dwheatley's Blog
Odds of breaking even or better at Craps - Pass Line
Suppose you make a prop/side bet with someone at a craps table that you can finish even or up over a certain # of pass line bets.[Lifted from a post I made]
For a small # of trials, there is a fair chance of breaking even in a -EV game by flat betting. If you win the side bet by finishing even or ahead, then the side bet is +EV. Your advantage comes from the chance of breaking even.
As the # of trials increases, the chance of breaking even decreases, and eventually your chance of finishing even or ahead drops below 50%.
Consult table below, which shows the probability of finishing even or up after N trials on the pass line (f=244/495). Your bet is +EV up to 70 pass lines.
20 0.563020692
22 0.557764082
24 0.553065187
26 0.548820611
28 0.544952395
30 0.541400455
32 0.538117601
34 0.535066167
36 0.53221565
38 0.529541038
40 0.527021588
42 0.524639929
44 0.522381376
46 0.520233417
48 0.518185311
50 0.516227772
52 0.514352726
54 0.512553111
56 0.510822715
58 0.509156051
60 0.507548246
62 0.505994959
64 0.504492303
66 0.503036786
68 0.501625262
70 0.500254886
72 0.498923075
74 0.497627482
76 0.496365965
78 0.495136565
80 0.493937485
Comments
as I mentioned recently, you can quickly prove this to yourself by looking at all the possible the outcomes of 2 bets, then 4 bets, etc, with the assumption that the chance of a win is roughly equal to that of a loss.
Thanks for doing the hard work!
Very nice job.
The side bet is very cool. I am going to use it this weekend.
In my Blog for 30 pass line decisions I also added a table up to 200 rolls.
keep up the good work.
Uh,,, what am I missing?
The bet is that you will go "x" number of line bets and your net result after a pre-determined "x" bets will be either a net gain or "no loss".
Now what are the chances for the shooter? What are the chances for everyone else at the table?
They are all at a negative expectation for each line bet made and the casino books that bet, but if its a player who books your bet, you have either a positive or neutral expectation?
I think you are missing that this is a side bet between players. For the line bet, the shooter or anybody else is looking at negative expectation because when you break even, you don't gain anything by it and your losses in the long run outweigh your wins.
If someone takes your action on the side bet, you have positve expectation as long as he fail to insist on enough trials. Here is the exercise to prove it:
you propose a side bet that you will break even or better with 2 pass line bets. This would be a bad idea as it should highlight how much advantage you have. For this small trial, that the odds of winning one bet is something like 49.5% instead of 50% is not much of a factor. So,
*roughly 25% chance you win both bets, 1 win + 1 win
*roughly 25% win the first, lose the second, 1 win + 1 loss= break even
*roughly 25% lose the first bet, win the second, 1 win + 1 loss= break even
*roughly 25% lose both, 1 loss + 1 loss
roughly 75% chance you win or break even. Get enough action on this and you don't have to work for a living.
increase the number of trials and the advantage wanes. However, another player is likely to either have no intuition that something like 20 trials is not enough, even if his intuition guides him that a sufficient number of trials is what he needs to win.
I believe it was you who mentioned before other players don't want to be bugged by side bets at Craps. I have one idea I might play out, though, stay tuned for my trip report in about 10 days.