The Dice Institute

One of our West Coast friends, bigDave, recently asked:

Which is better: a $20 flat Don’t Pass bet, or a $10 Passline bet backed with $10 in Odds?

As always, to give us a basis of comparison, we first have to look at how a random-roller would fare with this bet.


On The Come-Out
A $20 DP wager will enjoy an instant Craps-2 or Craps-3 win about 8.3% of the time, and will suffer an instant 7 or 11 loser about 22.2% of the time.

 - That instant 3-out-of-11 win-ratio compared to it’s instant 8-out-of-11 loss-ratio (27% vs. 73%) during the Come-Out is an important factor when we look at the DP wager’s total overall performance.

 - A $10 PL wager will enjoy an instant 7 or 11 win about 22.2% of the time, and will suffer an instant Craps-2, Craps-3, or Craps-12 loser about 11.1% of the time.

 - That instant 8-out-of-12 win-ratio compared to it’s instant 4-out-of-12 loss-ratio (66.6% vs. 33.3%) during the Come-Out is also an important factor when we look at the PL wager’s total overall performance.

 - That means that during the Come-Out, a $20 DP wager will win another $20 even-money payout about 8.3% of the time, and lose the whole value of the wager about 22.2% of the time.

 - That also means that the Come-Out cycle is net-negative in terms of Don’t Pass wagers; however, as soon as a randomly-tossed outcome enters the point-cycle phase, a DP wagers immediately turns much less negative (but still negative, nevertheless).

 - Meanwhile, during the Come-Out, a $10 PL wager will win another $10 even-money payout about 22.2% of the time, and lose the whole value of the wager about 11.1% of the time.

 - That means that the Come-Out cycle itself is net-positive for a Passline bet. Unfortunately though, as soon as a randomly-tossed outcome enters the point-cycle phase, it immediately turns net-negative.



During the Point-Cycle
 - Once the PL-Point is established, a $20 DP will win about 60% of the time, and lose the other 40% of the time. We know this because a PL-Point of 4 or 10 in the hands of a random-roller will repeat (and therefore win) only about 33.3% of the time, while the DP will win the other 66% of the time. Similarly a PL-Point of 5 or 9 will successfully repeat about 40% of the time, while the DP prevails the other 60% of the time, and a PL-Point of 6 or 8 will only repeat about 45% of the time, while a hand-ending DP will show up around 55% of the time.

 -  So on that basis, it’s safe to say that a random-roller will throw a PL-Point repeater, on average, about 40% of the time…and the DP will prevail about 60% of the time.

 - During the Point-cycle, a $20 DP wager will win another $20 even-money payout about 60% of the time, and lose the whole value of the wager about 40% of the time. That means that the Point-cycle itself (when viewed in total isolation from the Come-Out cycle) is net-positive in terms of Don’t Pass wagers. Unfortunately though, when combined with the Come-Out cycle, a Don’t Pass wager still produces an expected net-loss of –1.40%.

 - Meanwhile, a $10 PL wager will win another $10 even-money payout about 40% of the time, but we’ve also added the power of 1x-odds, so that helps to the tune of producing an average 1.4:1 Odds-payout about 40% of the time. Unfortunately though, even when combined with the positive-expectation of the Come-out cycle, the end-product still produces an expected net-loss of –1.41%.

The net cost-difference between these two opposite betting scenarios works out to just fractions of a cent; and even during one lap around a fully crowded 14-player table, the difference between the two only works out to about 4-cents per lap.

In Part Two, we’ll look at what effect dice-influencing has on bigDave’s question, and we'll find out if PL-Odds has anything to do with leveraging your D-I skills.


Until then,


Good Luck and Good Skill at the Tables…and in Life.


The Mad Professor
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