Your EV with $1 bets is of course -$12.50 . It looks like the EV when you bet $100 x25 is around -10.5. But for EV ignoring bonuses (contextual EV I’ll call it) I’m just having it calculate the total amount wagered for 10k runthroughs and applying the .5% edge over that. When you calculate EV based on the amount actually won including bonuses (actual EV) it’s a pretty standard $86-87 for $1 bets and it fluctuates quite a bit for $100. I’ve only eyeballed those stats but it seems to stay in the 90s although I’ve seen it plummet down to the 50s on some runs.
That got me thinking about the bonus:buyin ratio, along with playthrough amount, and how it influences things if at all. Initially with the original problem I thought the higher contextual EV you get for risking bustso would be counter-balanced by the hit taken to your actual EV when you consider the substantial amount of times where you bust and lose advantage of the 25% bonus. That is to say, with the ~33% risk of ruin you get for betting $100, wouldn’t the bonus money lost on those runs alter the overall outlook of the deposit bonus?
So I experimented a little and made the buyin $100 and the deposit bonus $400 with the same playthrough req: would we see a different outcome in the simulation between $1 bets and $100? What about a $1 buyin and 499 bonus? Turns out, which makes sense now but didn’t to me at first, that it doesn’t seem to have much of an impact at all. Contextual EV is identical across the board (-12.5 vs. -10.5) of course, and overall EV (”I buyin for $1, gamble with 500, and come away with X”) shows the same trends where the $1 bet has a very consistant range and the $100 bet is a bit wider.
Unfortunately I don’t have more time to spend on this, but my next step with simulating would be to generate a curve on total $ won, factoring in bonuses, because right now I’m just eyeballing results on 10k run throughs and its’ still pretty swingy. I’d be interested to see how the bonus ratio influences things because it seems like it should. My thought now is that the smaller the bonus, the more you want to minimize your risk of ruin and the larger the bonus the more you want to gamble with it. Of course it could affect nothing and you’re always better off taking the bigger gamble whether the bonus is $0 or 100x your buyin.]]>
If you haven’t Martingaled for breakfast in Vegas I highly recommend it. Free breakfast buffet never tasted so good.]]>
Kelly criterion states that you bet f = (bp – q)/b, where f = percentage of bankroll you bet, b = odds if you win, p = probability of winning, and q = probability of losing
b = 1.035 (Our expected value is 3.5% so we expect to get $1.035 back for every dollar we bet)
p = 0.5
q = 0.5
bp = 0.5015
bp – q = .0015
(bp – q) / b = ~0.0014 = f
So you would want to bet 14 cents for every hundred dollars in your current bankroll, or $1, whichever is greater. This assumes you want to make the full Kelly bet. Betting any more than that increases risk of ruin without increasing your chance of clearing the $100 bonus.]]>
The answer is the size of the bet won’t change the EV, it will only increase or decrease variance. So it doesn’t matter.]]>