Something like 15x instead of 4x would make more sense, and it would still leave a 6.25% house edge (15/16 = 0.9375 EV = 6.25% house edge)
At 15x, EV = (-15 × 1 ÷ 16) + (14 × 1 ÷ 16) = -0.0625 (more reasonable->but I still wouldn't take it)
Thanks for pointing out the difference between house edge and expected value.
At 8x, EV = (-15 × 1 ÷ 16) + (7 × 1 ÷ 16) = -0.5 (still extremely unreasonable proposition)
What are the EVs of established Dice sites?
And, people wonder why they walk away with empty pockets! They make things too complicated to formulate reasonably efficient decisions.
Gambling is not charity. People are expected to lose as well as multiply their wealth. It is part of the game.
EV= (-15*1/16) + (3*1/16) = -0.75........Translation: expect to lose 75% of your money on average.
Interpretation: don't be stupid enough to play against the house.
You did not consider the fact that, unlike dice sites, you can bet on multiple options at a time here and thereby significantly
raise reduce your chance of win.
If you bet on all 16 possibilities you do have a 100% chance of winning the game, but you also have a 100% chance of losing 3/4 of your money in doing so! So, you can win the game but lose your money.(strike thru of "reduce" and red font in the above quote added by me)
Betting more does not increase the expected value. Let's use the extremes to test that logic so as to avoid the math. If I bet on every number, what would my highest possible result be? Lowest result? (H:-12, L: -12) If I bet on four numbers, what would my highest possible result be? Lowest result? (H:0,L:-4) If I bet on three numbers, what would be my highest possible result? Lowest result? (H:1, L:-3)
Let's make a table for purposes of illustration:
For B=Number of Bets, H=Highest Result, L=Lowest Result
(Bets 1-4) (Bets 4-8) (Bets 9-12) (Bets 13-16)B:01, H:03, L:-01, B:05, H:-01, L:-05 B:09, H:-05, L:-09 B:13, H:-09, L:-13
B:02, H:02, L:-02, B:06, H:-02, L:-06 B:10, H:-06, L:-10 B:14, H:-10, L:-14
B:03, H:01, L:-03, B:07, H:-03, L:-06 B:11, H:-07, L:-11 B:15, H:-11, L:-15
B:04, H:00, L:-04, B:08, H:-04, L:-08 B:12, H:-08, L:-12
B:16, H:-12, L:-12Notice that the only quantity of wagers capable of realizing profit are 1, 2, and 3. Also, notice that with one wager you're receiving the highest possible return on your investment, with two wagers you're risking 2 to win 2 with 14:2 odds against (
even money prop with a 12.5% chance of success!!!), with 3 wagers you're risking 3 to win 1 with 13:3 odds against. Most importantly recognize that at four wagers you're risking 4 to win 0 with 12:4 odds against (
25% chance to break even, 75% chance to lose 4) and any number of wagers above four guarantees a loss.
Conclusion: the more wagers one places, the more inept one's gambling prowess.Similar tables can be constructed for 8x return....it might be a fun exercise to compare them; however, the math associated with calculating expected value should be sufficient enough to make sound decisions.