A Case Against the Multi-Unit “Lock” Bet

If you are active in the sports gambling community, you are no doubt familiar with the many touts that offer their “10x Unit Bombs!”  The concept is simple, the tout has identified a “can’t miss” bet that the tout will sell to you and recommends that you risk 10, and sometimes even 40 (Mega Bomb!), times your normal unit size.20180331_084451-525237435.png  These same touts will also seek to entice you by claiming outstanding returns for their “Bomb” wagers. For example, “[w]e have won seven of the last ten times on this wager!” Immediately below is a slide show of some of these types of touts and their claims.  A cursory search of Twitter and just five minutes of my time found all of these claims.

 

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There are two general problems with the purported concept that some bets are such locks that they merit a ten, twenty, thirty or forty times increase in your bet size.  The first, more obvious problem, is the marketing manipulation involved in these claims.  The second, more catastrophic problem, is that with the “10x Unit” wager you are almost certain to lose money betting these “locks,” even if we accept the tout’s proclamation that the wagers have gone 7-3 against the spread in the last ten wagers.  With the facially absurd “40x Unit” wager, you are guaranteed to lose all of your bankroll.

Marketing Manipulation

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Assuming, for the sake of argument, that the tout is accurately relaying the last ten results, this is simply too small of a sample size to be statistically significant.  In order to obtain a confidence level of 95% in the tout’s prediction abilities, we would need a record in excess of a 400 such results, not ten.  With approximately 400 wagers we could determine the tout’s winning percentage within plus or minus 5%.  If we wanted 99% confidence in the tout’s percentage, we would need almost 27,000 results.  In all matters it is dangerous, and here costly, to judge ability based on short-term results.

Moreover, the tout will, no doubt, cherry pick the date from which he is relaying his latest statistics and it will always be a win.  For example, we have all heard a broadcaster during a sporting contest state, “Team A is really on a roll having won two of their last three games.”  Another way of saying this is that team A has won two of their last four games.  The reason we know the fourth game must have been a loss is that the announcer would have said they have won three of their last four, if accurate.  So while our tout may have won seven of his last ten such wagers, it follows that the tout has won seven of his last eleven such wagers.  This disparity drops his percentage from 70% to 63%.  If he had won the eleventh wager, he would have been touting a 72% win percentage based on winning eight of the last eleven such wagers.

A final consideration, again assuming the tout is accurately relaying results, how the tout will change from offering 10x Unit bets to 20x Unit bets, or 40x Unit bets once the odds catch up to the tout.  For example, when our tout encounters even a short losing streak of two such wagers in a row, something that will happen 13% of the time, the tout is not going to advertise that his “10x Unit” wager is now five wins in the last ten attempts — that is a losing proposition on its face.  He is going to change to a different multiplier and start over with new stats.  The tout will go strangely silent on his “10x Unit” wagers, but will start promoting a “Sure Fire 40x Unit wager of the year.”  Thus, even if we assume the tout is accurately relaying the results, we cannot ignore the obvious deception implicit in the method.

The 10x, 20X and 40X Unit Wagers are a Losing Proposition

First, a word about unit size.  If you regularly wager on sports, you likely have your set unit size.  That is, the amount you bet whenever you believe you have an edge.  If your unit size varies on a whim, I strongly encourage you to rethink that position.  You can use one of the many online wager verification services to record your bets based on unit size and develop an accurate understanding of your abilities.  Most people will determine their unit size based on one of two accepted theories.  The Kelly Criterion is a mathematical calculation designed to find the optimal unit size based on your bankroll and winning percentage.  The Kelly Criterion is a very aggressive model and most that follow it employ either a half or quarter of its recommendation.  Another well accepted, and far more conservative, approach states that your unit size is equal to 2.5% of your bankroll.

The 40x Unit Wager aka Bankroll Suicide

Before moving on to debunk the efficacy of the 10x Unit wager, lets pause here to immediately expose the utter lunacy of a 40x Unit wager.  You likely see the problem already.  If your unit size is 2.5% of your bankroll, and you wager 40x your unit size, then you are wagering your entire bankroll on a single bet.  Touts’ pleas to the contrary aside, 40 times 2.5% Shylock_filmwill always equal 100%.  This tout is suggesting you wager your entire bankroll on one of his predictions.  I certainly hope you never lose!  If you follow the more aggressive quarter-Kelly for unit size, a 40x unit wager will be more than your entire bankroll.  Perhaps your tout also serves as a Shylock?  Despite the undeniable absurdity of a 40x Unit wager, these touts persist and even thrive.  The reason they do is, as studies have shown, the more outrageous the tout’s claim, the more expensive the tout’s picks, the more people that will buy-in.  If the 10x unit tout is a wolf in sheep’s clothing, the 40x Unit tout puts on no airs — he is the Grim Reaper.  Whenever his 40x unit wager loses, which it most certainly will, you will lose your entire bankroll.

The 10x Unit Wager aka An Expensive Lesson in Loss

Now back to the more plausible, but still losing proposition of our tout that offers 10x unit wagers and boasts of going seven out of his last ten (errr, seven out of his last eleven) on such wagers.11  Even with the tout’s 63% win percentage, you are most likely to lose money tailing these picks.

To demonstrate, I will create a hypothetical sports bettor named Charlie.  Suppose Charlie has a bank roll of $5000. Charlie employs a quarter-Kelly Criterion for unit sizing and has a win percentage of 58 percent.  This results in Charlie’s unit size being $147.25.  If Charlie follows the touts “Bomb” wager, his unit size will jump to $1,472.50 and represent 29% of his bankroll.

Charlie bites and decides to tail the tout’s next two “10x Unit Bomb” wagers.  After all, if this wager has an edge, it is certainly worth doing more than once.  Over his next two bets there are three possible outcomes.  Charlie could win both bets, he could lose both bets, or he could win one and lose one.  Since we have established the tout is predicting at 63%, not 70%, we can assign probabilities to the three possible outcomes.  Charlie will win the two bets 39% of the time.  Charlie will lose both bets 13% of the time.  Finally, Charlie will win one and lose one 48% of the time.

Let us start with the ideal scenario from Charlie’s perspective, that he wins both bets.  His first bet will risk $1472.50, he will win $1338.64, and his bankroll will increase to $6338.64.  Charlie’s new unit size will be $186.50 pursuant to the quarter-Kelly Criterion. On his second bet, Charlie will wager $1865.  He will win $1695.45.  His new bankroll will be $8034.10.  This is a remarkable increase of $3034.10. Charlie should receive this return 39% of the time.

Next, let us skip to the nightmare scenario for Charlie, and assume that both bets lose.  We know Charlie’s first bet was for $1472.50.  So his bankroll will decrease to $3527.50. Charlie’s new unit size will be $104 pursuant to the quarter-Kelly Criterion.  So Charlie will risk $1040 on his second wager.  After losing the second wager, Charlie’s bankroll will be $2487.40.  Charlie will have lost over half his bankroll in two bets.  This will happen 13% of the time.

As for the final, and far most likely result, 48 percent of the time Charlie will lose one bet and win one bet.  Charlie has an equal chance at losing the first bet as he does the second bet.  Let us first suppose he loses the first bet and wins the second bet.  Charlie’s bankroll is initially reduced to $3527.50 based on his losing wager of $1472.50. Charlie then wagers $1040 on the second bet. Charlie wins the second bet and collects $945.45 bringing his total bankroll to $4472.95.  Thus, Charlie will lose $527.05 on the two “10x Unit Bomb” wagers he placed.  Conversely, let us assume Charlie wins the first wager, but loses the second.  His first wager will risk $1472.50, he will win $1338.64, and his bankroll will increase to $6338.64. Charlie’s new unit size will be $186.50 pursuant to the quarter-Kelly Criterion.  On his second bet, Charlie will wager $1865, and lose.  Charlie’s bankroll will be reduced to $4473.64.  Thus, Charlie will lose $526.36 on the two “10x Unit Bomb” wagers he placed.

Under the most likely scenario of two successive tails, Charlie will lose approximately 10% of his bankroll.

10x, 20x and 40x Unit Wagers, A Bankroll Wrecking Ball

By tailing the tout in this manner, Charlie has a whopping 61% chance of losing money. In fact, the only way he makes money is in the 39% of scenarios where the tout wins both bets.  The more tails, the likelihood of a loss only increases.  For example, If Charlie wonmiley_cyrus_wrecking_ball_0 the first two bets, his unit size would become $447.50, and his next 10 unit wager will be $4475.  If he loses that bet, his initial bankroll will be reduced to $3559.10.  That is a soul crushing loss of $1440.90, or 28% of his bankroll.  And on and on until the tout loses and your bankroll is negative.  Fear not though Charlie, the generous tout will likely throw in two free weeks of picks as a consolation for his very picks wrecking your bankroll.

The most likely outcome is that Charlie loses 10% – 20% of his bankroll plus whatever amount he actually paid the tout for the picks that lost him money.  The only people that will make money on this endeavor are the tout, because Charlie paid him for the picks, and the lucky.  If you are wagering your money on sports with the aim of luck carrying you through, then by all means, follow the tout.  Otherwise, stay disciplined.

It should also be pointed out that the tout is hitting this bet at 63% while our fictitious Charlie is hitting his wagers at 58%.  So what about the argument that Charlie will only place one bet, and thus has a 63% chance of winning?  In other words, is the increased accuracy of the tout over Charlie worth the 10 times increase in unit size even for a single bet?  Pursuant to the quarter-Kelly Criterion Charlie’s unit size would increase if he correctly predicted 63% of the contests as opposed to 58%, but it would increase from $147.25 to $278.  That is to say his unit size would not even double, let alone increase 10 fold.  In fact, even if the tout correctly predicted 90 percent of the contests, Charlie’s unit size under the aggressive quarter-Kelly Criterion would only increase to $987.50.  This represents a 6.7 multiple of Charlie’s current unit size.  Thus, not even a verified 90% prediction rate would warrant the 10 times unit bet proposed by the tout.

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Maybe this tout can help?

If instead you employed the 2.5% unit size wager, you would fare better than if you employed the Kelly on the 10x unit wager.  Still, any two loss sequence will destroy your profits.  Take note, even the tout with a 63% winning percentage has a 29% chance of losing five or more of his next ten wagers.

Bottom line: Even if Charlie enjoys an initial remarkable win streak tailing the tout on the 10x unit wagers, the increase of your unit size on the winning wagers will ultimately negate not only all of your profit, but deplete your initial roll when the inevitable losing wager hits.

If you are a consistent winner at the sports book, you needn’t gild the Lily with multi-unit wagers.