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25 Points to whoever can solve this
I have 5 individual plays that all hit at 60%.
I will parlay them in as many 2-teamer combinations possible
I will risk 50 dollars to win 300 on each parlay (ie. a profit of 250)
1. What is the probability that I turn a profit after all the parlays are over?
2. Given that the first 2 plays win, what is the probability that I turn a profit?
Last edited by Rich Boy; 12-29-10 at 01:24 AM.
e=7/5x**4657^98923 + 765.333__ 786732;4 = 4%
100% in both scenarios.
scenario 1..
you hit your parlays at 60%..
this means you hit 3 of the 5 parlays...
the parlays require an average of approx. +125 bets to pay out 50 to win 250 (300)
so, you bet 250 (5 x 50) and win 3/5, or 900 total (3 x 300)
That's a profit of 650 dollars.
scenario 2, you win 2 out of 5 .. cashing 600 dollars total (300 x 2)
on 250 bet, so you win 350 dollars.
In both cases you turn a profit. A guaranteed profit.
The only exception would be if 3 of your bets were heavy favorites -1000 and -900 and -500 then 2 of your bets were +20000 and +15000, or something extreme, in which case, there is a possibility that the combinations of the super heavy favorites would not return a profit.
However if you calculate the bets at the average which is about +125, then a profit would be 100% if you go 2/5 or 3/5.
Without knowing the exact odds of your five bets there is no way to know the exact probability of turning a profit.
If the individual plays hit at 60%...
Again, if some of the plays are extreme -1000, -600, and -450 and +3000, +2000.. There is no way to give an exact probability of turning a profit.
If all the plays are -110...
You'd have 120 parlays (5x4x3x2x1) at $50 each for a risked $6000.
each bet hits 60%, so
your odds of winning each bet is .6 x .6 or .36 for a payout (european ) of 50(x1.9)>95 (x1.9)=181.
so 181 x .36 = EV of 65.16 on 50 bet... for a total Expected profit of $7819.20 on $5000 bet or $1819.20
for 100% probability to turn a profit.
Each play (ie each leg) hits at 60%Originally Posted by GELATINOUS CUBE
nobody is correct so far...
If your first 2 bets win, you'd be up $362 on $100 bet,
and your probability would still be 100% if your bets hit at 60%.
Of course the variance...
There is a tiny chance that after 120 bets, you keep losing or the 40% probability of the bet losing keeps happening, however with a sample size of 120 or 118 + 2 winners, that minute variance would be less than 1%, in fact it would be less than .0000001%
Thanks rich,
i calculated originally that each parlay hits at 60%.
If each leg hits at 60%, even with the juice of -110, you would be very close to 100%.
What is the juice on the bets?
Re-read the question.
Well.
It be 120 parlays,
with a 36% chance of turning $50 into $181
and a 64% chance of turning $50 into $0.
10 diff combinations of parlays
36% chance for each 2 team parlay will hit
10 * .36 = 3.6 = 4 / 10 parlays will hit =
4(250) - 6(50) = 1000 - 300 = 700
#1)100% chance profit
#2)100% chance profit
im a little high, so my math might be a little off
Last edited by 36mafia; 12-29-10 at 02:04 AM. Reason: high than i thought i was
Re-read it very slowly
It will be very sad if nobody on SBR can answer this...
Maybe I should have posted this in the think-tank
Oh yeah.
The bets are +125... Or 50 to win 300
so 120 parlays with a 36% chance of turning $50 into $300
and a 64% chance of turning $50 into $0.
For the first scenario...
Well this is tough, you have 120 parlays... It's a long problem.
actually I have 10 parlays.
1,2
1,3
1,4
1,5
2,3
2,4
2,5
3,4
3,5
4,5
with 120 different outcomes.1w,2w,3w,4w,5w;;1w,2w,3w,4w,5l, ...etc.
each leg with a .6 chance of winning...
There are actually only 32 possible outcomes...
I think you should give this up
john buck best player in mlb is my answer..
1
2
3
4
5
1+2
1+3
1+4
1+5
2+3
2+4
2+5
3+4
3+5
4+5
1+2+3
1+2+4
1+2+5
1+3+4
1+3+5
1+4+5
2+3+4
2+3+5
2+4+5
3+4+5
1+2+3+4
1+2+3+5
1+2+4+5
1+3+4+5
2+3+4+5
1+2+3+4+5
None
if youre exclusively doing 2 teamers, then you only have 10 possible combinations
The probability of turning a profit after all the parlay are over is 1.
Reason - You must always have a profit. win ratio of the parlay is 3:7
3*250 = 750
7*50 = 350
750 - 350 = 400
is collerated parlay combination possible?
The probability is also 1 in the second scenario
Easy equation Rich Boy = Idiot
Slim and None
68.7%
if the first 2 plays win...
80%
explanation;
you need 3 winners to profit..
10 parlays will cost you 500 so you need to hit 3 legs, to win at least 900.
5 winners, at 60% each 1+2+3+4+5 = .6 x .6 x .6 x .6 x .6 =7.7% times 1 possible outcome.
4 winners at 60% x 1 loser at 40% = 5.2% prob. x 5 poss. outcomes = 26% prob.
3 winners at 60% x 2 losers at 40% = 3.5% prob x 10 poss. outcomes =35% prob.
7.7% + 26% + 35% = 68.7% chance of profiting.
If you hit the first two bets,
you only need one more.
www
wwl
wlw
lww
lwl
lll
6 possible outcomes..
.4 x .4 x. 4 =.064 or 6.4% of losing..
so 93.6% if you hit the first two legs.
correction
68.7% overall
93.6% if the first two legs hit.
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= 4%
Rich Boy gave GELATINOUS CUBE 25 SBR Point(s) for this post.