Ok - here goes nothing! I will try to keep this as simple as I can - if anyone has questions or constructive comments I will be happy to try to answer them.
Please note: throughout this example I have used Equine Investors strike rate, average div and staking plan as an illustration (basically because he has posted his figures here) so it is based on place bets - but it would apply equally to the systems proposed by Bhagwan, etc and also to win or exotic bets as well.
STAKING PLANS v EVEN BETTING
First a couple of basic definitions:
STRIKE RATE: How often you have a winning bet (as % of bets placed). Eg If you place 100 bets and have 56 winners then the strike rate is 56% or .56. An important note here is that you cannot place 10 bets, have 8 winners and conclude your system has an 80% strike rate - you must have at least a hundred bets to get something close to an accurate strike rate and preferably several hundred or even several thousand (the more bets the more accurate your strike rate calculation will be).
AVERAGE DIVIDEND: The average dividend you have received on your WINNING Bets. Simply add up the winning divs, divide by the number of winners and you get your average dividend.
EG. Lets say we have 2 winning betting sequences of 10 bets each:
1. 1.80, 1.80, 1.90, 1.80, 1.80, 1.90, 1.80, 1.80, 1.90, 1.80
2. 5.00, 1.10, 1.30, 3.20, 1.20, 1.20, 1.80, 1.00, 1.20, 1.30
If you add both of these up they total $18.30 so the average dividend is $1.83
Now before I go any further lets have a look at the idea that "good dividends" somehow give better return than average dividends. In the sequences of divs. above the first consists of divs of around the average only - the second has 2 "good divs" of 5.00 and 3.20, one average div of 1.80 and the rest pretty ordinary divs of 1.10-1.30. However if you add them up you end up with the same total dividend of $18.30 (or 183.00 with $10 bets, 1830 with $100, etc). Therefore it makes no difference whether we have 10 1.83 divs, 10 divs of around 1.80 - 1.90 or a range between 1.10 and 5.00. The important thing is the AVERAGE.
THE STAKING PLAN
Lets have a look at EI's staking plan - for those of you that missed it he bets 1 unit, 2 units, 6 units then 18 units (place betting) - if he does not hit a winner after the 4th bet (18 units) then he stops and goes back to 1 unit. Now he has given his long term average dividend as $1.83 and his long term strike rate at 56%. Multiplying these two figures together gives us the projected return on his system -
So we have $1.83 * .56 = 1.025 or a 2.5% profit on investment.
Now lets look at how it goes with his staking plan. Lets assume we will bet his system for 100 sequences (ie. we will start the betting sequence 100 times and continue until either we hit a winner or we have placed 4 bets).
Out of the 100 single unit bets we place we expect 56% to win so we will get 56 winners on the first bet and 44 times we will have to continue the sequence and place a 2 unit bet. Out of the 44 2-unit bets we again expect 56% to win - this should give us around 25 winners and 19 times we will have to continue to the 6 unit bet.
Out of the 19 6-unit bets we again expect 56% to win - this should give us 11 winners and 8 times we will have to continue to the final 18-unit bet
Out of the 8 or 9 18-unit bets we again expect 56% to win - this will give us 4 or 5 winners (for the purposes of the calculation we will call it 4.5 - sometimes you will get 4 and sometimes 5) and 3 or 4 times we will "strike-out" and lose our money.
So in summary we have placed 171 bets (100+44+19+8=171) and the total number of units bet is 100 + (44*2) + (19*6) + (8.5*18) = 100+88+114+153 = 455 units
Now what about the dividends?
We have 56 single unit winners @ 1.83 (ave div) = 102.5
We have 25 2-unit winners @ 1.83 = (25 * 2 * 1.83) = 91.5
We have 11 6-unit winners @ 1.83 = (11 * 6 * 1.83) = 120.8
We have 4.5 18-unit winners @ 1.83 = (4.5 * 18 * 1.83) = 148.2
So the total dividends are 463 units
So our return on investment using this plan is (drum roll please) 463/455 = 1.02 so we have a 2% profit on investment (by the way the difference between this and the 2.5% forecast is due to the rounding errors in the calculation above - if you do it without rounding it comes out to exactly 2.5%).
EVEN BETTING
The return from even betting is very easy to calculate as it is just the number of bets multiplied by strike rate multiplied by average dividend (multiplied again by your stake amount).
In this example we have 171 bets, strike rate is 56% and ave div is 1.83.
If we multiply these together we get 171 * .56 * 1.83 = 175.25
Of course given we were betting up to 18 units at a time in the staking plan we wouldn't only be betting one unit with even betting. Lets say we bet 3 units per time. This means our total dividend would be 175.25 * 3 = 525.75
So betting up to 18 units with our staking plan we get a return of 463 units less our 455 investment leaves 8 units profit.
Betting 3 units with even betting we get a return of 523 units less 513 units gives us a 10 unit profit.
Of course if you miss 4 consecutive bets on the staking plan you are down 27 units, miss 4 on the even betting plan and you are down 12.
WHY DO PEOPLE BELIEVE STAKING PLANS WORK?
This is a good question and I don't really know for certain. I suspect it is because in the staking plan your losses are effectively "hidden" in the rare 4-miss scenario (with this particular plan) than only happens around 3.5% of the time. So if you are starting 3 or 4 "sequences" of bets per day then you could go for weeks without hitting a bad patch - therefore you seem to be making higher profits (which, of course, largely get wiped out by your bad day so that you are back to the 2.5% profit again). With even betting you probably see each bet as an individual occurance and hence you feel like you are losing nearly half the time (with the 56% ratio) - with the staking plan you don't look at the individual bets as much but rather each sequence. This means that you feel like you are winning about 96.5% of the time and only losing 3.5% of the time - that has got to be better than only winning 56% of the time. Of course the problem is that your losses, when the happen, are much larger and so you end up in the same place overall.
Sorry for such a large post but some people expressed interest and I thought it would be useful to some of you. I hope I have explained myself well enough for you to follow it - if there are any questions I am happy to try to answer them.
:smile:
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