Lottery Wheeling vs Random Number Combinations 2

By Joe Roberts / CDEX Lottery Director

Three Financial Benefits of Wheeling versus Random Play

For a given quantity of combinations, comparing wheeled ones against randomized ones:

... Properly-designed wheels tend to cover a greater percentage of the subsets within the game's field of numbers.

... Randomized lines tend to contain "holes", i.e. subsets which are unmatched. They make up for those holes by having greater redundancy in those subsets which are matched.

For example, when a 6-number combination is drawn as a winner, it contains 15 4-number subsets. If 4, 5, or 6 of those numbers fall within the set of numbers that are played:

... A wheeled set of lines (designed as an Abbreviated wheel with L=1 exactly) will match one (and only one) of those 15.

... A randomized set of lines may match zero, one, two, ... of those 15. The amount matched depends only on how unevenly dispersed the 4-number subsets are, within those lines.

Any group of 15 4-number subsets has an equal chance of being drawn, compared to any other group of 15.


... For that reason, because of their more equalized coverage of the subsets, wheels tend to produce smaller and more-equalized wins at more-frequent intervals of time.

... For that same reason, because of their spottier coverage of the subsets owing to multiple "holes" and multiple redundancies, randomized lines tend to vary more widely from zero wins to multiple wins, with those wins spaced apart at larger intervals of time.

Both methods (wheeled combinations or randomized combinations) will produce the same gross total of matches in extended play, because they contain the same total matches.

However the more-frequent and more-level wins from the wheeled combinations can benefit the player's ROI. The benefits happen in three ways. These can be substantial, or they can be slight, depending on the size of the amount won (i.e., the size of the subset matched).

One of the beneficial areas pertains to taxes. and the benefit there can be substantial in areas where lottery winnings are taxed. It will be of nil value in areas where lottery winnings are not taxed.

Here are the three ways in which wheeled combinations offer some financial benefit to the player, compared to playing the same amount of randomized lines. They are:

A. The Parimutuel,

B. Money Management,

C. Taxes.

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A. The Parimutuel:

Some games pay prizes to the winning players on a "parimutuel" basis. The total prize pool is shared equally by all winning tickets held by the winning players.

There is a slight benefit in dividing a sequence of separate parimutuel prizes, compared to taking a single larger chunk of one prize.

For example, a typical 6/49 game shows about 200 5-number matches in a draw. Here is the difference between winning 6 prizes in 6 separate drawings versus winning 6 prizes all in the same drawing.

... A player who wheels subsets evenly might garner six (6) separate prizes (in 6 separate draws, not necessarily consecutively). In each case, the player would be sharing 1/200 of the prize pool on each of those six (6) separate occasions. (That is, 0.5 percent of the prize money on each win, times 6 wins.)

... A player who makes one solitary win, on one draw, with six (6) matching subsets in that draw, shares 6/205 of that one prize pool. (That is, 2.93 percent of the prize money on that 1 win.)

If the 5-match prize pool was $400,000 each time:

... The 'wheeling' player took home a total of ($400,000 x 0.005 x 6): $12,000.00

... The 'randomized' player took home a total of ($400,000 x 6/205): $11,707.32

Where the game makes parimutuel payouts, the difference may be slight but it exists. Of course it does not apply to prizes of fixed amounts (e.g. a straight $10 for a 3-number match).

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B. Money Management:

Until a player wins a huge amount, like the Jackpot or large second-tier prize, funds for playing will come from two sources:

... The player's pocket,

... Smaller-prize wins, recycled into new play.

With wheeled combinations: If smaller-prize wins tend to come in relatively steady amounts at relatively frequent intervals, the player's budget can be more easily managed. The amount of current prize money to be recycled into new play is more predictable.

With randomized combinations: If smaller-prize wins tend to come as differing amounts at relatively wider intervals, the player's budget becomes more difficult to manage. The amount of current prize money to be recycled into new play is less predictable.

With randomized combinations, a multiple win could occur early into playing -- in which case the player begins with some "seed" money from an early prize. However it's more likely, using a set of combinations containing a large proportion of "holes" compared to covered subsets, that the player will see zero win at any given point in play, early or otherwise. That's the more likely case, and "seed" money is nonexistent. The player must supply a larger portion of the playing funds out of pocket.

Here we're considering a player who is going to continue to play (i.e., will not stop playing due to a series of losses). We're also considering that the player is using completely available, discretionary funds for playing (not playing with the mortgage or the kids' milk money). Therefore it's relevant to consider the player's other options for making use of that out-of-pocket money.

Instead of ploughing more out-of-pocket money into new lottery tickets to compensate for a series of no-matches (i.e. "holes" in randomized combinations), he could invest that available money elsewhere with some return on that non-lottery investment.

A simple example is in the 163-line 6/49 wheel which averages 2.9 3-number matches in extended play. Assuming the player sees nothing greater than 3-number wins, and they pay a straight 10 units of prize money:

... For an extended series of 163-unit costs, the player receives (2.90 x 10) units of prize money.

... The player's net cost in extended play is (163 - 29): 134 units (e.g. $134.)

In effect, the player sees 163 Jackpot chances per play for an average cost of $134 per play.

By contrast, 163 randomized lines which contain 80 percent "holes" (unmatched 3-number subsets), which are compensated for by redundancy in the remaining 20 percent of 3-number subsets, gives the player zero win in an average of 4 out of 5 draws in extended play, followed by a larger multiple win in an average of 1 of 5 draws.

If that "1 of 5" happens early on, the player has "seed" money for the next series of draws. If it does not occur (which is likely 4 times out of 5), the player must supply the entire cost of 163 following each draw without a win, out of pocket. And of course, those 4 of 5 times do not occur like clockwork. It's entirely possible that the player may go two or three times that span without "seed" money.

The total amount won over an extended time will be the same, regardless of whether the player played the wheeled set or the randomized set.

It's simply the more even distribution of wins from the wheeled set, both in terms of prize amounts and of time, that allows more accurate budgeting for playing -- and therefore, it also allows more accurate use of the player's discretionary money for other non-lottery purposes that may be desirable to the individual.

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C. Taxes.

Normally, Lotto play is at an ongoing cost until a very substantial win occurs.

Where lottery winnings are taxed (as in the USA, at the Federal level and also in most States), the winning player is taxed on the net amount won per calendar year, less costs for tickets. Against lottery winnings, the player may deduct the cost of lottery tickets expended during that calendar year only. That is, the taxable amount is the net of winnings minus cost of tickets in that year.

Nor can the player claim a net lottery-playing loss against other taxable income. That is, if the player loses money in playing the lottery, he or she cannot claim that loss as a deduction against salary, wages, or other earnings. As an entity, the net amount of lottery winnings cannot go below zero for tax purposes.

Also it is usual for lottery prizes above $600 to have estimated taxes withheld in advance, with the net amount then going to the player.

For example, if the player wins a single prize of $800 and is in the 31% tax bracket, he or she will receive a net prize of ($800 - 31%) $552.00 after tax is withheld.

On the other hand if he or she wins $200 on each of 4 separate occasions, nothing is withheld and the player receives the full amount of $800.

In both cases, both players must still declare the amounts won in their tax returns at the end of the calendar year. However the second player retains the full $800 as discretionary funds until the year-end accounting (which typically can be deferred until about April of the following year), while the first player retains just $552 as discretionary funds during that time.

Here is another instance of how the more-equalized cost of wheeling, compared to randomized play, can affect taxes.

Consider a case of two players in extended play -- over eight (8) years of play.

One player plays wheeled combinations with a relatively steady return of 20% (in prizes) against the playing cost.

The second player plays the same amount of randomized combinations with "holes" and redundancy, and with correspondingly irregular returns in prizes against playing cost. Returns vary from zero to 1.3-times cost (i.e., net profit). The net profit occurs at rare intervals, whenever the winning numbers happen to match the redundancy in the randomized combinations.

The relative returns of the players, as a fraction of their playing cost over 8 years:

... For the wheeled player: 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2.

... For the randomized player: 0.0, 0.1, 1.3, 0.0, 0.1, 0.0, 0.0, 0.1.

Note that both players finish the full span of eight years with approximate winnings of 20% of cost.

The wheeled player does not achieve a net win in any year.

The randomized player achieves a net win in the third year, with taxable earnings. That is, the amount he or she won in that calendar year will be less the tickets cost, but also less the amount of taxes the player had to pay on the net winnings.

Note however that the randomized player did *not* achieve a net positive income from the lottery play over the full eight years of play. That is, it can't be said that the randomized player "made money" while the wheeled player did not. At the end of the eight years of play, neither player made a profit.

... Both the wheeled player and the randomized player probably matched approximately the same total amount of prizes, because both the wheeled set and randomized set contain the same total amount of matches at each prize level. The total matches are determined by the amount of combinations played, which is the same in both sets.

Over the eight years, the total amount expended will be the same for both players. And the total *net* amounts won will be approximately the same, with one difference:

... The wheeled player received a net prize total of about 20% of cost.

... The randomized player received a net prize total of about 20% of cost, minus the amount (e.g. 31%) that had to be paid in taxes during the one winning year.

At the end of the eight years, the wheeled player retained more of the 20% prize money won, than did the randomized player. In different terms, the randomized player expended more money out-of-pocket over the eight years, compared to the wheeled player.

Another way of viewing it:

... In all eight years, the wheeled player lost an amount of money and could not claim that loss against other income.

... In seven of the eight years, the randomized player lost a greater amount of money than did the wheeled player, but could not claim that loss against other income.

... In one of the eight years, the randomized player won money, but had to pay a percentage of wins as tax. His or her net was less than the prize amount.

... After eight years, neither player retained a net profit from the prizes won, but the wheeled player retained a larger proportion of that money than did the randomized player.

In each case, each player had exactly the same chances for hitting the ultimate prize goal: the big Jackpot win. Neither the wheeled player nor the randomized player had any greater or lesser chance for that win.

Winning that ultimate prize takes time. Part of the goal of playing is to use as much of the lottery game's money as possible, compared to the player's out-of-pocket money.

The difference between wheeled play and randomized play of the same amount of combinations is in how each player's discretionary funds can be allocated, maintained, and managed most efficiently.

There are financial benefits to wheeling.

Joe Roberts

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