Gambler's Ruin discussion

Reply #3

Orange71 — Mon, 05 Sep 2022 21:15:54 GMT

My example assumed a 0.1% house advantage. If you take a 1.414% house advantage, which is Craps Pass Line (without side odds bet), i=30 and N=40, then the player can expect to 15.16% of capital in the long run.

Reply #2

Stat$talker — Sat, 03 Sep 2022 15:45:17 GMT

The House ALWAYZ typically haz a GREATER advantage than the Player...therefore yo example iz out of the norm..

While yo Math may seem advantageous in YO example..only true Probabilistic calculationz.. will render more reazonable rezultz..

-Stat$talker

Reply #1

Orange71 — Fri, 12 Aug 2022 18:29:34 GMT

The numbers get more dismal as you increase the number of units at risk with a negative expectation and given the same % increase goal. This is something that may not be so obvious until you do the calculations.

Let's say 300 units are at risk, and we stop at 400.

Then, P=0.6708 and EV/unit-at-risk = -31.6715/300 = -0.1056

Finally, let's go to 3000 units at risk, and we stop at 4000.

Then, P=0.1350 and EV/unit-at-risk = -2459.82/3000 = -0.8199.

If you are only risking a portion o... [ More ]

Gambler's Ruin discussion

Orange71 — Fri, 12 Aug 2022 18:12:57 GMT

There's a famous problem in Probability called Gambler's Ruin, and it's quite interesting. Cottoneyedjoe had a recent post called Are you smarter than a Finance major? that broadly ties to this problem.

Suppose you start with i units (dollars, euros, crypto-currency, or whatever...) and your goal is to achieve N units, where N i. Next you gamble a single unit at a time with a probability p of winning a single unit and q (=1-p) of losing the unit. You continue this until you either go broke (l... [ More ]