = 4.26%

Well, maybe both ways work out to the same answers. I'd be curious to know. But for what's it's worth, this is how I have been figuring it out. But I was guessing I would come up with a lower percentage since there's more money on the last bet with a lower edge.

Quote: Ahigh

In the case of a different bet amount, though, there's not proper weighting with that formula.

Let's say you make a $6 eight, do a full press to $12 on the first hit, then move to a $25 buy on the four for the last hit.

$6 -> $12 -> $25 -> $74 and down

The edge per your forumula is:

100% - ( 100% - 1.51% ) * ( 100% - 1.51% ) * ( 100% - 1.33% ) = 1 - .9849 * .9849 * .9866 = 4.29%

If you look at the way I describe it with no edge:

$6 would pay $7.20 - put a dollar in the rack
$12.20 would pay $14.64 - put a dollar in the rack
$25.84 would pay $77.52
$77.52 + the two dollars in the rack would be $79.52

With an edge you get $74 + two = $76

$79.52 - $76 = $3.52 which is how much the house kept to pay you $76 for your sequence of bets.

3.52 / 82.52 = 4.26%

Well, maybe both ways work out to the same answers. I'd be curious to know. But for what's it's worth, this is how I have been figuring it out. But I was guessing I would come up with a lower percentage since there's more money on the last bet with a lower edge.

Ok but this assumes you move the total investment around. what if u hit the $6 6 for $7, then made a $5 bet on the 9 so now u have two numbers covered but only paid for one. what would b the total vig against only the money that you invested on the 6?

Quote: nickdel

what if u hit the $6 6 for $7, then made a $5 bet on the 9

Huh? OK. How about this.
You won $7. Who's money is that? Yours. It is added to your rack.
Your bankroll grew by $7 from the value before the last roll.

Now you take $5 of your money from your rack and make a $5 place9.
You are betting your money. Both bets are paid for by you.

Quote: nickdel

so now u have two numbers covered but only paid for one.
what would b the total vig against only the money that you invested on the 6?

You mean you only paid for one bet currently from the initial starting fortune you had.
So?

But because it was not from your initial fortune before the last roll, the new $5 Place9
you want to keep that action separate from your total action currently
only counting the money that was from your fortune before the last roll.

Sounds like you are trying to cook some books.

As an example:
You want to show a syndicate some very low edges based off of the initial fortune and the total action only from that initial fortune.
Like Enron accounting tricks to convince some investors (suckers) that your combined house edge is
only -.39% instead of -1.46% and you pocket the difference.
Slick move.

Simulations can easily give you your answers
Then you can match those results to the math (do it both ways - two sets of books)
just add the EV for the different bets and divide by the total action you want to use.

No you don't have to move the total investment around. You just have to compare if the bet were a zero edge bet, and whatever you put in the rail instead of pressing the bet is that same and any extra pay goes into the bet to figure out the zero edge half.

lmao No, no cooking, just curious. i guess since you would be using the winnings from a previous bet then you would be increasing the vig against you on that previous bet since the money you get from a win would be much smaller if you fully intended to reinvest most of the win?

ok i gotcha i think. add the EVs and divide.

one other thing. is this regardless of when you make the bets? like if you had multiple bets at the same time or intended to make subsequent bets, the math is the same?

Somebody else can clarify how to do this better. But this is just a rough layman's guide for figuring out edges on parlayed bets.

When you do more complex things than effectively pressing all the way up, there's more to it than what I could easily explain to you.

The dollar change, for example, means my answer is off a little bit.

But I'm just not worrying about that part.

Here's another example:

Hard 8 for $1, parlay -> $10, parlay -> $100, parlay $1,000 and down.

If it were a "free" bet, $1, parlay -> $11, parlay -> $121, parlay -> $1,331 and down

331/1331 = 24.86% combined house edge .. IE: should pay $1331 and down, but pays $1000 and down. Cost is $331 out of $1331 expected pay for true odds.

Doing the other way:

100% - ( 100% - 9.09% ) * ( 100% - 9.09% ) * ( 100% - 9.09% ) =
1.0 - .909^3 = 1 - 0.751337340571 = 0.248662659429

The answers work out to be the same...